-
Poles of astronomical bodies | Wikipedia audio article
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Poles_of_astronomical_bodies
00:00:23 1 Geographic poles
00:03:40 2 Magnetic poles
00:04:29 3 Orbital pole
00:04:58 4 Near, far, leading and trailing poles
00:06:52 5 See also
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while ...
published: 28 Dec 2018
-
Iceberg of Celestial Bodies Explained
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published: 23 Dec 2022
-
Circumpolar Bodies Celestial Navigation - Theory
This video explains the theory behind circumpolar bodies using the rational horizon diagram for the mariner's understanding. Future videos will also explain the calculations involved.
Student mariners should also watch the Playlist on Celestial Navigation (attached at the end of this video) to enhance their knowledge of the topic.
published: 13 Sep 2019
-
What If We Nuked Mars? #Shorts
Elon Musk wants to nuke Mars. What are the consequences? Without nukes, life on Mars might be like this: You'd live in giant glass domes, and grow small portions of food inside. Watch the full episode here: https://youtu.be/bBZmO6dcmnY
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published: 25 Nov 2021
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published: 17 Jan 2023
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What Are Celestial Bodies? | Black Holes, Nebulas, Satellites and More!
Celestial Bodies, Astronomical Objects, Celestial objects. Lots of names, and lots to learn!
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published: 09 Mar 2023
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Class 6 Geography Chapter 1 | Celestial Bodies - The Earth in the Solar System
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✔️ Class:6th
✔️ Subject: Geography
✔️ Chapter: The Earth in the Solar System (Chapter 1)
✔️ Topic Name: Explanation of The Celestial Bodies, Phases of the Moon
===============================================
📢 🔥 Available ...
published: 25 Dec 2019
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Formation of universe and celestial bodies
Formation of universe and other celestial bodies
Celestial Bodies & the Universe
All astronomical objects in the sky, such as the Sun, the Moon and the stars, are collectively known as celestial bodies. They are separated from each other by immense regions of emptiness called space. The space, along with the celestial bodies, make up what we call the Universe. The universe, in effect, is mostly empty space.
Measuring distances in space
The size of the universe is so beyond human comprehension that the common units of distance, like the kilometer, make little utility sense. Instead, distances in space are measured using the speed of light.
The speed of light is the greatest speed that can be attained by any material object in the universe, and is about 300000km/s. This is equivalent to...
published: 04 Nov 2015
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What If You Fell Into the Deepest Hole on Earth? #Shorts
For 20 years, Russian scientists and engineers drilled deeper and deeper, hoping to uncover whatever mysteries the hole may hold. This has garnered / Earning it the ominous nickname of "The Well to Hell." So, what would happen if you fell in? Watch the full episode here: https://youtu.be/ZeXv1mBa5oc
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published: 08 Jun 2022
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The Bizarre Behavior of Rotating Bodies
Spinning objects have strange instabilities known as The Dzhanibekov Effect or Tennis Racket Theorem - this video offers an intuitive explanation.
Part of this video was sponsored by LastPass, click here to find out more: https://ve42.co/LP
References:
Prof. Terry Tao's Math Overflow Explanation: https://ve42.co/Tao
The Twisting Tennis Racket
Ashbaugh, M.S., Chicone, C.C. & Cushman, R.H. J Dyn Diff Equat (1991) 3: 67. https://doi.org/10.1007/BF01049489
Janibekov’s effect and the laws of mechanics
Petrov, A.G. & Volodin, S.E. Dokl. Phys. (2013) 58: 349. https://doi.org/10.1134/S1028335813080041
Tumbling Asteroids
Prave et al. https://doi.org/10.1016/j.icarus.2004.07.021
The Exact Computation of the Free Rigid Body Motion and Its Use in Splitting Methods
SIAM J. Sci. Comput., 30(4), 208...
published: 19 Sep 2019
7:05
Poles of astronomical bodies | Wikipedia audio article
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Poles_of_astronomical_bodies
00:00:23 1 Geographic poles
00:03:40 2 Magne...
