A space station is in circular orbit around the earth at an altitude h of 5.0x105m. If the station makes one revolution every 95min, compute for its orbital speed.

Question

anonymous · Answer

Well the orbital speed would just be it's frequency which is 

$$\nu = f = (1/95\min) = [1/(95*60)]$$

Frequency is how many times it goes around in 1 second.  But if by "orbital speed" you mean how fast it's moving at any given time, then you need to do some work...

First you need to find out how far the satellite is from the center of the earth, since altitude usually means how high above the Earth's surface.  Which is given by

$$R = R_E + r$$

where R_e is the radius of the Earth, which you'll have to look up somewhere, and r is the altitude given.  Now you need to find how fast it's moving in a straight line, the tangential velocity as it's called, using

$$v_T = \omega r$$

where omega is the angular velocity given by

$$\omega =  2 \pi f$$

and the little r is the distance from the center of the Earth as defined above.  Plug all this in and that's your answer.