- published: 17 Apr 2020
- views: 335093
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Lunar orbit
In astronomy, lunar orbit (also known as a Selenocentric orbit) refers to the orbit of an object around the Moon.
As used in the space program, this refers not to the orbit of the Moon about the Earth, but to orbits by various manned or unmanned spacecraft around the Moon. The altitude at apoapsis (point farthest from the surface) for a lunar orbit is known as apolune, apocynthion or aposelene, while the periapsis (point closest to the surface) is known as perilune, pericynthion or periselene.
Low Lunar orbit (LLO)—orbits below 100 kilometres (62 mi) altitude—are of particular interest in exploration of the moon, but suffer from gravitational perturbation effects that make most unstable, and leave only a few orbital inclinations possible for indefinite frozen orbits, useful for long-term stays in LLO.
Robotic spacecraft
The Soviet Union sent the first spacecraft to the vicinity of the Moon, the robotic vehicle Luna 1, on January 4, 1959. It passed within 6,000 kilometres (3,200 nmi; 3,700 mi) of the Moon's surface, but did not achieve lunar orbit.Luna 3, launched on October 4, 1959, was the first robotic spacecraft to complete a circumlunar free return trajectory, still not a lunar orbit, but a figure-8 trajectory which swung around the far side of the Moon and returned to the Earth. This craft provided the first pictures of the far side of the Lunar surface.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Lunar_orbit
Group action
In mathematics, a symmetry group is an abstraction used to describe the symmetries of an object. A group action formalizes the relationship between the group and the symmetries of the object. It relates each element of the group to a particular transformation of the object.
In this case, the group is also called a permutation group (especially if the set is finite or not a vector space) or transformation group (especially if the set is a vector space and the group acts like linear transformations of the set). A permutation representation of a group G is a representation of G as a group of permutations of the set (usually if the set is finite), and may be described as a group representation of G by permutation matrices. It is the same as a group action of G on an ordered basis of a vector space.
A group action is an extension to the notion of a symmetry group in which every element of the group "acts" like a bijective transformation (or "symmetry") of some set, without being identified with that transformation. This allows for a more comprehensive description of the symmetries of an object, such as a polyhedron, by allowing the same group to act on several different sets of features, such as the set of vertices, the set of edges and the set of faces of the polyhedron.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Group_action
Orbit (horse)
Orbit (foaled 1885) was a Thoroughbred racehorse. He was trained at Kingsclere by John Porter for the 1st Duke of Westminster. As a three-year-old he won the Eclipse Stakes.
Breeding
Orbit was the son of Epsom Derby and Champion Stakes winner Bend Or. His dam was Fair Alice, a daughter of July Stakes winner Cambuscan.
Racing career
Orbit won three races as a two-year-old; the Criterion Nursery Handicap at Newmarket, the Kempton Park Champion Nursery Handicap and the Daveridge Stakes. Orbit started his three-year-old career by winning the Craven Stakes at Newmarket by ¾ length from Cotillon. His next race came in the 2000 Guineas at Newmarket. Friar's Balsam started as the 1/3 favourite for the race, with Ayrshire at 100/12 and Orbit at 100/8. Orbit ran on well in the closing stages to finish in third place. Ayrshire won the race by two lengths from Johnny Morgan, who was a head in front of Orbit. After winning the 2000 Guineas win Ayrshire started as the 5/6 favourite for the Epsom Derby and Orbit was second favourite at 11/2. Orbit could only finish in fifth place, over seven lengths behind winner Ayrshire. He then finished second in the Triennial Stakes at Ascot. Orbit started as the 9/4 favourite for the Eclipse Stakes and in the final 100 yards of the race Orbit gradually edged away from stablemate Ossory and beat him by a length.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Orbit_(horse)
Orbit (disambiguation)
Orbit is the gravitationally curved path of one object around a point or another body.
Orbit may also refer to:
Computing
Science and mathematics
People
Popular culture
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Orbit_(disambiguation)
Symbian (disambiguation)
Symbian may refer to:
See also
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Symbian_(disambiguation)
Symbian Ltd.
Symbian Ltd. was a software development and licensing company, known for the Symbian OS, a smartphone operating system, and other related technologies. Its headquarters were in Southwark, London, England, with other offices opened in Cambridge UK, Sweden, Silicon Valley, Japan, India, China, South Korea, Sydney Australia.
It was established on 24 June 1998 as a partnership between Nokia, Ericsson, Motorola, SONY and Psion to exploit the convergence between PDAs and mobile phones. Ten years to the day after it was established, on 24 June 2008, Nokia announced that they intended to acquire the shares that they did not already own, at a cost of €264 million. On the same day the Symbian Foundation was announced, with the aim to "provide royalty-free software and accelerate innovation", and the pledged contribution of the Symbian OS and user interfaces.
The acquisition of Symbian Ltd. by Nokia was completed on 2 December 2008, at which point all Symbian employees became Nokia employees. Transference of relevant Symbian Software Ltd. leases, trademarks and domain names from Nokia to the Symbian Foundation was completed in April 2009.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Symbian_Ltd.
Behind (disambiguation)
Behind is a method of scoring in Australian rules football, awarding one point.
Behind may also refer to:
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Behind_(disambiguation)
Podcasts:
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How the Moon orbits Earth
Using real data for the month of April 2020 I'm showing the exact rotations, tilts, inclination, orbital velocity, sunlight angles & views of our Earth-Moon system. Earth-Moon distance is not to scale, but Earth and Moon *sizes* are (in the middle row). FAQs/info 1. The green caps on the Moon are to indicate the position of the poles 2. The green circle around Earth (bottom middle, lol, middle Earth) is just a reference 3. The Moon is tilted 1.5° to its orbit around the Sun, so it has virtually no seasons 4. When the Moon is close to Earth it's pulled more strongly by Earth's gravity, so it goes faster, but when the Moon is far, it's pulled less and goes slower 5. Remember the SUPERMOON the other day? On April 7-8 have a look how there was a full Moon during a time when the Moon was closes...
published: 17 Apr 2020 -
How the Moon orbit - Motion of the Moon #shorts #moon #interstellar #space #animation
How the Moon orbit - Motion of the Moon #shorts #moon #interstellar #space #animation From your astronaut’s viewpoint, you can see that the Moon is an average of 238,855 miles (384,399 km) from Earth, or about the space that could be occupied by 30 Earths. It travels around our planet once every 27.322 days in an elliptical orbit, an elongated circle. The Moon is tidally locked with Earth, which means that it spins on its axis exactly once each time it orbits our planet. Because of this, people on Earth only ever see one side of the Moon. We call this motion synchronous rotation. The Moon’s orbit is tilted about 5 degrees compared to the plane of Earth’s orbit around the Sun. Because of this tilt, the Moon as seen from Earth’s perspective usually passes above or below the Sun when it pa...
published: 03 May 2023 -
Phases of moon explained using an orrery
As the moon rotates around the earth it travels through phases. The alignment of the sun, earth, and moon create the phases. I use an orrery to explain the moon's alignment during, new moon, waxing crescent, ist quarter, waxing gibbous, full moon, waning gibbous, last quarter, waning crescent, and back to new moon. The sidereal period is 27.3 and the moon is measured against stars. The synodic period is 29.5 days and the moon is measured against the sun. If you enjoyed this video you may enjoy the Earth Science Course with an emphasis on Astronomy. The course includes 13 videos along with a study guide and an answer key for each guide. In addition there is a short enrichment activity for each video. Link to the playlist here. https://youtube.com/playlist?list=PLurjkZV1ykGaCbqkU_0z82I_40J...
published: 03 Jun 2019 -
Moon 101 | National Geographic
What is the moon made of, and how did it form? Learn about the moon's violent origins, how its phases shaped the earliest calendars, and how humans first explored Earth's only natural satellite half a century ago. ➡ Subscribe: http://bit.ly/NatGeoSubscribe About National Geographic: National Geographic is the world's premium destination for science, exploration, and adventure. Through their world-class scientists, photographers, journalists, and filmmakers, Nat Geo gets you closer to the stories that matter and past the edge of what's possible. Get More National Geographic: Official Site: http://bit.ly/NatGeoOfficialSite Facebook: http://bit.ly/FBNatGeo Twitter: http://bit.ly/NatGeoTwitter Instagram: http://bit.ly/NatGeoInsta Moon 101 | National Geographic https://youtu.be/6AviDjR9mmo ...
published: 26 Jul 2018 -
The Moon's Orbit and Eclipses
A look at the nature of the Moon's orbit around Earth, and how that results in the libration of the Moon and the occasional solar and lunar eclipse. -~-~~-~~~-~~-~- Watch next: Solar Orbiter Discovers Surprising new Phenomenon in the Sun https://www.youtube.com/watch?v=VOrl2QlPCMI -~-~~-~~~-~~-~-
published: 26 Feb 2018 -
Moon Phases Demonstration
Emily Morgan, author of Next Time You See the Moon, takes you through the phases of the Moon in a demonstration that will be easy to replicate in your own classroom. http://www.nsta.org/store/product_detail.aspx?id=10.2505/9781938946332 http://www.nsta.org/nexttime-moon
published: 16 Sep 2014 -
The Moon doesn't orbit Earth's center. They orbit around a common center of mass, the barycenter.
published: 11 Oct 2022 -
Why Spacecraft Are Using These Crazy Routes To The Moon - Weak Stability and Ballistic Capture.
