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

https://www.physicsforums.com/showthread.php?t=44239 except the planet is Saturn.

2. Relevant equations

[tex]r = (t / (2pi)) ^ {2 / 3} * (G * M) ^ {1 / 3}[/tex]

3. The attempt at a solution

I tried many things, so I thought I would give tony873004's solution attempt from the thread I linked to a shot.

"where r is the radius of your orbit (distance from the center of Saturn), t is the period of your orbit, which is the same as the rotational period of Saturn (38,745 seconds), G is the gravitational constant [tex]6.67 * 10^{-11}[/tex], M is the mass of Saturn ([tex]5.6851 * 10^{26} kg[/tex]).

Subtract from this the radius of Saturn (60,268 km) to get your altitude."

I calculated from all of that 456,708 km, which is apparently wrong.

Am I doing something wrong here with finding the right rotational period or mass of Saturn?

The second question is:

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

A 25.0-kg satellite has a circular orbit with a period of 2.35 h and a radius of 7.30×10^6 m around a planet of unknown mass. If the magnitude of the gravitational acceleration on the surface of the planet is 9.10 m/s2, what is the radius of the planet?

3. The attempt at a solution

GMm/r^2 = m*v^2/r

v = 2*pi*r/T

so GM/r^2 = (4*pi^2*r)/T^2

So the mass of the planet M = 4*pi^2*r^3/(G*T^2) = (4*pi^2*(7.30*10^6)^3)/(6.67x10^-11*(2.35*3600)^2)= 3.22*10^24 kg

b) Now Using the law of gravitation we get GMm/R^2 =m*g at the surface we get

GM/R^2 = g So R = sqrt(GM/g) = sqrt(6.67x10^-11*3.22*10^24/9.10) = 4.89*10^6

That is somehow also wrong. Are the formulas set-up correctly?

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# Homework Help: Two Kepler Questions

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