Solve Gravitation Problem: Find Planet Radius from 11 kg Satellite Orbit

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An 11 kg satellite orbits a planet with a period of 1.0 hour and a radius of 4.9 × 10^6 m, while the gravitational acceleration at the planet's surface is 41 m/s^2. The correct formula to find the planet's radius involves using the satellite's orbital period and gravitational acceleration. Initial calculations led to confusion, particularly with squaring the time value. After clarifying the calculations, one participant successfully derived the planet's radius as approximately 2.96 million meters. The discussion highlights the importance of careful algebraic manipulation in solving gravitational problems.
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Homework Statement
A 11 kg satellite has a circular orbit with a period of 1.0 h and a radius of 4.9 × 10^6 m around a planet of unknown mass. If the magnitude of the gravitational acceleration on the surface of the planet is 41 m/s^2, what is the radius of the planet?


The attempt at a solution
I used the formula:
(4pi^2 Rs^3) / (a T^2) = Rp^2


I'm on my last try.
I got 177000000 and then 935000.
I know the formula is right for sure.
I'm not sure what's going on with my calculations. It's basic algebra, easy stuff, but I'm making some mistake... >.>
 
Last edited:
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What You wrote seems right...
What did You plug for T?i hope 3600sec
i got 2956411 meters
approx:
3*10^6
 
Last edited:
The first answer you got was because you didn't square the time. I am unsure how you got to the second answer, however I do get the same answer as Dweirdo.
 
Okay I don't know how I got that second one either.
I kept plugging in the numbers and got that second answer.
For some reason, after I read Dweirdo's post, I plugged it in again and this time it worked.
Don't know what I did back then but thank you very much!
 

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