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Poles_of_astronomical_bodies
00:00:23 1 Geographic poles
00:03:40 2 Magnetic poles
00:04:29 3 Orbital pole
00:04:58 4 Near, far, leading and trailing poles
00:06:52 5 See also
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.9332040693620841
Voice name: en-US-Wavenet-D
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
The poles of astronomical bodies are determined based on their axis of rotation in relation to the celestial poles of the celestial sphere. Astronomical bodies include stars, planets, dwarf planets and small Solar System bodies such as comets and minor planets (i.e. asteroids), as well as natural satellites and minor-planet moons.
https://wn.com/Poles_Of_Astronomical_Bodies_|_Wikipedia_Audio_Article
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Poles_of_astronomical_bodies
00:00:23 1 Geographic poles
00:03:40 2 Magnetic poles
00:04:29 3 Orbital pole
00:04:58 4 Near, far, leading and trailing poles
00:06:52 5 See also
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.9332040693620841
Voice name: en-US-Wavenet-D
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
The poles of astronomical bodies are determined based on their axis of rotation in relation to the celestial poles of the celestial sphere. Astronomical bodies include stars, planets, dwarf planets and small Solar System bodies such as comets and minor planets (i.e. asteroids), as well as natural satellites and minor-planet moons.
- published: 28 Dec 2018
- views: 7
12:24
Iceberg of Celestial Bodies Explained
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- published: 23 Dec 2022
- views: 1440796
8:52
Circumpolar Bodies Celestial Navigation - Theory
This video explains the theory behind circumpolar bodies using the rational horizon diagram for the mariner's understanding. Future videos will also explain the...
This video explains the theory behind circumpolar bodies using the rational horizon diagram for the mariner's understanding. Future videos will also explain the calculations involved.
Student mariners should also watch the Playlist on Celestial Navigation (attached at the end of this video) to enhance their knowledge of the topic.
https://wn.com/Circumpolar_Bodies_Celestial_Navigation_Theory
This video explains the theory behind circumpolar bodies using the rational horizon diagram for the mariner's understanding. Future videos will also explain the calculations involved.
Student mariners should also watch the Playlist on Celestial Navigation (attached at the end of this video) to enhance their knowledge of the topic.
- published: 13 Sep 2019
- views: 11703
1:00
What If We Nuked Mars? #Shorts
Elon Musk wants to nuke Mars. What are the consequences? Without nukes, life on Mars might be like this: You'd live in giant glass domes, and grow small portion...
Elon Musk wants to nuke Mars. What are the consequences? Without nukes, life on Mars might be like this: You'd live in giant glass domes, and grow small portions of food inside. Watch the full episode here: https://youtu.be/bBZmO6dcmnY
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#Shorts #Whatif #Mars #SpaceX #ElonMusk
https://wn.com/What_If_We_Nuked_Mars_Shorts
Elon Musk wants to nuke Mars. What are the consequences? Without nukes, life on Mars might be like this: You'd live in giant glass domes, and grow small portions of food inside. Watch the full episode here: https://youtu.be/bBZmO6dcmnY
Produced with love by Underknown in Toronto: https://underknown.com
Contact us at https://underknown.com/contact/
#Shorts #Whatif #Mars #SpaceX #ElonMusk
- published: 25 Nov 2021
- views: 16161038
0:18
🌟 What Are Celestial Bodies? 🌟 #Shorts #PhysicsWallah
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- published: 17 Jan 2023
- views: 830
1:04:12
What Are Celestial Bodies? | Black Holes, Nebulas, Satellites and More!
Celestial Bodies, Astronomical Objects, Celestial objects. Lots of names, and lots to learn!
Subscribe to KLT: https://www.youtube.com/channel/UC7EFWpvc1wYuUw...
Celestial Bodies, Astronomical Objects, Celestial objects. Lots of names, and lots to learn!
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Celestial Bodies, Astronomical Objects, Celestial objects. Lots of names, and lots to learn!
