Calculate Geosynchronous Orbit Dist. to Earth's Center

[Shaunzio]

Homework Statement

A satellite is in a circular, geosynchronous orbit (makes one revolution around Earth in 24 hours). Calculate the distance in meters from the satellite to the Earth's center. Mass of Earth = 5.97 x 1024 kg

Homework Equations

T=((2*Pi)*r^(3/2))/sqrt(GM)

The Attempt at a Solution

I thought T equals the period 2Pi. So the the 2Pi's cancel and then you just plug in the variables. Unfortunately I'm not getting the right answer which is supposed to be: 4.2*10^7.

Any help would be greatly appreciated.

 

[gneill]

Check to see what units the formula will produce.

 

[Shaunzio]

Would the units for T be radians?

 

[gneill]

Would the units for T be radians?

You're guessing? Why don't you expand the units from the formula and actually see what it is?

 

[rwisz]

Your approach is on the right track, but there are a few errors in your calculation. First, the value of T should be 24 hours, not 2Pi. This is because the period of a geosynchronous orbit is equal to the time it takes for the satellite to complete one full revolution around the Earth, which in this case is 24 hours. Second, the equation you are using is for the period of an orbit, not the distance. To calculate the distance, you will need to rearrange the equation and solve for r. The correct equation to use is r = (GMT^2 / 4π^2)^(1/3). Plugging in the values given, the distance from the satellite to the Earth's center is approximately 4.2*10^7 meters. It's important to double check your equations and make sure you are using the correct units for each variable. Keep up the good work!