Calculating Mars' Orbital Period in Earth Years

In summary, the period of Mars in Earth years can be calculated using Kepler's third law, which states that the ratio of the period to the semimajor axis is constant for all planets. Using this formula, and considering the orbital radius of Mars to be 1.52 times that of Earth, we can calculate the period of Mars in Earth years by using the constant for the period of orbit around the sun.
  • #1
Inertialforce
68
2

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?
 
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  • #3
fluidistic said:
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?
 
  • #4
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
fluidistic said:
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 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?
 
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  • #6
Inertialforce said:
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 [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.
 

1. How is the orbital period of Mars calculated in Earth years?

The orbital period of Mars in Earth years can be calculated using Kepler's Third Law, which states that the square of a planet's orbital period is directly proportional to the cube of its average distance from the sun.

2. What is the average distance between Mars and the sun?

The average distance between Mars and the sun is approximately 227.9 million kilometers.

3. How long is Mars' orbital period in Earth years?

Mars' orbital period in Earth years is approximately 1.88 Earth years or 687 Earth days.

4. Why is Mars' orbital period longer than Earth's?

Mars' orbital period is longer than Earth's because it is farther away from the sun and therefore travels a greater distance in its orbit. Additionally, Mars has a larger orbit and slower orbital speed than Earth.

5. Can the orbital period of Mars change?

Yes, the orbital period of Mars can change due to the influence of other planets and gravitational forces. However, these changes are relatively small and occur over long periods of time.

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