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- published: 09 Mar 2023
- views: 550961
13:09
Class 6 Geography Chapter 1 | Celestial Bodies - The Earth in the Solar System
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✔️ Subject: Geography
✔️ Chapter: The Earth in the Solar System (Chapter 1)
✔️ Topic Name: Explanation of The Celestial Bodies, Phases of the Moon
===============================================
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- published: 25 Dec 2019
- views: 279517
3:37
Formation of universe and celestial bodies
Formation of universe and other celestial bodies
Celestial Bodies & the Universe
All astronomical objects in the sky, such as the Sun, the Moon and the stars,...
Formation of universe and other celestial bodies
Celestial Bodies & the Universe
All astronomical objects in the sky, such as the Sun, the Moon and the stars, are collectively known as celestial bodies. They are separated from each other by immense regions of emptiness called space. The space, along with the celestial bodies, make up what we call the Universe. The universe, in effect, is mostly empty space.
Measuring distances in space
The size of the universe is so beyond human comprehension that the common units of distance, like the kilometer, make little utility sense. Instead, distances in space are measured using the speed of light.
The speed of light is the greatest speed that can be attained by any material object in the universe, and is about 300000km/s. This is equivalent to light being able to circle the Earth seven times in one second! Accordingly, light-second (light-sec), a unit of distance, is defined as
1 light-sec=300000km
The distance that a light beam can travel in a year is known as a light-year (ly). Since there are 86400 seconds in a day, and there are 365 days in a year, a light year equals , or 9.46 trillion kilometers! Thus,
Celestial Bodies
Rotation and Revolution
rotation.gif
Fig 1: Rotation. (Adapted from: Purdue University, Theory of Tropics)
A celestial body spins around an imaginary line through itself called an axis. This spinning motion is called rotation (see Fig. 1). The axis of rotation passes into and out of the body at two points known as the north (N) and south (S) poles.
A celestial body may also move around another in a closed path called an orbit. This motion is referred to as revolution. Orbits may be oval paths or circular paths.
The orbital revolution of a celestial body around another is the result of the pull of the gravitational force that one celestial body exerts on another. The larger a celestial body, the larger will be its gravitational force. Just as you can make a stone tied to a string revolve around your hand, a large celestial body can make a smaller body revolve around it in an orbit.
Stars
binary-stars-sirius-a-sirius-b.jpg
Fig 2: The binary stars Sirius A (white) and Sirius B (blue). (Source: HEIC, Sirius A)
Stars are huge balls of burning gases, mostly hydrogen and helium (see Fig. 2). However, they look like tiny points of twinkling lights in the night sky because they are extremely far from us. In fact, only a very small percentage of the actual number of stars is visible to the naked eye at night. Sagan (Cosmos, ch. VIII) vividly states that the total number of stars in the universe exceeds the total of all the grains of sand in all the beaches of our world.
Stars are the only celestial bodies which generate heat and light. Our Sun is actually an average-sized star. It is the nearest star, and appears so big because it is only about 500 light-sec from Earth (which means that light from the Sun takes about 500 seconds, or about 8½ minutes, to reach us).
Some stars, like our Sun, occur singly. Stars occurring in pairs, orbiting around each other, are called binary stars. In other cases, there are three or more stars grouped together.
A good example of a binary star system is the Sirius system comprising Sirius A and Sirius B (Fig. 2). Sirius A, visible to the naked eye, is the brightest star in the night sky. It is also known as the Dog Star. It is about twice the size of our Sun. Its companion, Sirius B, is much smaller.
The closest star to us (not counting the Sun) is Proxima Centauri, which is 4.3 light-years away. This implies that if, hypothetically speaking, Proxima Centauri suddenly increases its brightness, we will know about it only after 4.3 years—the time taken by light from Proxima to travel across space and reach us. Proxima actually belongs to the triple-star system called the Alpha Centauri System. Two stars in the system, Alpha Centauri A and Alpha Centauri B, are comparable in size to our Sun, while Proxima Centauri is much smaller.
