# Orbital period

1. Dec 7, 2008

### Inertialforce

1. The problem statement, all variables and given/known data
Mars orbits the sun at 1.52 Earth's orbital radius. What is the period of Mars in Earth years?

2. Relevant 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?

2. Dec 7, 2008

3. Dec 8, 2008

### Inertialforce

So I should use the harmonic's law equation for this question?

4. Dec 8, 2008

### fluidistic

I think you can use the formula $$\frac{T_{\text {Earth}}}{a_{\text {Earth}}}=\frac{T_{\text {Mars}}}{a_{\text {Mars}}}$$ where $$T$$ is the period and $$a$$ is the semimajor axis of the orbit. I think that in your case you can consider $$a$$ as being the orbital radius.

5. Dec 8, 2008

### Inertialforce

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: Dec 8, 2008
6. Dec 9, 2008

### fluidistic

You're welcome!
For $$T_{\text {Earth}}$$ I'd keep it like that. (I wouldn't plug any number instead of it). This way you will get $$T_{\text {Mars}}$$ in term of $$T_{\text {Earth}}$$ as they are asking you.