How far above the earth's surface is the satellite orbit?

[Julie323]

Homework Statement

A. Suppose you are at the Earth's equator and observe a satellite passing directly overhead and moving from west to east in the sky. Exactly 15.0 hours later, you again observe this satellite to be directly overhead. How far above the Earth's surface is the satellite's orbit?

B. You observe another satellite directly overhead and traveling east to west. This satellite is again overhead in 15.0 hours. How far is this satellite's orbit above the surface of the earth?

Homework Equations

T²=4π²r³/GM

The Attempt at a Solution

I was not sure how to account for the rotation of the earth, but I tried 15/(1+15/24)=9.23 hours, and then used that for T. I plugged in 6.67*10^-11 for G and 5.97 *10²⁴ for M. I solved for r giving me 2.23*10⁷ meters.

Where did I go wrong? Thanks so much for any help!

 

[Delphi51]

Suggest you draw a picture of the Earth and show the 15/24th turn the Earth makes. And the turn that the satellite makes going the other way round (for part a).

After you find how far round it goes in 15 hours, use a proportion to find its time to go a full orbit.

 

[ehild]

You got the radius of the orbit. The question is the distance of the satellite from the surface of Earth.

ehild

 

[Julie323]

O right! I forgot to subtract the radius of the earth. I got both parts, thank you so much!