For decades spacecraft would fly direct to the moon and then brake into lunar orbit, but these days most spacecraft take long circuitous routes, dancing on the edge of stability near the lagrange points of the sun-earth-moon system. These techniques save propellent at the expense of time and navigation complexity. They use the theory of weak stability boundaries and ballistic capture in the 3 body problem, to make this possible, and it's an idea which was first discovered in the early 1990's and has now become the main route for modern spacecraft. Some of the orbit visualizations use Universe Sandbox https://universesandbox.com/ Follow me on Twitter for more updates: https://twitter.com/DJSnM I have a discord server where I regularly turn up: https://discord.gg/zStmKbM If you really...
published: 19 Dec 2022 -
Elita - Lunar Orbit
DYSANIA https://oppo.sition.link/Dysania Shop: https://elitaharkov.com https://elitamusicworld.com/ Artwork by Nick Knight Mixed by: Chris Perry Mastered by: João Carvalho Instagram: @yungelita @elitamusic @elitaemporium @elitaharkov2 Tiktok: @elitaharkov
published: 22 Mar 2023 -
The Moon Does Not Go Around the Earth
The Moon is our planet's sole natural satellite and nearest celestial body. The Moon orbits the Earth and it takes about one month to complete the full cycle from New Moon to New Moon. But there's a common misconception that the Moon goes around the Earth. Which isn't true. Why do we believe in this myth and why is it completely wrong? Let's take a look at the phases of the Moon and its rotation cycle. We'll see that the Moon is not going around the Earth - it is traveling along with the Earth - around the Sun. #brightside TIMESTAMPS The Sun doesn't go around the Earth 00:00 Myths about the Moon 00:37 Sun-centered -Solar system 01:12 The Phases of Venus 02:40 Moon and Earth 05:19 Barycenter 07:32 Earthling 09:30 Animation is created by Bright Side. --------------------------------...
published: 26 Jan 2022
developed with YouTube
0:43
How the Moon orbits Earth
- Order: Reorder
- Duration: 0:43
- Uploaded Date: 17 Apr 2020
- views: 335093
Using real data for the month of April 2020 I'm showing the exact rotations, tilts, inclination, orbital velocity, sunlight angles & views of our Earth-Moon sys...
Using real data for the month of April 2020 I'm showing the exact rotations, tilts, inclination, orbital velocity, sunlight angles & views of our Earth-Moon system. Earth-Moon distance is not to scale, but Earth and Moon *sizes* are (in the middle row).
FAQs/info
1. The green caps on the Moon are to indicate the position of the poles
2. The green circle around Earth (bottom middle, lol, middle Earth) is just a reference
3. The Moon is tilted 1.5° to its orbit around the Sun, so it has virtually no seasons
4. When the Moon is close to Earth it's pulled more strongly by Earth's gravity, so it goes faster, but when the Moon is far, it's pulled less and goes slower
5. Remember the SUPERMOON the other day? On April 7-8 have a look how there was a full Moon during a time when the Moon was closest to Earth... and you'll know why it looked bigger. A nice coincidence
6. Because of the 5.1° inclination and 1.5° axial tilt of the Moon, we actually see ~6.6° beneath and above the Moon's poles during it's orbit, which is why it looks like it wobbles up and down, from our point of view
Imagery from: NASA / Solar System Scope processing https://www.solarsystemscope.com/textures/ under CC BY 4.0
NASA ephemeris data: https://ssd.jpl.nasa.gov/horizons.cgi#top
https://wn.com/How_The_Moon_Orbits_Earth
Using real data for the month of April 2020 I'm showing the exact rotations, tilts, inclination, orbital velocity, sunlight angles & views of our Earth-Moon system. Earth-Moon distance is not to scale, but Earth and Moon *sizes* are (in the middle row).
FAQs/info
1. The green caps on the Moon are to indicate the position of the poles
2. The green circle around Earth (bottom middle, lol, middle Earth) is just a reference
3. The Moon is tilted 1.5° to its orbit around the Sun, so it has virtually no seasons
4. When the Moon is close to Earth it's pulled more strongly by Earth's gravity, so it goes faster, but when the Moon is far, it's pulled less and goes slower
5. Remember the SUPERMOON the other day? On April 7-8 have a look how there was a full Moon during a time when the Moon was closest to Earth... and you'll know why it looked bigger. A nice coincidence
6. Because of the 5.1° inclination and 1.5° axial tilt of the Moon, we actually see ~6.6° beneath and above the Moon's poles during it's orbit, which is why it looks like it wobbles up and down, from our point of view
Imagery from: NASA / Solar System Scope processing https://www.solarsystemscope.com/textures/ under CC BY 4.0
NASA ephemeris data: https://ssd.jpl.nasa.gov/horizons.cgi#top
0:12
How the Moon orbit - Motion of the Moon #shorts #moon #interstellar #space #animation
- Order: Reorder
- Duration: 0:12
- Uploaded Date: 03 May 2023
- views: 2800847
How the Moon orbit - Motion of the Moon #shorts #moon #interstellar #space #animation
From your astronaut’s viewpoint, you can see that the Moon is an average...
How the Moon orbit - Motion of the Moon #shorts #moon #interstellar #space #animation
From your astronaut’s viewpoint, you can see that the Moon is an average of 238,855 miles (384,399 km) from Earth, or about the space that could be occupied by 30 Earths. It travels around our planet once every 27.322 days in an elliptical orbit, an elongated circle. The Moon is tidally locked with Earth, which means that it spins on its axis exactly once each time it orbits our planet. Because of this, people on Earth only ever see one side of the Moon. We call this motion synchronous rotation.
The Moon’s orbit is tilted about 5 degrees compared to the plane of Earth’s orbit around the Sun. Because of this tilt, the Moon as seen from Earth’s perspective usually passes above or below the Sun when it passes between us and the Sun. The tilt of the Moon’s orbit prevents us from having monthly solar and lunar eclipses.
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https://wn.com/How_The_Moon_Orbit_Motion_Of_The_Moon_Shorts_Moon_Interstellar_Space_Animation
How the Moon orbit - Motion of the Moon #shorts #moon #interstellar #space #animation
From your astronaut’s viewpoint, you can see that the Moon is an average of 238,855 miles (384,399 km) from Earth, or about the space that could be occupied by 30 Earths. It travels around our planet once every 27.322 days in an elliptical orbit, an elongated circle. The Moon is tidally locked with Earth, which means that it spins on its axis exactly once each time it orbits our planet. Because of this, people on Earth only ever see one side of the Moon. We call this motion synchronous rotation.
The Moon’s orbit is tilted about 5 degrees compared to the plane of Earth’s orbit around the Sun. Because of this tilt, the Moon as seen from Earth’s perspective usually passes above or below the Sun when it passes between us and the Sun. The tilt of the Moon’s orbit prevents us from having monthly solar and lunar eclipses.
moon,moon orbit,orbit of the moon,orbit,low moon orbit,new moon,extreme low moon orbit,orbits,moon's orbit,orbit (orbit type),moon orbit animation,he moon's orbit,the moon,full moon,galilean moons orbit,how the moon was formed,inclination of the moon's orbit,dark side of moon,how to get to the moon,does the moon really orbit the earth,moons,scientists found a second moon orbiting earth!,moon (celestial object with coordinate system),moon phases, moon,motion of the moon,stop motion,new moon,moon wheels of motion,stop motion animation,full moon,motion of moon around earth,moon phases,moon rotation,moon (moon),earth's motion,rotation moon,dark side of moon,orbit of the moon,motion graphics,wheels of motion,stop motion film,phases of the moon,the moon,moon cycle,rotation of moon,fabio wheels of motion,moon missions,moon landing,motion of earth around sun,moon animation, moon,nasa,moon landing,video,moon mission,moon phases,nasa loses moon tapes,what happened to the nasa moon landing tapes,planets and moons,moon made of,short video,ufo videos,nasa footage,aliens video,shorts video,neil armstrong video,short videos,viral videos,the moon,nasa film,nasa 16mm,moon walk,full moon,nasa's,ancient ufo video,moon cycle,on the moon,space related animation and video,nasa audio,moon landing movie, space,space videos,space video,space station,spacex,outer space,video,international space station,nasa video,video about space,videos from space,nasa videos of space,living in space,space facts,earth from space,facts about space,space exploration,learning videos,deep space,eva 4k space,space 4k,in space,video in,space diving,space voyage,space living,videos,space man,go pro video del espacio,gravity space,ufo video, interstellar,interstellar movie,interstellar piano,interstellar soundtrack,interstellar (film),hans zimmer interstellar,interstellar music,interstellar ending,interstellar reaction,interstellar explained,interstellar breakdown,interstellar easter egg,interstellar piano tutorial,interstellar ending explained,first time watching interstellar,interstelar,interstellar film,interstellar epic,interstellar imax,interstellar 2014,music interstellar, solar system,moon,moon orbit,solar system moon,moons of the solar system,planets in our solar system,solar system working,solar system animation,solar system for kids,solar system planets,space engine solar system,orbit,how solar system really moves,actual solar system movement,kids planets solar system,moon orbit animation,orbit of the moon,how solar system really moves #shorts,galilean moons orbit,amazing facts about solar system 😲
- published: 03 May 2023
- views: 2800847
3:20
Phases of moon explained using an orrery
- Order: Reorder
- Duration: 3:20
- Uploaded Date: 03 Jun 2019
- views: 2883484
As the moon rotates around the earth it travels through phases.
