# Calculating free-fall acceleration of other planets

1. Nov 30, 2011

### menglish20

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

Here is the text of the question:
"A satellite circles planet Roton every 2.8 h in an orbit having a radius of 1.2 X 10^7 m. If the radius of Roton is 5.0 X 10^6 m, what is the magnitude of the free-fall acceleration on the surface of Roton?"

2. Relevant equations

v=d/t

M= [(Ve)^2*R]/(2G)

a=GM/r^2

3. The attempt at a solution

This is presented as multiple choice, and I've been able to find the answer as 27 m/s^2 but I haven't been able to figure it out on my own.

What I tried to do is find the mass of Roton using the orbit speed.
I took the distance traveled by the satellite, 2*pi*1.2e7, and diving it by the time of one complete orbit, 2.8 hr or 10080 s. I calculated this velocity as 7479.98 m/s.

To find mass, I used the second formula I listed, and used the radius of Roton as R. I'm not sure if this is correct. I used this mass in the third formula, using the sum of Roton's radius plus the orbit radius. I think this may also be incorrect. I got an answer that was significantly different than the multiple choice answers provided. Can someone steer me in the right direction?

2. Nov 30, 2011

### Barakn

No, it's not correct. The orbital radius should have been used as R.
Indeed. You should have used just Roton's radius.

3. Nov 30, 2011

### Zula110100100

If you know the velocity and the orbit radius you can find the acceleration, no need for mass

4. Nov 30, 2011

### menglish20

I had a guess that mass isn't needed but I couldn't figure out a way to calculate acceleration without it. Am I overthinking this? Given velocity and orbit radius, could you use:

Fc= m*ac, so ac=v2/r ?

If so, this is way easier than I thought.

Edit: I don't think this is correct. First, I don't even know if that equation is true, and if so, the ac would not be the free-fall acceleration, but the centripetal acceleration that maintains the satellite in a circular path.

Edit 2: I've figured it out! You do indeed need mass. Calculate it using v=sqrt(GM/R). Then use the mass in the formula a=GM/R^2. The R in the first equation is the orbital radius and the R in the second is the radius of Roton. This may have been what Barakn was explaining but I was using the wrong formula for calculating the mass. Thanks for the help, Barakn and Zula!

Last edited: Nov 30, 2011
5. Dec 1, 2011

### Barakn

You can calculate the mass, but it's not necessary. We know that M= Ve2*R/G (you typed out the formula wrong) and a = GM/r2. Substitute M into the second equation to get a = G * Ve2*R/(r2*G) = Ve2*R/r2. Everything performed in one calculation in which G and M have magically disappeared.