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Orbital period

  • #1
1. Homework Statement
Mars orbits the sun at 1.52 Earth's orbital radius. What is the period of Mars in Earth years?


2. Homework Equations
ΣFc = mac


3. The Attempt at a Solution
I am unsure how to do this problem as this is the first "orbital period" question that I have encountered. Do I use the equation ΣFc = mac to solve this question, or is there another equation specifically for orbital periods that I don't know about?

because if I go the ΣFc = mac route I get:

ΣFc = mac
Fg = m4(pie)^2r/T^2
GMem/r^2 = m4(pie)^2(1.52)r/T^2
GMe/r^2 = 4(pie)^2(1.52)r/T^2
(GMe)(T^2) = 4(pie)^2(1.52)r^3
T = √4(pie)^2(1.52)r^3/GMe

This is my first orbital period question so I was just wondering would this be the correct way to solve it?
 

Answers and Replies

  • #2
fluidistic
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  • #3
  • #4
fluidistic
Gold Member
3,626
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I think you can use the formula [tex]\frac{T_{\text {Earth}}}{a_{\text {Earth}}}=\frac{T_{\text {Mars}}}{a_{\text {Mars}}}[/tex] where [tex]T[/tex] is the period and [tex]a[/tex] is the semimajor axis of the orbit. I think that in your case you can consider [tex]a[/tex] as being the orbital radius.
 
  • #5
I think you can use the formula [tex]\frac{T_{\text {Earth}}}{a_{\text {Earth}}}=\frac{T_{\text {Mars}}}{a_{\text {Mars}}}[/tex] where [tex]T[/tex] is the period and [tex]a[/tex] is the semimajor axis of the orbit. I think that in your case you can consider [tex]a[/tex] as being the orbital radius.
Oh okay, that makes this question so much easier :) thanks alot for the help.

Oh and by the way for Tearth (the period), do I use the constant given for period of rotation given or do I use the constant given for period of orbit around the sun (both found on the Chart titled "Fundamental Constants and Physical Data")? I use the constant for period of orbit around the sun right?
 
Last edited:
  • #6
fluidistic
Gold Member
3,626
97
Oh okay, that makes this question so much easier :) thanks alot for the help.

Oh and by the way for Tearth (the period), do I use the constant given for period of rotation given or do I use the constant given for period of orbit around the sun (both found on the Chart titled "Fundamental Constants and Physical Data")? I use the constant for period of orbit around the sun right?
You're welcome!
For [tex]T_{\text {Earth}}[/tex] I'd keep it like that. (I wouldn't plug any number instead of it). This way you will get [tex]T_{\text {Mars}}[/tex] in term of [tex]T_{\text {Earth}}[/tex] as they are asking you.
 

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