The alignment of the sun, earth, and moon create the phases.
I use an orrery to explain the moon...
As the moon rotates around the earth it travels through phases.
The alignment of the sun, earth, and moon create the phases.
I use an orrery to explain the moon's alignment during,
new moon, waxing crescent, ist quarter, waxing gibbous, full moon, waning gibbous, last quarter, waning crescent, and back to new moon.
The sidereal period is 27.3 and the moon is measured against stars.
The synodic period is 29.5 days and the moon is measured against the sun.
If you enjoyed this video you may enjoy the Earth Science Course with an emphasis on Astronomy.
The course includes 13 videos along with a study guide and an answer key for each guide.
In addition there is a short enrichment activity for each video.
Link to the playlist here.
https://youtube.com/playlist?list=PLurjkZV1ykGaCbqkU_0z82I_40JinIbtl&si=lMBhAg7-Uj-QhgTu
You may also enjoy
Rotation and Revolution of the Earth with an Orrery
https://youtu.be/-iztiJz7SJQ
Phases of the moon with pictures.
https://moomoomath.com/phases-of-moon-explained-using-an-orrery/
Moon Phases Quiz
https://youtu.be/QMWkhB_vUrU
https://wn.com/Phases_Of_Moon_Explained_Using_An_Orrery
As the moon rotates around the earth it travels through phases.
The alignment of the sun, earth, and moon create the phases.
I use an orrery to explain the moon's alignment during,
new moon, waxing crescent, ist quarter, waxing gibbous, full moon, waning gibbous, last quarter, waning crescent, and back to new moon.
The sidereal period is 27.3 and the moon is measured against stars.
The synodic period is 29.5 days and the moon is measured against the sun.
If you enjoyed this video you may enjoy the Earth Science Course with an emphasis on Astronomy.
The course includes 13 videos along with a study guide and an answer key for each guide.
In addition there is a short enrichment activity for each video.
Link to the playlist here.
https://youtube.com/playlist?list=PLurjkZV1ykGaCbqkU_0z82I_40JinIbtl&si=lMBhAg7-Uj-QhgTu
You may also enjoy
Rotation and Revolution of the Earth with an Orrery
https://youtu.be/-iztiJz7SJQ
Phases of the moon with pictures.
https://moomoomath.com/phases-of-moon-explained-using-an-orrery/
Moon Phases Quiz
https://youtu.be/QMWkhB_vUrU
- published: 03 Jun 2019
- views: 2883484
3:06
Moon 101 | National Geographic
- Order: Reorder
- Duration: 3:06
- Uploaded Date: 26 Jul 2018
- views: 5396613
What is the moon made of, and how did it form? Learn about the moon's violent origins, how its phases shaped the earliest calendars, and how humans first explor...
What is the moon made of, and how did it form? Learn about the moon's violent origins, how its phases shaped the earliest calendars, and how humans first explored Earth's only natural satellite half a century ago.
➡ Subscribe: http://bit.ly/NatGeoSubscribe
About National Geographic:
National Geographic is the world's premium destination for science, exploration, and adventure. Through their world-class scientists, photographers, journalists, and filmmakers, Nat Geo gets you closer to the stories that matter and past the edge of what's possible.
Get More National Geographic:
Official Site: http://bit.ly/NatGeoOfficialSite
Facebook: http://bit.ly/FBNatGeo
Twitter: http://bit.ly/NatGeoTwitter
Instagram: http://bit.ly/NatGeoInsta
Moon 101 | National Geographic
https://youtu.be/6AviDjR9mmo
National Geographic
https://www.youtube.com/natgeo
https://wn.com/Moon_101_|_National_Geographic
What is the moon made of, and how did it form? Learn about the moon's violent origins, how its phases shaped the earliest calendars, and how humans first explored Earth's only natural satellite half a century ago.
➡ Subscribe: http://bit.ly/NatGeoSubscribe
About National Geographic:
National Geographic is the world's premium destination for science, exploration, and adventure. Through their world-class scientists, photographers, journalists, and filmmakers, Nat Geo gets you closer to the stories that matter and past the edge of what's possible.
Get More National Geographic:
Official Site: http://bit.ly/NatGeoOfficialSite
Facebook: http://bit.ly/FBNatGeo
Twitter: http://bit.ly/NatGeoTwitter
Instagram: http://bit.ly/NatGeoInsta
Moon 101 | National Geographic
https://youtu.be/6AviDjR9mmo
National Geographic
https://www.youtube.com/natgeo
- published: 26 Jul 2018
- views: 5396613
17:31
The Moon's Orbit and Eclipses
- Order: Reorder
- Duration: 17:31
- Uploaded Date: 26 Feb 2018
- views: 105407
A look at the nature of the Moon's orbit around Earth, and how that results in the libration of the Moon and the occasional solar and lunar eclipse.
-~-~~-~~~-...
A look at the nature of the Moon's orbit around Earth, and how that results in the libration of the Moon and the occasional solar and lunar eclipse.
-~-~~-~~~-~~-~-
Watch next: Solar Orbiter Discovers Surprising new Phenomenon in the Sun
https://www.youtube.com/watch?v=VOrl2QlPCMI
-~-~~-~~~-~~-~-
https://wn.com/The_Moon's_Orbit_And_Eclipses
A look at the nature of the Moon's orbit around Earth, and how that results in the libration of the Moon and the occasional solar and lunar eclipse.
-~-~~-~~~-~~-~-
Watch next: Solar Orbiter Discovers Surprising new Phenomenon in the Sun
https://www.youtube.com/watch?v=VOrl2QlPCMI
-~-~~-~~~-~~-~-
- published: 26 Feb 2018
- views: 105407
4:16
Moon Phases Demonstration
- Order: Reorder
- Duration: 4:16
- Uploaded Date: 16 Sep 2014
- views: 4923799
Emily Morgan, author of Next Time You See the Moon, takes you through the phases of the Moon in a demonstration that will be easy to replicate in your own class...
Emily Morgan, author of Next Time You See the Moon, takes you through the phases of the Moon in a demonstration that will be easy to replicate in your own classroom.
http://www.nsta.org/store/product_detail.aspx?id=10.2505/9781938946332
http://www.nsta.org/nexttime-moon
https://wn.com/Moon_Phases_Demonstration
Emily Morgan, author of Next Time You See the Moon, takes you through the phases of the Moon in a demonstration that will be easy to replicate in your own classroom.
http://www.nsta.org/store/product_detail.aspx?id=10.2505/9781938946332
http://www.nsta.org/nexttime-moon
- published: 16 Sep 2014
- views: 4923799
0:15
The Moon doesn't orbit Earth's center. They orbit around a common center of mass, the barycenter.
- Order: Reorder
- Duration: 0:15
- Uploaded Date: 11 Oct 2022
- views: 344176
- published: 11 Oct 2022
- views: 344176
14:00
Why Spacecraft Are Using These Crazy Routes To The Moon - Weak Stability and Ballistic Capture.
- Order: Reorder
- Duration: 14:00
- Uploaded Date: 19 Dec 2022
- views: 305064
For decades spacecraft would fly direct to the moon and then brake into lunar orbit, but these days most spacecraft take long circuitous routes, dancing on the ...
For decades spacecraft would fly direct to the moon and then brake into lunar orbit, but these days most spacecraft take long circuitous routes, dancing on the edge of stability near the lagrange points of the sun-earth-moon system. These techniques save propellent at the expense of time and navigation complexity.
They use the theory of weak stability boundaries and ballistic capture in the 3 body problem, to make this possible, and it's an idea which was first discovered in the early 1990's and has now become the main route for modern spacecraft.
Some of the orbit visualizations use Universe Sandbox
https://universesandbox.com/
Follow me on Twitter for more updates:
https://twitter.com/DJSnM
I have a discord server where I regularly turn up:
https://discord.gg/zStmKbM
If you really like what I do you can support me directly through Patreon
https://www.patreon.com/scottmanley
https://wn.com/Why_Spacecraft_Are_Using_These_Crazy_Routes_To_The_Moon_Weak_Stability_And_Ballistic_Capture.
For decades spacecraft would fly direct to the moon and then brake into lunar orbit, but these days most spacecraft take long circuitous routes, dancing on the edge of stability near the lagrange points of the sun-earth-moon system. These techniques save propellent at the expense of time and navigation complexity.
They use the theory of weak stability boundaries and ballistic capture in the 3 body problem, to make this possible, and it's an idea which was first discovered in the early 1990's and has now become the main route for modern spacecraft.
