# Homework Help: Compare centripetal acceleration of Mars and Earth

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1. Nov 7, 2011

### shnigglefratz

1. The problem statement, all variables and given/known data

Is the centripetal acceleration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Earth?

2. Relevant equations

I assume that the relevant equation is a=v$^{2}$/r since you are trying to compare the centripetal accelerations of Mars and Earth, however it is supposed to be a concept question according to the book so no data or variables should be needed to answer the question.

3. The attempt at a solution

So i know that Mars is farther away from the Sun than the Earth is, so r is obviously greater for Mars. Therefore the perimeter of Mars' orbit around the sun is greater than the perimeter of the Earth's orbit around the Sun. What I am confused about is how to figure out the velocity of Mars, or Earth for that matter. Is the velocity not needed to answer the question and I am merely missing something, or can you just assume that because Mars is farther away from the Sun it has a greater centripetal acceleration based on a trend?

If I did anything against the forum rules/policies please forgive me as this is my first post on Physics Forums.

2. Nov 7, 2011

### rock.freak667

Considering the Earth only. The gravitational force between the sun and the earth provides the centripetal force for the Earth. Can you find an expression for this acceleration?

(Hint: What does the law of universal gravitation say?)

3. Nov 7, 2011

### shnigglefratz

So with Newton's law of universal gravitation it's: F = $\frac{G(m_{Earth})(m_{Sun})}{r^{2}}$?

4. Nov 7, 2011

### rock.freak667

Right, so the centripetal acceleration of the Earth is therefore? (Newton's second law)

Do the same with Mars now.

5. Nov 7, 2011

### shnigglefratz

so: m$_{earth}$a = $\frac{G*m_{Earth}*m_{Sun}}{r^2}$

divide by m$_{Earth}$: a = $\frac{G*m_{Sun}}{r_{Earth's Orbit}^2}$

Therefore for Mars the equation will be: a = $\frac{G*m_{Sun}}{r_{Mars' Orbit}^2}$

6. Nov 7, 2011

### rock.freak667

Right, so you can see that if you take aearth/amars then GMsun will cancel out.

7. Nov 7, 2011

### shnigglefratz

So the only factor that matters when comparing the two centripetal accelerations is the radius of their orbits. Therefore Mars has a larger centripetal acceleration because its radius is larger. Is that right?

8. Nov 7, 2011

### rock.freak667

That should be correct.

9. Nov 7, 2011

### shnigglefratz

Thanks, I really appreciate all of the help . I just thought that the solution would involve more than one variable.

10. Mar 5, 2012

### notsosmartman

wrong if radius is larger acceleration is less

11. Mar 6, 2012