The stars are always present in the sky, but can be seen only at night when the Sun is not around to hide them with its brightness. Although the entire night sky rotates from east to west, the positions of the stars in the sky, in relation to each other, appear “fixed”. Stars do move relative to each other, but their immense distances, from us and from each other, give us the impression of their positions being fixed over the normal course of human history. Such positional shifts can be detected only when comparing the night skies over thousands of years.
https://wn.com/Formation_Of_Universe_And_Celestial_Bodies
Formation of universe and other celestial bodies
Celestial Bodies & the Universe
All astronomical objects in the sky, such as the Sun, the Moon and the stars, are collectively known as celestial bodies. They are separated from each other by immense regions of emptiness called space. The space, along with the celestial bodies, make up what we call the Universe. The universe, in effect, is mostly empty space.
Measuring distances in space
The size of the universe is so beyond human comprehension that the common units of distance, like the kilometer, make little utility sense. Instead, distances in space are measured using the speed of light.
The speed of light is the greatest speed that can be attained by any material object in the universe, and is about 300000km/s. This is equivalent to light being able to circle the Earth seven times in one second! Accordingly, light-second (light-sec), a unit of distance, is defined as
1 light-sec=300000km
The distance that a light beam can travel in a year is known as a light-year (ly). Since there are 86400 seconds in a day, and there are 365 days in a year, a light year equals , or 9.46 trillion kilometers! Thus,
Celestial Bodies
Rotation and Revolution
rotation.gif
Fig 1: Rotation. (Adapted from: Purdue University, Theory of Tropics)
A celestial body spins around an imaginary line through itself called an axis. This spinning motion is called rotation (see Fig. 1). The axis of rotation passes into and out of the body at two points known as the north (N) and south (S) poles.
A celestial body may also move around another in a closed path called an orbit. This motion is referred to as revolution. Orbits may be oval paths or circular paths.
The orbital revolution of a celestial body around another is the result of the pull of the gravitational force that one celestial body exerts on another. The larger a celestial body, the larger will be its gravitational force. Just as you can make a stone tied to a string revolve around your hand, a large celestial body can make a smaller body revolve around it in an orbit.
Stars
binary-stars-sirius-a-sirius-b.jpg
Fig 2: The binary stars Sirius A (white) and Sirius B (blue). (Source: HEIC, Sirius A)
Stars are huge balls of burning gases, mostly hydrogen and helium (see Fig. 2). However, they look like tiny points of twinkling lights in the night sky because they are extremely far from us. In fact, only a very small percentage of the actual number of stars is visible to the naked eye at night. Sagan (Cosmos, ch. VIII) vividly states that the total number of stars in the universe exceeds the total of all the grains of sand in all the beaches of our world.
Stars are the only celestial bodies which generate heat and light. Our Sun is actually an average-sized star. It is the nearest star, and appears so big because it is only about 500 light-sec from Earth (which means that light from the Sun takes about 500 seconds, or about 8½ minutes, to reach us).
Some stars, like our Sun, occur singly. Stars occurring in pairs, orbiting around each other, are called binary stars. In other cases, there are three or more stars grouped together.
A good example of a binary star system is the Sirius system comprising Sirius A and Sirius B (Fig. 2). Sirius A, visible to the naked eye, is the brightest star in the night sky. It is also known as the Dog Star. It is about twice the size of our Sun. Its companion, Sirius B, is much smaller.
The closest star to us (not counting the Sun) is Proxima Centauri, which is 4.3 light-years away. This implies that if, hypothetically speaking, Proxima Centauri suddenly increases its brightness, we will know about it only after 4.3 years—the time taken by light from Proxima to travel across space and reach us. Proxima actually belongs to the triple-star system called the Alpha Centauri System. Two stars in the system, Alpha Centauri A and Alpha Centauri B, are comparable in size to our Sun, while Proxima Centauri is much smaller.
The stars are always present in the sky, but can be seen only at night when the Sun is not around to hide them with its brightness. Although the entire night sky rotates from east to west, the positions of the stars in the sky, in relation to each other, appear “fixed”. Stars do move relative to each other, but their immense distances, from us and from each other, give us the impression of their positions being fixed over the normal course of human history. Such positional shifts can be detected only when comparing the night skies over thousands of years.
- published: 04 Nov 2015
- views: 36275
0:45
What If You Fell Into the Deepest Hole on Earth? #Shorts
For 20 years, Russian scientists and engineers drilled deeper and deeper, hoping to uncover whatever mysteries the hole may hold. This has garnered / Earning it...