Some of the orbit visualizations use Universe Sandbox
https://universesandbox.com/
Follow me on Twitter for more updates:
https://twitter.com/DJSnM
I have a discord server where I regularly turn up:
https://discord.gg/zStmKbM
If you really like what I do you can support me directly through Patreon
https://www.patreon.com/scottmanley
- published: 19 Dec 2022
- views: 305064
2:55
Elita - Lunar Orbit
- Order: Reorder
- Duration: 2:55
- Uploaded Date: 22 Mar 2023
- views: 16671
DYSANIA
https://oppo.sition.link/Dysania
Shop: https://elitaharkov.com
https://elitamusicworld.com/
Artwork by Nick Knight
Mixed by: Chris Perry
Mastered by:...
DYSANIA
https://oppo.sition.link/Dysania
Shop: https://elitaharkov.com
https://elitamusicworld.com/
Artwork by Nick Knight
Mixed by: Chris Perry
Mastered by: João Carvalho
Instagram: @yungelita @elitamusic @elitaemporium @elitaharkov2
Tiktok: @elitaharkov
https://wn.com/Elita_Lunar_Orbit
DYSANIA
https://oppo.sition.link/Dysania
Shop: https://elitaharkov.com
https://elitamusicworld.com/
Artwork by Nick Knight
Mixed by: Chris Perry
Mastered by: João Carvalho
Instagram: @yungelita @elitamusic @elitaemporium @elitaharkov2
Tiktok: @elitaharkov
- published: 22 Mar 2023
- views: 16671
10:01
The Moon Does Not Go Around the Earth
- Order: Reorder
- Duration: 10:01
- Uploaded Date: 26 Jan 2022
- views: 556163
The Moon is our planet's sole natural satellite and nearest celestial body. The Moon orbits the Earth and it takes about one month to complete the full cycle fr...
The Moon is our planet's sole natural satellite and nearest celestial body. The Moon orbits the Earth and it takes about one month to complete the full cycle from New Moon to New Moon. But there's a common misconception that the Moon goes around the Earth. Which isn't true.
Why do we believe in this myth and why is it completely wrong? Let's take a look at the phases of the Moon and its rotation cycle. We'll see that the Moon is not going around the Earth - it is traveling along with the Earth - around the Sun.
#brightside
TIMESTAMPS
The Sun doesn't go around the Earth 00:00
Myths about the Moon 00:37
Sun-centered -Solar system 01:12
The Phases of Venus 02:40
Moon and Earth 05:19
Barycenter 07:32
Earthling 09:30
Animation is created by Bright Side.
----------------------------------------------------------------------------------------
Music by Epidemic Sound https://www.epidemicsound.com
Check our Bright Side podcast on Spotify and leave a positive review! https://open.spotify.com/show/0hUkPxD34jRLrMrJux4VxV
Subscribe to Bright Side: https://goo.gl/rQTJZz
----------------------------------------------------------------------------------------
Our Social Media:
Facebook: https://www.facebook.com/brightside
Instagram: https://www.instagram.com/brightside.official
TikTok: https://www.tiktok.com/@brightside.official?lang=en
Stock materials (photos, footages and other):
https://www.depositphotos.com
https://www.shutterstock.com
https://www.eastnews.ru
----------------------------------------------------------------------------------------
For more videos and articles visit:
http://www.brightside.me
https://wn.com/The_Moon_Does_Not_Go_Around_The_Earth
The Moon is our planet's sole natural satellite and nearest celestial body. The Moon orbits the Earth and it takes about one month to complete the full cycle from New Moon to New Moon. But there's a common misconception that the Moon goes around the Earth. Which isn't true.
Why do we believe in this myth and why is it completely wrong? Let's take a look at the phases of the Moon and its rotation cycle. We'll see that the Moon is not going around the Earth - it is traveling along with the Earth - around the Sun.
#brightside
TIMESTAMPS
The Sun doesn't go around the Earth 00:00
Myths about the Moon 00:37
Sun-centered -Solar system 01:12
The Phases of Venus 02:40
Moon and Earth 05:19
Barycenter 07:32
Earthling 09:30
Animation is created by Bright Side.
----------------------------------------------------------------------------------------
Music by Epidemic Sound https://www.epidemicsound.com
Check our Bright Side podcast on Spotify and leave a positive review! https://open.spotify.com/show/0hUkPxD34jRLrMrJux4VxV
Subscribe to Bright Side: https://goo.gl/rQTJZz
----------------------------------------------------------------------------------------
Our Social Media:
Facebook: https://www.facebook.com/brightside
Instagram: https://www.instagram.com/brightside.official
TikTok: https://www.tiktok.com/@brightside.official?lang=en
Stock materials (photos, footages and other):
https://www.depositphotos.com
https://www.shutterstock.com
https://www.eastnews.ru
----------------------------------------------------------------------------------------
For more videos and articles visit:
http://www.brightside.me
- published: 26 Jan 2022
- views: 556163
-
Chapter 7: Group actions, symmetric group and Cayley’s theorem | Essence of Group Theory
Group action can be thought of as a homomorphism to a symmetric group, so apart from orbit-stabiliser theorem, we can also use the isomorphism theorem to analyse any group action. It turns out that this correspondence between group action and homomorphism can be visualised rather easily. This correspondence is very important in group theory, but often neglected. Symmetric group is also briefly mentioned here as a concept to facilitate the introduction of the above correspondence, but a more detailed analysis of the symmetric group would not be in this video series, because I don't think it is as intuitive as concepts discussed in the video series and therefore does not fit the theme of the series too well. However, I will do a video on Burnside's lemma and its interesting application, but...
published: 28 Jun 2020 -
Group Theory, lecture 5.1: Group actions
We discuss group actions
published: 15 Nov 2020 -
Chapter 1: Symmetries, Groups and Actions | Essence of Group Theory
Start of a video series on intuitions of group theory. Groups are often introduced as a kind of abstract algebraic object right from the start, which is not good for developing intuitions for first-time learners. This video series hopes to help you develop intuitions, which are useful in understanding group theory. In particular, this video is going to be about thinking groups as symmetries (or isometries to be precise) because they are much more visualisable, and that symmetries of an object do form a group using the abstract definition of the group that is usually given. Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels: https://forms.gle/QJ29hocF9uQAyZyH6 If you want to kn...
published: 06 Feb 2020 -
Group Theory: Lecture 15/30 - Introduction to Group Actions
This video series is not endorsed by the University of Cambridge. These videos are primarily inspired from Dexter Chua's lecture notes, which can be found here: https://dec41.user.srcf.net/notes/IA_M/groups.pdf Additionally, problem sets for this video series can be found here: https://dec41.user.srcf.net/notes/IA_M/groups_eg.pdf
published: 26 Jun 2023 -
Lecture 33 - Group actions
published: 06 May 2019 -
Chapter 2: Orbit-Stabiliser Theorem | Essence of Group Theory
An intuitive explanation of the Orbit-Stabilis(z)er theorem (in the finite case). It emerges very apparently when counting the total number of symmetries in some tricky but easy way. This video series continues to develop your intuition towards some fundamental concepts and results in Group theory. Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels: https://forms.gle/QJ29hocF9uQAyZyH6 If you want to know more interesting Mathematics, stay tuned for the next video! SUBSCRIBE and see you in the next video! #mathemaniac #math #grouptheory #groups #orbitstabiliser #orbitstabilizer
published: 17 Feb 2020 -
GT15. Group Actions
Abstract Algebra: Group actions are defined as a formal mechanism that describes symmetries of a set X. A given group action defines an equivalence relation, which in turn yields a partition of X into orbits. Orbits are also described as cosets of the group. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theory Master list at http://mathdoctorbob.org/UReddit.html
published: 23 Jan 2012 -
Group Actions
published: 01 Dec 2020 -
What is a Group Action? : A Group as a Category and The Skeleton Operation ☠
This week I try to take a more Categorical approach to answering and expanding upon the question of "what is a group action". Along the way I'll go over thinking about a group as a category and eventually hit on the skeleton operation on a category and use it to present an example of the categorification of the Orbit-Stabilizer theorem. Here are some videos that are "pre-reqs", that is, they introduce some topics in a bit more detail than I do here. What are groups: https://youtu.be/uraPtd0yCI4 What are categories: https://youtu.be/ZaLB0MF2TMQ Also, Here is the Category Theory Book that inspired this video: https://amzn.to/317hxMc CORRECTIONS: 1. When introducing Groups, while glossing over the group axioms I forget to mention that a group, G, must be closed under the binary operation. ...
published: 09 Jul 2020 -
Group Actions: Stabilizers
Introducing the stabilizer subgroup. Setup for Sylow's Theorem. For more math, subscribe to my channel: https://www.youtube.com/jeffsuzuki1
published: 20 Apr 2022
developed with YouTube
10:51
Chapter 7: Group actions, symmetric group and Cayley’s theorem | Essence of Group Theory
- Order: Reorder
- Duration: 10:51
- Uploaded Date: 28 Jun 2020
- views: 31414
Group action can be thought of as a homomorphism to a symmetric group, so apart from orbit-stabiliser theorem, we can also use the isomorphism theorem to analys...
Group action can be thought of as a homomorphism to a symmetric group, so apart from orbit-stabiliser theorem, we can also use the isomorphism theorem to analyse any group action. It turns out that this correspondence between group action and homomorphism can be visualised rather easily. This correspondence is very important in group theory, but often neglected.
