Category Archives: Sun

Astronomy, NASA, Parker Solar Probe, Space Travel, Sun

Parker Solar Probe Perihelia data

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Dr. Sten Odenwald

NASA/HEAT

Artistic rendering of the Parker encounter. (Credit: ASA/Johns Hopkins APL/Steve Gribben)

Here is a handy table that summarizes the circumstances for the Parker Solar Probe perihelia since 2018. Nothing fancy – just a one-stop-shop for those of you who want a convenient summary of all of the encounters, rather than having to scour the internet to find them.

Surface = center – 0.6957

Methodology. 

For those of you who are interested in how I put this table together, here are the 14 steps I used.

1) Found perihelion dates from the PSP Timeline at

https://www.parkersolarprobe.jhuapl.edu/The-Mission/index.php#Timeline

2) Entered the perihelion date into the Spacecraft Tracker

https://psp-gateway.jhuapl.edu/website/Tools/SpacecraftTracker

3) At bottom of the web page, selected ‘Get Data (csv)’ and saved the .csv file as OrbitN.xls Excel Workbook file.  The columns give: A) UT date and time; B-D the x,y,z coordinates of the spacecraft in kilometers.

4) Computed the distance to the sun’s center using  R = (x2+y2+z2)1/2 in 5th column.

5) Plotted R

6) Found date, time and R for the minimum distance shown with the star in the above plot.

7) Found the indicated sample number (712) in the file

8) Entered this information in the above perihelia table.

9) Returned to the PSP portal page at

https://psp-gateway.jhuapl.edu/

10) At the bottom of the page, selected ‘Instrument Data Plots’. Data is not yet available for dates after June 2024, so the next example is for March 30, 2024 Orbit 19. Enter this date in the input bar. The following plot will appear. Data on the ambient density will be in the top plot. If it is missing, click on the ‘Next’ or ‘Previous’ bar to call up the next data in the time series.

11)  Clicking on ‘Next’ brought the following data panel

12) This shows the proton density in the top panel. The valid data starts at the far-right. The data is in logarithmic units. The data appears between Log(100) = 2.0 and Log(1000) = 3.0 ,so estimate that it is at Log (D) = 2.5 so that the density D = 316 protons/cm3. Enter this number rounded to 300 in the above table for Orbit 19. The actual date for the measurement is indicated in the parenthesis. The most reliable densities occur for measurements made close to the date of the perihelion, example, Orbits 1, 2 and 4.

13) The ambient spacecraft temperature on the heat shield is calculated from the formula

Where L is the solar luminosity  3.86×1026 Watts, R is the distance to the sun in meters, and ‘sigma’ is the Stefan-Boltzmann Constant  5.67 x 10-8. Solving for the temperature and evaluating the constants we get

14) For Orbit 22 at a distance of R = 6.863 million km, we get T = 1841 kelvins or  T = 1841.8-273.15 = 1569o Celsius, which is entered in the table column 6.

Astronomy, Physics, Sun

How much energy does the Sun produce in one hour?

This image was taken from the International Space Station and displays the most important feature of the sun for life on Earth: Its light and heat!

The Sun is a spectral type G2 V dwarf star that emits 3.8 x 1033 ergs/sec or 3.8 x 1026 watts of electromagnetic power from gamma ray to radio wavelengths, with most of the energy emitted in the visible light spectrum between 400 nanometers and 800 nanometers. This is illustrated by the spectrum provided by Nick84 [CC BY-SA 3.0(link is external)], via Wikimedia Commons.

This is the spectrum seen at Earth’s surface where molecules of water vapor and carbon dioxide obscure some of the radiation to form the various dips in solar intensity. The common measure of solar brightness is called Irradiance. It represents the amount of energy (watts) that pass through a 1-meter2 surface facing the sun, and measured over a 1 nanometer bandwidth. Earth is located 150 million km from the sun, so if you surround the sun with a spherical surface with this radius, the surface area is A = 4piD2 or 2,8×1023 meters2. If we divide the solar luminosity by A we get 3.8×1026 watts/2.8×1023 m2 = 1,344 watts/m2 at the top of Earth’s atmosphere. Most of this is emitted in the spectrum between 300 to 900 nm for a 600 nm bandwidth, so the average irradiance over this spectral window is 1,344/600nm = 2.2 watts/m2/nm., which more or less matches the vertical axis of the above plot.

In one hour, or 3600 seconds, the sun produces 3.8×1026 joules/sec x 3600 sec = 1.4 x 1030 Joules of energy or 3.8 x 1023 kilowatt-hours.

Since E = mc2, and c = 3×108 m/s, in 1 hour the sun looses (1.4 x 1030 ergs)/(9 x 1016) = 1.5 x 1013 kilograms or 15 billion metric tons of mass each hour. It’s been doing this for about 4.5 billion years! So its mass loss over this time (3.9×1013 hours) = 5.9×1026 kg . But the sun’s mass is 2×1030 kg, so it has only lost about 0.0003 or 0.05% of its mass so far.

Astronomy, Planets, Sun

Has the loss of mass by the Sun over the last 4 billion years been enough to affect planetary orbits?

Fron the ISS ,our sun is a dazzling star (Credit: NASA/ISS). The luminosity of the Sun is 200 trillion trillion watts or 2 x 10^33 ergs per second. From Einstein’s famous equation, E = mc^2, and using c = 3 x 10^10 centimeters/sec, the Sun’s luminosity is equal to a loss of mass from the fusion cycle of about 2 x 10^12 grams/second. Over one year this is 7 x 10^19 grams, and over the entire life of the Sun to date is about 3.1 x 10^29 grams. The mass of the Sun is 4 x 10^33 grams so this loss equals 0.008 percent of its current mass. The mass of Jupiter is about 0.1 percent of the Sun’s current mass, so over the Sun’s entire lifetime to date, it has lost barely 0.08 percent of Jupiter’s mass, or about the mass of the Earth.

We can estimate how much this mass loss would have changed the orbit of the Earth by approximating the orbital dynamics as the balance between kinetic and gravitational potential energy or 1/2 mV^2 = GMm/R where m = mass of Earth, and M = mass of Sun. We see that a reduction in the Sun’s mass by a factor of of 0.00008 causes an increase in the Earth-Sun distance if the kinetic energy of the Earth is held constant. This means that over the last 4.5 billion years, we can estimate that the Earth’s orbit has increased by about 0.00008 x 93 million miles or about 7,000 miles; about the Earth’s own diameter!

The Sun also produces a ‘solar wind’ of particles at a rate of about 10^-14 solar masses per year. The NASA illustration shows the general idea of what this wind does as it travels through interplanetary space. In 4 billion years this amounts to about 0.001 percent of the Sun’s mass, which to the level of our approximations is a factor of 8 times smaller that the mass loss from converting some of its mass into light. However, both the solar luminosity and solar wind have not been constant over 4 billion years, with the sun having been fainter long ago, and its wind having been much stronger when it was first born.

The overall effects of these mass loss rates can be significant when dynamicists try to predict the long-term orbits of planets. We know that small changes in any physical parameter in these ‘non-linear’ mathematical theories can produce substantial changes in the locations of planets in their orbits. It would not surprise me if the sun loosing 1 Earth mass over 4 billion years might also have a significant effect in predictions of where planets are in the distant future.