Why Does the Equation mg = mv^2/r Work for Calculating Satellite Altitude?

[ys2050]

A remote-sensing satellite travels in a circular orbit at a constant speed of 8.2x10^3m/s. Determine the altitude above Earth's surface.

I thought that I should do GMm/r^2 = mv^2/r and solve for r
but if I do it that way i get a wrong answer.
Instead, if I do mg = mv/r^2 and find r, I get the right answer...
For all the other questions involving satellites and space telescopes and stuff, I always used GMm/r^2 somehow... but how come i just use mg for this question?

Thanks for you help! :)

 

[dynamicsolo]

A remote-sensing satellite travels in a circular orbit at a constant speed of 8.2x10^3m/s. Determine the altitude above Earth's surface.

Sounds like numerical coincidence to me. Read the question you are to answer again. The equation you used,

GMm/r^2 = mv^2/r ,

is correct. However, this will give you the radius of the satellite's orbit. They asked for the altitude of the satellite, so you have to subtract one Earth radius from your answer. (The radius of the orbit is measured from the center of Earth, while the altitude is measured from its surface.)

I will give you the standard warning that this is a favorite "dirty trick" used on exams, particularly in multiple choice questions (including the SAT, GRE, AP Physics, etc.).