Calculating Mars' Orbital Period in Earth Years

[Inertialforce]

Homework Statement

Mars orbits the sun at 1.52 Earth's orbital radius. What is the period of Mars in Earth years?

Homework Equations

ΣFc = mac

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?

 

[fluidistic]

Hi Inertialforce,
Are you familiar with Kepler's Laws? Check out the third on this page : http://en.wikipedia.org/wiki/Kepler's_law.

 

[Inertialforce]

Hi Inertialforce,
Are you familiar with Kepler's Laws? Check out the third on this page : http://en.wikipedia.org/wiki/Kepler's_law.

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

 

[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.

 

[Inertialforce]

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.

Oh okay, that makes this question so much easier :) thanks a lot 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?

 

[fluidistic]

Oh okay, that makes this question so much easier :) thanks a lot 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 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.