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

  • Thread starter ChazyChazLive
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    Gravitation
In summary, the conversation discusses finding the radius of a planet with an unknown mass using the formula for circular motion and gravitational acceleration. After some trial and error, the correct answer is determined to be approximately 3*10^6 meters.
  • #1
ChazyChazLive
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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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  • #2
What You wrote seems right...
What did You plug for T?i hope 3600sec
i got 2956411 meters
approx:
3*10^6
 
Last edited:
  • #3
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.
 
  • #4
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!
 

1. What is the formula for calculating a planet's radius using the orbit of a satellite?

The formula for calculating a planet's radius using the orbit of a satellite is: r = (GMpT2)/4π2, where r is the planet's radius, G is the gravitational constant, Mp is the planet's mass, and T is the satellite's orbital period.

2. Can the mass of the satellite impact the accuracy of the calculation?

Yes, the mass of the satellite can impact the accuracy of the calculation. This is because the gravitational force between the satellite and the planet is directly proportional to the mass of the satellite. Therefore, a more massive satellite will experience a stronger gravitational force, resulting in a slightly different orbital period and potentially affecting the accuracy of the calculated radius.

3. How is the gravitational constant determined in this calculation?

The gravitational constant (G) is a fundamental constant in physics and is determined through experimental measurements. It is typically calculated by measuring the gravitational force between two objects with known masses and distances, such as a small object and the Earth. The value of G is approximately 6.67 x 10-11 N*m2/kg2.

4. Are there any assumptions made in this calculation?

Yes, there are a few assumptions made in this calculation. First, it assumes that the satellite is in a circular orbit around the planet, which may not always be the case. Second, it assumes that the planet's mass is concentrated at its center, which may not be true for planets with irregular mass distributions. Lastly, it assumes that there are no other gravitational influences on the satellite besides the planet it is orbiting.

5. How accurate is this calculation?

The accuracy of this calculation depends on the accuracy of the input values (orbital period, planet's mass, and gravitational constant) and the assumptions made. If the input values are precise and the assumptions hold true, the calculated radius should be relatively accurate. However, there may be slight variations due to factors such as the planet's non-uniform mass distribution or the satellite's mass affecting its own orbit.

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