Symmetric group is also briefly mentioned here as a concept to facilitate the introduction of the above correspondence, but a more detailed analysis of the symmetric group would not be in this video series, because I don't think it is as intuitive as concepts discussed in the video series and therefore does not fit the theme of the series too well. However, I will do a video on Burnside's lemma and its interesting application, but it is not "Essence of Group Theory" anymore, because it is an application of the orbit-stabiliser theorem. I haven't mentioned in the video that I will also not do a video on matrix groups because it requires the knowledge of linear algebra, and again, the concepts discussed in the matrix groups will usually be algebraic.
The next few videos will be a summary of this video series with one very cool example that really covers all the concepts discussed in this video series; another video on the current epidemic explaining an alternative model to the SIR discussed on this channel before, and will be about a stochastic branching process; then the Burnside's lemma video. There might be some videos in between these, but I will definitely do all of these videos in some time in the future.
Cayley's theorem is named in honour of Arthur Cayley, a British (Cambridge) mathematician who is also known for a lot of mathematical results, like Cayley table, Cayley graph, Cayley's theorem and the famous Cayley-Hamilton theorem in linear algebra. However, even though it is a motivation for the study of symmetric groups, you might not see Cayley's theorem too often in more advanced studies of group theory. It mainly acts as a direct application of the correspondence discussed in this video.
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
SUBSCRIBE and see you in the next video!
If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe!
#mathemaniac #math #grouptheory #groupaction #homomorphism #Cayley
Social media:
Facebook: https://www.facebook.com/mathemaniacyt
Instagram: https://www.instagram.com/_mathemaniac_/
Twitter: https://twitter.com/mathemaniacyt
https://wn.com/Chapter_7_Group_Actions,_Symmetric_Group_And_Cayley’S_Theorem_|_Essence_Of_Group_Theory
Group action can be thought of as a homomorphism to a symmetric group, so apart from orbit-stabiliser theorem, we can also use the isomorphism theorem to analyse any group action. It turns out that this correspondence between group action and homomorphism can be visualised rather easily. This correspondence is very important in group theory, but often neglected.
Symmetric group is also briefly mentioned here as a concept to facilitate the introduction of the above correspondence, but a more detailed analysis of the symmetric group would not be in this video series, because I don't think it is as intuitive as concepts discussed in the video series and therefore does not fit the theme of the series too well. However, I will do a video on Burnside's lemma and its interesting application, but it is not "Essence of Group Theory" anymore, because it is an application of the orbit-stabiliser theorem. I haven't mentioned in the video that I will also not do a video on matrix groups because it requires the knowledge of linear algebra, and again, the concepts discussed in the matrix groups will usually be algebraic.
The next few videos will be a summary of this video series with one very cool example that really covers all the concepts discussed in this video series; another video on the current epidemic explaining an alternative model to the SIR discussed on this channel before, and will be about a stochastic branching process; then the Burnside's lemma video. There might be some videos in between these, but I will definitely do all of these videos in some time in the future.
Cayley's theorem is named in honour of Arthur Cayley, a British (Cambridge) mathematician who is also known for a lot of mathematical results, like Cayley table, Cayley graph, Cayley's theorem and the famous Cayley-Hamilton theorem in linear algebra. However, even though it is a motivation for the study of symmetric groups, you might not see Cayley's theorem too often in more advanced studies of group theory. It mainly acts as a direct application of the correspondence discussed in this video.
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
SUBSCRIBE and see you in the next video!
If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe!
#mathemaniac #math #grouptheory #groupaction #homomorphism #Cayley
Social media:
Facebook: https://www.facebook.com/mathemaniacyt
Instagram: https://www.instagram.com/_mathemaniac_/
Twitter: https://twitter.com/mathemaniacyt
- published: 28 Jun 2020
- views: 31414
23:42
Group Theory, lecture 5.1: Group actions
- Order: Reorder
- Duration: 23:42
- Uploaded Date: 15 Nov 2020
- views: 7398
We discuss group actions
We discuss group actions
https://wn.com/Group_Theory,_Lecture_5.1_Group_Actions
We discuss group actions
- published: 15 Nov 2020
- views: 7398
6:07
Chapter 1: Symmetries, Groups and Actions | Essence of Group Theory
- Order: Reorder
- Duration: 6:07
- Uploaded Date: 06 Feb 2020
- views: 112388
Start of a video series on intuitions of group theory. Groups are often introduced as a kind of abstract algebraic object right from the start, which is not goo...
Start of a video series on intuitions of group theory. Groups are often introduced as a kind of abstract algebraic object right from the start, which is not good for developing intuitions for first-time learners. This video series hopes to help you develop intuitions, which are useful in understanding group theory.
In particular, this video is going to be about thinking groups as symmetries (or isometries to be precise) because they are much more visualisable, and that symmetries of an object do form a group using the abstract definition of the group that is usually given.
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
SUBSCRIBE and see you in the next video!
If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe!
#mathemaniac #math #grouptheory #groups #intuition
Social media:
Facebook: https://www.facebook.com/mathemaniacyt
Instagram: https://www.instagram.com/_mathemaniac_/
Twitter: https://twitter.com/mathemaniacyt
Patreon: https://www.patreon.com/mathemaniac (support if you want to and can afford to!)
For my contact email, check my About page on a PC.
See you next time!
https://wn.com/Chapter_1_Symmetries,_Groups_And_Actions_|_Essence_Of_Group_Theory
Start of a video series on intuitions of group theory. Groups are often introduced as a kind of abstract algebraic object right from the start, which is not good for developing intuitions for first-time learners. This video series hopes to help you develop intuitions, which are useful in understanding group theory.
In particular, this video is going to be about thinking groups as symmetries (or isometries to be precise) because they are much more visualisable, and that symmetries of an object do form a group using the abstract definition of the group that is usually given.
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
SUBSCRIBE and see you in the next video!
If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe!
#mathemaniac #math #grouptheory #groups #intuition
Social media:
Facebook: https://www.facebook.com/mathemaniacyt
Instagram: https://www.instagram.com/_mathemaniac_/
Twitter: https://twitter.com/mathemaniacyt
Patreon: https://www.patreon.com/mathemaniac (support if you want to and can afford to!)
For my contact email, check my About page on a PC.
See you next time!
- published: 06 Feb 2020
- views: 112388
48:59
Group Theory: Lecture 15/30 - Introduction to Group Actions
- Order: Reorder
- Duration: 48:59
- Uploaded Date: 26 Jun 2023
- views: 858
This video series is not endorsed by the University of Cambridge. These videos are primarily inspired from Dexter Chua's lecture notes, which can be found here:...
This video series is not endorsed by the University of Cambridge. These videos are primarily inspired from Dexter Chua's lecture notes, which can be found here:
https://dec41.user.srcf.net/notes/IA_M/groups.pdf
Additionally, problem sets for this video series can be found here:
https://dec41.user.srcf.net/notes/IA_M/groups_eg.pdf
https://wn.com/Group_Theory_Lecture_15_30_Introduction_To_Group_Actions
This video series is not endorsed by the University of Cambridge. These videos are primarily inspired from Dexter Chua's lecture notes, which can be found here:
https://dec41.user.srcf.net/notes/IA_M/groups.pdf
Additionally, problem sets for this video series can be found here:
https://dec41.user.srcf.net/notes/IA_M/groups_eg.pdf
- published: 26 Jun 2023
- views: 858
24:53
Lecture 33 - Group actions
- Order: Reorder
- Duration: 24:53
- Uploaded Date: 06 May 2019
- views: 40495
- published: 06 May 2019
- views: 40495
12:27
Chapter 2: Orbit-Stabiliser Theorem | Essence of Group Theory
- Order: Reorder
- Duration: 12:27
- Uploaded Date: 17 Feb 2020
- views: 66226
An intuitive explanation of the Orbit-Stabilis(z)er theorem (in the finite case). It emerges very apparently when counting the total number of symmetries in som...
An intuitive explanation of the Orbit-Stabilis(z)er theorem (in the finite case). It emerges very apparently when counting the total number of symmetries in some tricky but easy way. This video series continues to develop your intuition towards some fundamental concepts and results in Group theory.
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
SUBSCRIBE and see you in the next video!
#mathemaniac #math #grouptheory #groups #orbitstabiliser #orbitstabilizer
https://wn.com/Chapter_2_Orbit_Stabiliser_Theorem_|_Essence_Of_Group_Theory
An intuitive explanation of the Orbit-Stabilis(z)er theorem (in the finite case). It emerges very apparently when counting the total number of symmetries in some tricky but easy way. This video series continues to develop your intuition towards some fundamental concepts and results in Group theory.
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
SUBSCRIBE and see you in the next video!
#mathemaniac #math #grouptheory #groups #orbitstabiliser #orbitstabilizer
- published: 17 Feb 2020
- views: 66226
20:19
GT15. Group Actions
- Order: Reorder
- Duration: 20:19
- Uploaded Date: 23 Jan 2012
- views: 45082
Abstract Algebra: Group actions are defined as a formal mechanism that describes symmetries of a set X. A given group action defines an equivalence relation, ...
