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Determine the Altitude of a Satellite above Earth Given it's Constant Speed

1. The problem statement, all variables and given/known data

A remote-sensing satellite travels in a circular orbit at a constant speed of 8.2 x 10^3 m/s. Determing the altitude in kilometres of the satellite above Earth's surface.

2. Relevant equations

Fc = FG

3. The attempt at a solution

mv^2/r = GMm/r^2
v^2 = GM/r
r = GM/v^2
r = (6.67 x 10^-11 * 5.98 x 10^24)/(8.2 x 10^3)^2
r = 5931975 m - radius of Earth (6.38 x 10^6 m)
r = NEGATIVE NUMBER

Why am I getting a negative number? Is there a mistake in my conversions or am I completely off as to how to solve this? Any help will be greatly appreciated. :)
 

LowlyPion

Homework Helper
3,079
4
Using μ = G*M ≈ 400,000 (if you keep things in km), I get V2= 400,000/(8.2)2 = 5948 km.

Maybe it's a fast earth worm?
 

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