What Are the Correct Calculations for a Geosynchronous Satellite's Orbit?

[jj8890]

[SOLVED] Circular orbit question...please check answers

Homework Statement

Given: G = 6.67259 × 10^-11 N m^2/kg^2 .
A 956 kg geosynchronous satellite orbits a planet similar to Earth at a radius 201000 km
from the planet’s center. Its angular speed at this radius is the same as the rotational speed of the Earth, and so they appear stationary in the sky. That is, the period of the satelliteis 24 h .

What is the force acting on this satellite? (Newtons)
What is the mass of this planet? (kgs)

I just need help checking my answers and make sure that I am using the correct equations. I would appreciate the help.

Homework Equations

v= (2*pi*R)/T
v= (Sqrt(G * Mcentral))/R; G=6.67259 *10^-11
F=(GmM)/r^2

The Attempt at a Solution

v= (2*pi*R)/T = (2*pi*201,000,000)/86400 = 14617.1 m/s

v= (Sqrt(G * Mcentral)); (v^2 *r)/G=Mcentral
Mcentral= (14617.1^2 * 201,000,000)/(6.67259 *10^-11)= 6.43615 * 10^26 kg

F=(GmM)/r^2
F= [(6.67259*10^-11) * (956) * (6.43615 *10^26)]/(86400^2)=5.49985 *10^9 N

 

[PingPong]

Where did the 86400 come from in your force equation?

Your speed seems fine, and I would probably use $F=m\frac{v^2}{r}$ for the force due to circular motion, which gives 1.016 kN. The mass of the planet is then 643*10^24 kg, as you have.

Recheck your force.

 

[jj8890]

The 86400 = 24 hrs in seconds, the period. I also thought that the force was high...I'll recalculate.

 

[jj8890]

I also got 1016.21 N when recalculated...thanks