For 20 years, Russian scientists and engineers drilled deeper and deeper, hoping to uncover whatever mysteries the hole may hold. This has garnered / Earning it the ominous nickname of "The Well to Hell." So, what would happen if you fell in? Watch the full episode here: https://youtu.be/ZeXv1mBa5oc
Questions or concerns? Contact us at https://underknown.com/contact/
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Watch more what-if scenarios:
Planet Earth: http://bit.ly/YT-what-if-Earth
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Produced with love by Underknown in Toronto: https://underknown.com
Contact us at https://underknown.com/contact/
https://wn.com/What_If_You_Fell_Into_The_Deepest_Hole_On_Earth_Shorts
For 20 years, Russian scientists and engineers drilled deeper and deeper, hoping to uncover whatever mysteries the hole may hold. This has garnered / Earning it the ominous nickname of "The Well to Hell." So, what would happen if you fell in? Watch the full episode here: https://youtu.be/ZeXv1mBa5oc
Questions or concerns? Contact us at https://underknown.com/contact/
Get our 100 best episodes in one mind-blowing book: http://bit.ly/ytc-the-what-if-100-book
Join this channel to get access to perks:
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Check out our other channels:
How to Survive: https://bit.ly/how-to-survive-show
Aperture: https://bit.ly/aperture-show
Crazy Creatures: https://bit.ly/crazy-creatures-show
Your Body On: https://bit.ly/your-body-on-show
Origins of Food: https://bit.ly/origins-of-food
Versus: https://bit.ly/versus-show
WTF Did I Just Watch: https://bit.ly/wtf-did-i-just-watch
Watch more what-if scenarios:
Planet Earth: http://bit.ly/YT-what-if-Earth
The Cosmos: http://bit.ly/YT-what-if-Cosmos
Technology: http://bit.ly/YT-what-if-Technology
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What If in Mandarin: http://bit.ly/YT-Chinese-what-if
Podcast: http://bit.ly/yt-what-if-show-podcast
What If is a mini-documentary web series that takes you on an epic journey through hypothetical worlds and possibilities. Join us on an imaginary adventure through time, space and chance while we (hopefully) boil down complex subjects in a fun and entertaining way.
Produced with love by Underknown in Toronto: https://underknown.com
Contact us at https://underknown.com/contact/
- published: 08 Jun 2022
- views: 806202
14:49
The Bizarre Behavior of Rotating Bodies
Spinning objects have strange instabilities known as The Dzhanibekov Effect or Tennis Racket Theorem - this video offers an intuitive explanation.
Part of this ...
Spinning objects have strange instabilities known as The Dzhanibekov Effect or Tennis Racket Theorem - this video offers an intuitive explanation.
Part of this video was sponsored by LastPass, click here to find out more: https://ve42.co/LP
References:
Prof. Terry Tao's Math Overflow Explanation: https://ve42.co/Tao
The Twisting Tennis Racket
Ashbaugh, M.S., Chicone, C.C. & Cushman, R.H. J Dyn Diff Equat (1991) 3: 67. https://doi.org/10.1007/BF01049489
Janibekov’s effect and the laws of mechanics
Petrov, A.G. & Volodin, S.E. Dokl. Phys. (2013) 58: 349. https://doi.org/10.1134/S1028335813080041
Tumbling Asteroids
Prave et al. https://doi.org/10.1016/j.icarus.2004.07.021
The Exact Computation of the Free Rigid Body Motion and Its Use in Splitting Methods
SIAM J. Sci. Comput., 30(4), 2084–2112
E. Celledoni, F. Fassò, N. Säfström, and A. Zanna
https://doi.org/10.1137/070704393
Animations by Ivy Tello and Isaac Frame
Special thanks to people who discussed this video with me:
Astronaut Don Pettit
Henry Reich of MinutePhysics
Grant Sanderson of 3blue1brown
Vert Dider (Russian YouTube channel)
Below is a further discussion by Henry Reich that I think helps summarize why axes 1 and 3 are generally stable while axis 2 is not:
In general, you might imagine that because the object can rotate in a bunch of different directions, the components of energy and momentum could be free to change while keeping the total momentum constant.