Abstract Algebra: Group actions are defined as a formal mechanism that describes symmetries of a set X. A given group action defines an equivalence relation, which in turn yields a partition of X into orbits. Orbits are also described as cosets of the group.
U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theory Master list at http://mathdoctorbob.org/UReddit.html
https://wn.com/Gt15._Group_Actions
Abstract Algebra: Group actions are defined as a formal mechanism that describes symmetries of a set X. A given group action defines an equivalence relation, which in turn yields a partition of X into orbits. Orbits are also described as cosets of the group.
U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theory Master list at http://mathdoctorbob.org/UReddit.html
- published: 23 Jan 2012
- views: 45082
41:51
Group Actions
- Order: Reorder
- Duration: 41:51
- Uploaded Date: 01 Dec 2020
- views: 7168
- published: 01 Dec 2020
- views: 7168
20:53
What is a Group Action? : A Group as a Category and The Skeleton Operation ☠
- Order: Reorder
- Duration: 20:53
- Uploaded Date: 09 Jul 2020
- views: 3870
This week I try to take a more Categorical approach to answering and expanding upon the question of "what is a group action". Along the way I'll go over thinkin...
This week I try to take a more Categorical approach to answering and expanding upon the question of "what is a group action". Along the way I'll go over thinking about a group as a category and eventually hit on the skeleton operation on a category and use it to present an example of the categorification of the Orbit-Stabilizer theorem. Here are some videos that are "pre-reqs", that is, they introduce some topics in a bit more detail than I do here.
What are groups: https://youtu.be/uraPtd0yCI4
What are categories: https://youtu.be/ZaLB0MF2TMQ
Also, Here is the Category Theory Book that inspired this video: https://amzn.to/317hxMc
CORRECTIONS:
1. When introducing Groups, while glossing over the group axioms I forget to mention that a group, G, must be closed under the binary operation. That is for any a,b in G, ab must also be in G.
This video can be broken up into the following sections.
00:00 Intro
I once again fail to say "Hi I'm Nathan and Welcome to my YouTube Channel" but I still introduce the goal of the video lol.
00:32 What is a Group Action?
I briefly revisit the idea of what a group is before "complicating" it into the object that we'll spend most of the time interacting with, a group action. There are many different types of group actions but we will focus on 2 examples.
03:46 Example 1
The first of 2 group action examples. We look at probably the most accessible example of a group action, a group acting on itself with the action operating the same way as the group operation.
05:05 Example 2
In the second of 2 group action examples we look at another small but more complicated example of a group acting on itself, here we us the conjugate action and we'll continue to look at this example throughout the video.
After the second example, the video begins to bring in a lot more ideas from category theory and we'll spend a lot of time looking at categories and groups and how the two can correspond to one another.
09:30 A Group as a Category
Here I will begin translating the idea of what we have talked about with groups and group actions into a more category theoretic context. We won't dive too deep into the Category of G-Sets, but we do define what G-Sets are and how they can be described as functors.
11:21 The Translation Groupoid of A Group
Next we 'zoom in' on what our G-Set functor does to the categorical group and arrive at the directed graphs that we looked at previously by looking at the Translation Groupoid.
13:27 The Skeleton Operation
The last Category theoretic tool we will need for the categorification of the orbit-stabilizer theorem, the skeleton operator on a category fuses together identical (or isomorphic) objects, which allows us to see the information in the Translation Groupoid category more clearly.
15:50 The Orbit-Stabilizer Theorem
Here we introduce (not prove...) the theorem and then talk through how the skeleton operation on the translation groupoid generates a very nice picture of the theorem in a Category Theoretic context.
17:35 Another way of Thinking about the Skeleton Category
And lastly I pull away from the abstract nonsense of the skeleton construction to quickly walk through another way to interpret each of the orbits in the skeleton category that can help when trying to determine the size of other symmetry/dihedral groups.
_____________________
Last PhD Update: https://youtu.be/de_MVF1FiZU
Last Time: https://youtu.be/MjyBP7m12yg
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Subscriber Count as of release: 1,783
#CHALK #CategoryTheory #Skeleton
https://wn.com/What_Is_A_Group_Action_A_Group_As_A_Category_And_The_Skeleton_Operation_☠
This week I try to take a more Categorical approach to answering and expanding upon the question of "what is a group action". Along the way I'll go over thinking about a group as a category and eventually hit on the skeleton operation on a category and use it to present an example of the categorification of the Orbit-Stabilizer theorem. Here are some videos that are "pre-reqs", that is, they introduce some topics in a bit more detail than I do here.
What are groups: https://youtu.be/uraPtd0yCI4
What are categories: https://youtu.be/ZaLB0MF2TMQ
Also, Here is the Category Theory Book that inspired this video: https://amzn.to/317hxMc
CORRECTIONS:
1. When introducing Groups, while glossing over the group axioms I forget to mention that a group, G, must be closed under the binary operation. That is for any a,b in G, ab must also be in G.
This video can be broken up into the following sections.
00:00 Intro
I once again fail to say "Hi I'm Nathan and Welcome to my YouTube Channel" but I still introduce the goal of the video lol.
00:32 What is a Group Action?
I briefly revisit the idea of what a group is before "complicating" it into the object that we'll spend most of the time interacting with, a group action. There are many different types of group actions but we will focus on 2 examples.
03:46 Example 1
The first of 2 group action examples. We look at probably the most accessible example of a group action, a group acting on itself with the action operating the same way as the group operation.
05:05 Example 2
In the second of 2 group action examples we look at another small but more complicated example of a group acting on itself, here we us the conjugate action and we'll continue to look at this example throughout the video.
After the second example, the video begins to bring in a lot more ideas from category theory and we'll spend a lot of time looking at categories and groups and how the two can correspond to one another.
09:30 A Group as a Category
Here I will begin translating the idea of what we have talked about with groups and group actions into a more category theoretic context. We won't dive too deep into the Category of G-Sets, but we do define what G-Sets are and how they can be described as functors.
11:21 The Translation Groupoid of A Group
Next we 'zoom in' on what our G-Set functor does to the categorical group and arrive at the directed graphs that we looked at previously by looking at the Translation Groupoid.
13:27 The Skeleton Operation
The last Category theoretic tool we will need for the categorification of the orbit-stabilizer theorem, the skeleton operator on a category fuses together identical (or isomorphic) objects, which allows us to see the information in the Translation Groupoid category more clearly.
15:50 The Orbit-Stabilizer Theorem
Here we introduce (not prove...) the theorem and then talk through how the skeleton operation on the translation groupoid generates a very nice picture of the theorem in a Category Theoretic context.
17:35 Another way of Thinking about the Skeleton Category
And lastly I pull away from the abstract nonsense of the skeleton construction to quickly walk through another way to interpret each of the orbits in the skeleton category that can help when trying to determine the size of other symmetry/dihedral groups.
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- published: 09 Jul 2020
- views: 3870
4:37
Group Actions: Stabilizers
- Order: Reorder
- Duration: 4:37
- Uploaded Date: 20 Apr 2022
- views: 244
Introducing the stabilizer subgroup. Setup for Sylow's Theorem.
For more math, subscribe to my channel: https://www.youtube.com/jeffsuzuki1
Introducing the stabilizer subgroup. Setup for Sylow's Theorem.
For more math, subscribe to my channel: https://www.youtube.com/jeffsuzuki1
https://wn.com/Group_Actions_Stabilizers
Introducing the stabilizer subgroup. Setup for Sylow's Theorem.
For more math, subscribe to my channel: https://www.youtube.com/jeffsuzuki1
- published: 20 Apr 2022
- views: 244
0:43
How the Moon orbits Earth
Using real data for the month of April 2020 I'm showing the exact rotations, tilts, inclin...
published: 17 Apr 2020
How the Moon orbits Earth
How the Moon orbits Earth
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- published: 17 Apr 2020
- views: 335093
Using real data for the month of April 2020 I'm showing the exact rotations, tilts, inclination, orbital velocity, sunlight angles & views of our Earth-Moon system. Earth-Moon distance is not to scale, but Earth and Moon *sizes* are (in the middle row).
FAQs/info
1. The green caps on the Moon are to indicate the position of the poles
2. The green circle around Earth (bottom middle, lol, middle Earth) is just a reference
3. The Moon is tilted 1.5° to its orbit around the Sun, so it has virtually no seasons
4. When the Moon is close to Earth it's pulled more strongly by Earth's gravity, so it goes faster, but when the Moon is far, it's pulled less and goes slower
5. Remember the SUPERMOON the other day? On April 7-8 have a look how there was a full Moon during a time when the Moon was closest to Earth... and you'll know why it looked bigger. A nice coincidence
6. Because of the 5.1° inclination and 1.5° axial tilt of the Moon, we actually see ~6.6° beneath and above the Moon's poles during it's orbit, which is why it looks like it wobbles up and down, from our point of view
Imagery from: NASA / Solar System Scope processing https://www.solarsystemscope.com/textures/ under CC BY 4.0
NASA ephemeris data: https://ssd.jpl.nasa.gov/horizons.cgi#top
0:12
How the Moon orbit - Motion of the Moon #shorts #moon #interstellar #space #animation
How the Moon orbit - Motion of the Moon #shorts #moon #interstellar #space #animation
Fr...
published: 03 May 2023
How the Moon orbit - Motion of the Moon #shorts #moon #interstellar #space #animation
How the Moon orbit - Motion of the Moon #shorts #moon #interstellar #space #animation
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- published: 03 May 2023
- views: 2800847
How the Moon orbit - Motion of the Moon #shorts #moon #interstellar #space #animation
From your astronaut’s viewpoint, you can see that the Moon is an average of 238,855 miles (384,399 km) from Earth, or about the space that could be occupied by 30 Earths. It travels around our planet once every 27.322 days in an elliptical orbit, an elongated circle. The Moon is tidally locked with Earth, which means that it spins on its axis exactly once each time it orbits our planet. Because of this, people on Earth only ever see one side of the Moon. We call this motion synchronous rotation.
