Gravitational force, Speed, and period of a Satellite.

[Imuell1]

Homework Statement

A satellite that has a mass of 300 kg moves in a circular orbit 5.00 X 10⁷ m above Earth's surface. (a) What is the gravitational force on the satellite? (b) What is the speed of the satellite? (c) What is the period of the satellite?

Homework Equations

F_g= GM_Em/(r+r_E
T²= [4pi²/G(M_E+m)]*(r+r_E)³

The Attempt at a Solution

F_g= 38N
T=37 hours
V=9572517 m/h

I think the gravitational force might be right but the speed and period seem to be ridiculously too large.

 

[Dweirdo]

37 is not so much :D
a broadcasting satellite ,which has period of 24 hours around earth(like the Earth around it self!) has a distance of 3.6*10^7 meters from the surface of the Earth AFAIK.
But didnt get the same V as You did,did You write T as seconds?(37*60*60
EDIT1:
Oh I did, didn't see Your units ,You better solve it with seconds, and not m/h
EDIT2:
How did the mass of the satellite get to the equation of period?

 

[nlightner]

It is important to note that the gravitational force and speed of a satellite are dependent on the mass of the satellite, the mass of the Earth, and the distance between them.

To accurately calculate the speed and period of the satellite, we would need to use the correct equations and values for these variables. The equations used in the attempt at a solution are not the correct ones for calculating speed and period of a satellite in a circular orbit.

The correct equation for the speed of a satellite in a circular orbit is v= √(GM/r), where G is the gravitational constant, M is the mass of the Earth, and r is the distance between the satellite and the center of the Earth. Using this equation and the given values, the speed of the satellite can be calculated to be approximately 7,073 m/s.

Similarly, the correct equation for the period of a satellite in a circular orbit is T= 2π√(r3/GM). Using this equation and the given values, the period of the satellite can be calculated to be approximately 2.68 hours.

In conclusion, it is important to use the correct equations and values when calculating the gravitational force, speed, and period of a satellite. These values can vary greatly depending on the mass and distance of the satellite and the planet it is orbiting.