Astronomy related Calculus

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artttom

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I keep getting confused. Can someone help me? This is a problem that my professor said I was making too hard for myself. She said part of the problem is irrelevant and to focus on what's required, which I assume is the equation at the end in parenthesis. I got a few different answers and I'm unfortunately lost.

"The period of the Moon is 27.3 days and its orbital radius is 3.82 x 108 m.
Find the period of a satellite 6.90 x 106 m from the Earth's center. (
LaTeX: T^2=a^3
)"
 
Last edited:
artttom said:
I keep getting confused. Can someone help me? This is a problem that my professor said I was making too hard for myself. She said part of the problem is irrelevant and to focus on what's required, which I assume is the equation at the end in parenthesis. I got a few different answers and I'm unfortunately lost.

"The period of the Moon is 27.3 days and its orbital radius is 3.82 x 108 m.
Find the period of a satellite 6.90 x 106 m from the Earth's center. (
LaTeX: T^2=a^3
)"
Click to expand...
Have you posted the EXACT problem (verbatim) as it was given to you?

Was that equation (T2 = a3) GIVEN to you in the problem statement or you are supposed to derive it?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
artttom said:
I keep getting confused. Can someone help me? This is a problem that my professor said I was making too hard for myself. She said part of the problem is irrelevant and to focus on what's required, which I assume is the equation at the end in parenthesis. I got a few different answers and I'm unfortunately lost.

"The period of the Moon is 27.3 days and its orbital radius is 3.82 x 108 m.
Find the period of a satellite 6.90 x 106 m from the Earth's center. (
LaTeX: T^2=a^3
)"
Click to expand...
I suspect your quote of the equation relating T with a is not accurate. I guess you were asked to use Kepler's third law. Look here: https://pwg.gsfc.nasa.gov/stargaze/Skepl3rd.htm
 
artttom said:
"The period of the Moon is 27.3 days and its orbital radius is 3.82 x 108 m.
Find the period of a satellite 6.90 x 106 m from the Earth's center. (
LaTeX: T^2=a^3
)"
Click to expand...


Those 2nd and 3rd values are supposed to be in scientific notation. They need to be
\(\displaystyle (3.82 \ \times \ 10^8) \ m. \ \ and \ \ (6.90 \ \times \ 10^6) \ m., \ \) respectively.
 
There is another version for Kepler's third law where the constant of proportionality does not appear. If you have two different bodies obeying Kepler's third law (with the same proportionality constant), they satisfy the relationship (T1/T2)2=(r1/r2)3. Try to see why is that. Then your problem becomes a very simple substitution of numbers.
Second comment: when dealing with large or very small numbers, scientific notation is highly recommended.
 
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