The Moon’s orbit is tilted about 5 degrees compared to the plane of Earth’s orbit around the Sun. Because of this tilt, the Moon as seen from Earth’s perspective usually passes above or below the Sun when it passes between us and the Sun. The tilt of the Moon’s orbit prevents us from having monthly solar and lunar eclipses.
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3:20
Phases of moon explained using an orrery
As the moon rotates around the earth it travels through phases.
The alignment of the sun, ...
published: 03 Jun 2019
Phases of moon explained using an orrery
Phases of moon explained using an orrery
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- published: 03 Jun 2019
- views: 2883484
As the moon rotates around the earth it travels through phases.
The alignment of the sun, earth, and moon create the phases.
I use an orrery to explain the moon's alignment during,
new moon, waxing crescent, ist quarter, waxing gibbous, full moon, waning gibbous, last quarter, waning crescent, and back to new moon.
The sidereal period is 27.3 and the moon is measured against stars.
The synodic period is 29.5 days and the moon is measured against the sun.
If you enjoyed this video you may enjoy the Earth Science Course with an emphasis on Astronomy.
The course includes 13 videos along with a study guide and an answer key for each guide.
In addition there is a short enrichment activity for each video.
Link to the playlist here.
https://youtube.com/playlist?list=PLurjkZV1ykGaCbqkU_0z82I_40JinIbtl&si=lMBhAg7-Uj-QhgTu
You may also enjoy
Rotation and Revolution of the Earth with an Orrery
https://youtu.be/-iztiJz7SJQ
Phases of the moon with pictures.
https://moomoomath.com/phases-of-moon-explained-using-an-orrery/
Moon Phases Quiz
https://youtu.be/QMWkhB_vUrU
3:06
Moon 101 | National Geographic
What is the moon made of, and how did it form? Learn about the moon's violent origins, how...
published: 26 Jul 2018
Moon 101 | National Geographic
Moon 101 | National Geographic
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- published: 26 Jul 2018
- views: 5396613
What is the moon made of, and how did it form? Learn about the moon's violent origins, how its phases shaped the earliest calendars, and how humans first explored Earth's only natural satellite half a century ago.
➡ Subscribe: http://bit.ly/NatGeoSubscribe
About National Geographic:
National Geographic is the world's premium destination for science, exploration, and adventure. Through their world-class scientists, photographers, journalists, and filmmakers, Nat Geo gets you closer to the stories that matter and past the edge of what's possible.
Get More National Geographic:
Official Site: http://bit.ly/NatGeoOfficialSite
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Moon 101 | National Geographic
https://youtu.be/6AviDjR9mmo
National Geographic
https://www.youtube.com/natgeo
17:31
The Moon's Orbit and Eclipses
A look at the nature of the Moon's orbit around Earth, and how that results in the librati...
published: 26 Feb 2018
The Moon's Orbit and Eclipses
The Moon's Orbit and Eclipses
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- published: 26 Feb 2018
- views: 105407
A look at the nature of the Moon's orbit around Earth, and how that results in the libration of the Moon and the occasional solar and lunar eclipse.
-~-~~-~~~-~~-~-
Watch next: Solar Orbiter Discovers Surprising new Phenomenon in the Sun
https://www.youtube.com/watch?v=VOrl2QlPCMI
-~-~~-~~~-~~-~-
4:16
Moon Phases Demonstration
Emily Morgan, author of Next Time You See the Moon, takes you through the phases of the Mo...
published: 16 Sep 2014
Moon Phases Demonstration
Moon Phases Demonstration
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- published: 16 Sep 2014
- views: 4923799
Emily Morgan, author of Next Time You See the Moon, takes you through the phases of the Moon in a demonstration that will be easy to replicate in your own classroom.
http://www.nsta.org/store/product_detail.aspx?id=10.2505/9781938946332
http://www.nsta.org/nexttime-moon
0:15
The Moon doesn't orbit Earth's center. They orbit around a common center of mass, the barycenter.
published: 11 Oct 2022
The Moon doesn't orbit Earth's center. They orbit around a common center of mass, the barycenter.
The Moon doesn't orbit Earth's center. They orbit around a common center of mass, the barycenter.
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- published: 11 Oct 2022
- views: 344176
14:00
Why Spacecraft Are Using These Crazy Routes To The Moon - Weak Stability and Ballistic Capture.
For decades spacecraft would fly direct to the moon and then brake into lunar orbit, but t...
published: 19 Dec 2022
Why Spacecraft Are Using These Crazy Routes To The Moon - Weak Stability and Ballistic Capture.
Why Spacecraft Are Using These Crazy Routes To The Moon - Weak Stability and Ballistic Capture.
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- published: 19 Dec 2022
- views: 305064
For decades spacecraft would fly direct to the moon and then brake into lunar orbit, but these days most spacecraft take long circuitous routes, dancing on the edge of stability near the lagrange points of the sun-earth-moon system. These techniques save propellent at the expense of time and navigation complexity.
They use the theory of weak stability boundaries and ballistic capture in the 3 body problem, to make this possible, and it's an idea which was first discovered in the early 1990's and has now become the main route for modern spacecraft.
Some of the orbit visualizations use Universe Sandbox
https://universesandbox.com/
Follow me on Twitter for more updates:
https://twitter.com/DJSnM
I have a discord server where I regularly turn up:
https://discord.gg/zStmKbM
If you really like what I do you can support me directly through Patreon
https://www.patreon.com/scottmanley
2:55
Elita - Lunar Orbit
DYSANIA
https://oppo.sition.link/Dysania
Shop: https://elitaharkov.com
https://elitamusi...
published: 22 Mar 2023
Elita - Lunar Orbit
Elita - Lunar Orbit
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- published: 22 Mar 2023
- views: 16671
DYSANIA
https://oppo.sition.link/Dysania
Shop: https://elitaharkov.com
https://elitamusicworld.com/
Artwork by Nick Knight
Mixed by: Chris Perry
Mastered by: João Carvalho
Instagram: @yungelita @elitamusic @elitaemporium @elitaharkov2
Tiktok: @elitaharkov
10:01
The Moon Does Not Go Around the Earth
The Moon is our planet's sole natural satellite and nearest celestial body. The Moon orbit...
published: 26 Jan 2022
The Moon Does Not Go Around the Earth
The Moon Does Not Go Around the Earth
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- published: 26 Jan 2022
- views: 556163
The Moon is our planet's sole natural satellite and nearest celestial body. The Moon orbits the Earth and it takes about one month to complete the full cycle from New Moon to New Moon. But there's a common misconception that the Moon goes around the Earth. Which isn't true.
Why do we believe in this myth and why is it completely wrong? Let's take a look at the phases of the Moon and its rotation cycle. We'll see that the Moon is not going around the Earth - it is traveling along with the Earth - around the Sun.
#brightside
TIMESTAMPS
The Sun doesn't go around the Earth 00:00
Myths about the Moon 00:37
Sun-centered -Solar system 01:12
The Phases of Venus 02:40
Moon and Earth 05:19
Barycenter 07:32
Earthling 09:30
Animation is created by Bright Side.
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Check our Bright Side podcast on Spotify and leave a positive review! https://open.spotify.com/show/0hUkPxD34jRLrMrJux4VxV
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Lunar orbit
In astronomy, lunar orbit (also known as a Selenocentric orbit) refers to the orbit of an object around the Moon.
As used in the space program, this refers not to the orbit of the Moon about the Earth, but to orbits by various manned or unmanned spacecraft around the Moon. The altitude at apoapsis (point farthest from the surface) for a lunar orbit is known as apolune, apocynthion or aposelene, while the periapsis (point closest to the surface) is known as perilune, pericynthion or periselene.
Low Lunar orbit (LLO)—orbits below 100 kilometres (62 mi) altitude—are of particular interest in exploration of the moon, but suffer from gravitational perturbation effects that make most unstable, and leave only a few orbital inclinations possible for indefinite frozen orbits, useful for long-term stays in LLO.