However, in the case of axis 1, the kinetic energy is the highest possible for a given angular momentum, and in the case of axis 3, the kinetic energy is the lowest possible for a given angular momentum (which can be easily shown from conservation of energy and momentum equations, and is also fairly intuitive from the fact that kinetic energy is proportional to velocity squared, while momentum is proportional to velocity - so in the case of axis 1, the smaller masses will have to be spinning faster for a given momentum, and will thus have more energy, and vice versa for axis 3 where all the masses are spinning: the energy will be lowest). In fact, this is a strict inequality - if the energy is highest possible, there are no other possible combinations of momenta other than L2=L3=0, and vice versa for if the energy is the lowest possible.
Because of this, in the case of axis 1 the energy is so high that there simply aren't any other possible combinations of angular momentum components L1, L2 and L3 - the object would have to lose energy in order to spin differently. And in the case of axis 3, the energy is so low that there likewise is no way for the object to be rotating other than purely around axis 3 - it would have to gain energy. However, there's no such constraint for axis 2, since the energy is somewhere in between the min and max possible. This, together with the centrifugal effects, means that the components of momentum DO change.
https://wn.com/The_Bizarre_Behavior_Of_Rotating_Bodies
Spinning objects have strange instabilities known as The Dzhanibekov Effect or Tennis Racket Theorem - this video offers an intuitive explanation.
Part of this video was sponsored by LastPass, click here to find out more: https://ve42.co/LP
References:
Prof. Terry Tao's Math Overflow Explanation: https://ve42.co/Tao
The Twisting Tennis Racket
Ashbaugh, M.S., Chicone, C.C. & Cushman, R.H. J Dyn Diff Equat (1991) 3: 67. https://doi.org/10.1007/BF01049489
Janibekov’s effect and the laws of mechanics
Petrov, A.G. & Volodin, S.E. Dokl. Phys. (2013) 58: 349. https://doi.org/10.1134/S1028335813080041
Tumbling Asteroids
Prave et al. https://doi.org/10.1016/j.icarus.2004.07.021
The Exact Computation of the Free Rigid Body Motion and Its Use in Splitting Methods
SIAM J. Sci. Comput., 30(4), 2084–2112
E. Celledoni, F. Fassò, N. Säfström, and A. Zanna
https://doi.org/10.1137/070704393
Animations by Ivy Tello and Isaac Frame
Special thanks to people who discussed this video with me:
Astronaut Don Pettit
Henry Reich of MinutePhysics
Grant Sanderson of 3blue1brown
Vert Dider (Russian YouTube channel)
Below is a further discussion by Henry Reich that I think helps summarize why axes 1 and 3 are generally stable while axis 2 is not:
In general, you might imagine that because the object can rotate in a bunch of different directions, the components of energy and momentum could be free to change while keeping the total momentum constant.
However, in the case of axis 1, the kinetic energy is the highest possible for a given angular momentum, and in the case of axis 3, the kinetic energy is the lowest possible for a given angular momentum (which can be easily shown from conservation of energy and momentum equations, and is also fairly intuitive from the fact that kinetic energy is proportional to velocity squared, while momentum is proportional to velocity - so in the case of axis 1, the smaller masses will have to be spinning faster for a given momentum, and will thus have more energy, and vice versa for axis 3 where all the masses are spinning: the energy will be lowest). In fact, this is a strict inequality - if the energy is highest possible, there are no other possible combinations of momenta other than L2=L3=0, and vice versa for if the energy is the lowest possible.
Because of this, in the case of axis 1 the energy is so high that there simply aren't any other possible combinations of angular momentum components L1, L2 and L3 - the object would have to lose energy in order to spin differently. And in the case of axis 3, the energy is so low that there likewise is no way for the object to be rotating other than purely around axis 3 - it would have to gain energy. However, there's no such constraint for axis 2, since the energy is somewhere in between the min and max possible. This, together with the centrifugal effects, means that the components of momentum DO change.
- published: 19 Sep 2019
- views: 13301517