Communications satellites in geosynchronous orbit

[thor0403]

Homework Statement

Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the Earth rotates. These are called geosynchronous orbits. The altitude of a geosynchronous orbit is 3.58*10^7 m.

What is the apparent weight of a 2000 kg satellite in a geosynchronous orbit?

Homework Equations

F = MA

The Attempt at a Solution

I found the acceleration to be .223 m/s/s at it's altitude and I need to find the apparent weight.

I plugged the acceleration at that altitude and the mass given into the equation above and found the force to be 447.36 N. This answer was not correct.

Am I using the right equation?

 

[dynamicsolo]

What you have found is the centripetal acceleration of the satellite. Imagine placing a platform scale "under" the satellite to "weigh it". The centripetal acceleration points toward the center of the Earth, so this will certainly be one part of the "apparent weight".

But don't forget that the satellite is also in the Earth's "gravity field". How is the value of g at the surface of the Earth calculated (what equation do you use and what values go into it?) ? What is the value of g at geosynchronous radius*? That value -- call it g' -- goes into mg' ; that also points toward the center of Earth, and so is the other part of the "apparent weight", due to the attraction of Earth's mass.

*remember to use the RADIUS of the orbit, and not its altitude above the Earth's surface

 

[PeterO]

Homework Statement

Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the Earth rotates. These are called geosynchronous orbits. The altitude of a geosynchronous orbit is 3.58*10^7 m.

What is the apparent weight of a 2000 kg satellite in a geosynchronous orbit?

Homework Equations

F = MA

The Attempt at a Solution

I found the acceleration to be .223 m/s/s at it's altitude and I need to find the apparent weight.

I plugged the acceleration at that altitude and the mass given into the equation above and found the force to be 447.36 N. This answer was not correct.

Am I using the right equation?

Was the answer by any chance given as ZERO ?