Robotic spacecraft
The Soviet Union sent the first spacecraft to the vicinity of the Moon, the robotic vehicle Luna 1, on January 4, 1959. It passed within 6,000 kilometres (3,200 nmi; 3,700 mi) of the Moon's surface, but did not achieve lunar orbit.Luna 3, launched on October 4, 1959, was the first robotic spacecraft to complete a circumlunar free return trajectory, still not a lunar orbit, but a figure-8 trajectory which swung around the far side of the Moon and returned to the Earth. This craft provided the first pictures of the far side of the Lunar surface.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Lunar_orbit
10:51
Chapter 7: Group actions, symmetric group and Cayley’s theorem | Essence of Group Theory
Group action can be thought of as a homomorphism to a symmetric group, so apart from orbit...
published: 28 Jun 2020
Chapter 7: Group actions, symmetric group and Cayley’s theorem | Essence of Group Theory
Chapter 7: Group actions, symmetric group and Cayley’s theorem | Essence of Group Theory
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- published: 28 Jun 2020
- views: 31414
Group action can be thought of as a homomorphism to a symmetric group, so apart from orbit-stabiliser theorem, we can also use the isomorphism theorem to analyse any group action. It turns out that this correspondence between group action and homomorphism can be visualised rather easily. This correspondence is very important in group theory, but often neglected.
Symmetric group is also briefly mentioned here as a concept to facilitate the introduction of the above correspondence, but a more detailed analysis of the symmetric group would not be in this video series, because I don't think it is as intuitive as concepts discussed in the video series and therefore does not fit the theme of the series too well. However, I will do a video on Burnside's lemma and its interesting application, but it is not "Essence of Group Theory" anymore, because it is an application of the orbit-stabiliser theorem. I haven't mentioned in the video that I will also not do a video on matrix groups because it requires the knowledge of linear algebra, and again, the concepts discussed in the matrix groups will usually be algebraic.
The next few videos will be a summary of this video series with one very cool example that really covers all the concepts discussed in this video series; another video on the current epidemic explaining an alternative model to the SIR discussed on this channel before, and will be about a stochastic branching process; then the Burnside's lemma video. There might be some videos in between these, but I will definitely do all of these videos in some time in the future.
Cayley's theorem is named in honour of Arthur Cayley, a British (Cambridge) mathematician who is also known for a lot of mathematical results, like Cayley table, Cayley graph, Cayley's theorem and the famous Cayley-Hamilton theorem in linear algebra. However, even though it is a motivation for the study of symmetric groups, you might not see Cayley's theorem too often in more advanced studies of group theory. It mainly acts as a direct application of the correspondence discussed in this video.
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
SUBSCRIBE and see you in the next video!
If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe!
#mathemaniac #math #grouptheory #groupaction #homomorphism #Cayley
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23:42
Group Theory, lecture 5.1: Group actions
We discuss group actions
published: 15 Nov 2020
Group Theory, lecture 5.1: Group actions
Group Theory, lecture 5.1: Group actions
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- published: 15 Nov 2020
- views: 7398
We discuss group actions
6:07
Chapter 1: Symmetries, Groups and Actions | Essence of Group Theory
Start of a video series on intuitions of group theory. Groups are often introduced as a ki...
published: 06 Feb 2020
Chapter 1: Symmetries, Groups and Actions | Essence of Group Theory
Chapter 1: Symmetries, Groups and Actions | Essence of Group Theory
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- published: 06 Feb 2020
- views: 112388
Start of a video series on intuitions of group theory. Groups are often introduced as a kind of abstract algebraic object right from the start, which is not good for developing intuitions for first-time learners. This video series hopes to help you develop intuitions, which are useful in understanding group theory.
In particular, this video is going to be about thinking groups as symmetries (or isometries to be precise) because they are much more visualisable, and that symmetries of an object do form a group using the abstract definition of the group that is usually given.
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
SUBSCRIBE and see you in the next video!
If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe!
#mathemaniac #math #grouptheory #groups #intuition
Social media:
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For my contact email, check my About page on a PC.
See you next time!
48:59
Group Theory: Lecture 15/30 - Introduction to Group Actions
This video series is not endorsed by the University of Cambridge. These videos are primari...
published: 26 Jun 2023
Group Theory: Lecture 15/30 - Introduction to Group Actions
Group Theory: Lecture 15/30 - Introduction to Group Actions
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- published: 26 Jun 2023
- views: 858
This video series is not endorsed by the University of Cambridge. These videos are primarily inspired from Dexter Chua's lecture notes, which can be found here:
https://dec41.user.srcf.net/notes/IA_M/groups.pdf
Additionally, problem sets for this video series can be found here:
https://dec41.user.srcf.net/notes/IA_M/groups_eg.pdf
24:53
Lecture 33 - Group actions
published: 06 May 2019
Lecture 33 - Group actions
12:27
Chapter 2: Orbit-Stabiliser Theorem | Essence of Group Theory
An intuitive explanation of the Orbit-Stabilis(z)er theorem (in the finite case). It emerg...
published: 17 Feb 2020
Chapter 2: Orbit-Stabiliser Theorem | Essence of Group Theory
Chapter 2: Orbit-Stabiliser Theorem | Essence of Group Theory
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- published: 17 Feb 2020
- views: 66226
An intuitive explanation of the Orbit-Stabilis(z)er theorem (in the finite case). It emerges very apparently when counting the total number of symmetries in some tricky but easy way. This video series continues to develop your intuition towards some fundamental concepts and results in Group theory.
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
SUBSCRIBE and see you in the next video!
#mathemaniac #math #grouptheory #groups #orbitstabiliser #orbitstabilizer
20:19
GT15. Group Actions
Abstract Algebra: Group actions are defined as a formal mechanism that describes symmetri...
published: 23 Jan 2012
GT15. Group Actions
GT15. Group Actions
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- published: 23 Jan 2012
- views: 45082
Abstract Algebra: Group actions are defined as a formal mechanism that describes symmetries of a set X. A given group action defines an equivalence relation, which in turn yields a partition of X into orbits. Orbits are also described as cosets of the group.
U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theory Master list at http://mathdoctorbob.org/UReddit.html
20:53
What is a Group Action? : A Group as a Category and The Skeleton Operation ☠
This week I try to take a more Categorical approach to answering and expanding upon the qu...
published: 09 Jul 2020
What is a Group Action? : A Group as a Category and The Skeleton Operation ☠
What is a Group Action? : A Group as a Category and The Skeleton Operation ☠
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- published: 09 Jul 2020
- views: 3870
This week I try to take a more Categorical approach to answering and expanding upon the question of "what is a group action". Along the way I'll go over thinking about a group as a category and eventually hit on the skeleton operation on a category and use it to present an example of the categorification of the Orbit-Stabilizer theorem. Here are some videos that are "pre-reqs", that is, they introduce some topics in a bit more detail than I do here.
What are groups: https://youtu.be/uraPtd0yCI4
What are categories: https://youtu.be/ZaLB0MF2TMQ
Also, Here is the Category Theory Book that inspired this video: https://amzn.to/317hxMc
CORRECTIONS:
1. When introducing Groups, while glossing over the group axioms I forget to mention that a group, G, must be closed under the binary operation. That is for any a,b in G, ab must also be in G.
This video can be broken up into the following sections.
00:00 Intro
I once again fail to say "Hi I'm Nathan and Welcome to my YouTube Channel" but I still introduce the goal of the video lol.
00:32 What is a Group Action?
I briefly revisit the idea of what a group is before "complicating" it into the object that we'll spend most of the time interacting with, a group action. There are many different types of group actions but we will focus on 2 examples.
03:46 Example 1
The first of 2 group action examples. We look at probably the most accessible example of a group action, a group acting on itself with the action operating the same way as the group operation.
05:05 Example 2
In the second of 2 group action examples we look at another small but more complicated example of a group acting on itself, here we us the conjugate action and we'll continue to look at this example throughout the video.
After the second example, the video begins to bring in a lot more ideas from category theory and we'll spend a lot of time looking at categories and groups and how the two can correspond to one another.
09:30 A Group as a Category
Here I will begin translating the idea of what we have talked about with groups and group actions into a more category theoretic context. We won't dive too deep into the Category of G-Sets, but we do define what G-Sets are and how they can be described as functors.
11:21 The Translation Groupoid of A Group
Next we 'zoom in' on what our G-Set functor does to the categorical group and arrive at the directed graphs that we looked at previously by looking at the Translation Groupoid.
13:27 The Skeleton Operation
The last Category theoretic tool we will need for the categorification of the orbit-stabilizer theorem, the skeleton operator on a category fuses together identical (or isomorphic) objects, which allows us to see the information in the Translation Groupoid category more clearly.
15:50 The Orbit-Stabilizer Theorem
Here we introduce (not prove...) the theorem and then talk through how the skeleton operation on the translation groupoid generates a very nice picture of the theorem in a Category Theoretic context.
17:35 Another way of Thinking about the Skeleton Category
And lastly I pull away from the abstract nonsense of the skeleton construction to quickly walk through another way to interpret each of the orbits in the skeleton category that can help when trying to determine the size of other symmetry/dihedral groups.
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4:37
Group Actions: Stabilizers
Introducing the stabilizer subgroup. Setup for Sylow's Theorem.
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published: 20 Apr 2022
Group Actions: Stabilizers
Group Actions: Stabilizers
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- published: 20 Apr 2022
- views: 244
Introducing the stabilizer subgroup. Setup for Sylow's Theorem.
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