Newtonian gravitation?

Question

A dead satellite is in a circular orbit about the Earth with a speed of 6.3km/s. What is the distance from the satellite to the center of the Earth?

Answer 1

What is the force required on an object to keep it in a circular orbit?  F = mv^2 / r  ?

Well that force required is also the same as the gravitational force between (in this case) the earth and the satellite, which Newton gives us as F = GMm / r^2

If we equate these two things we get :-

GMm / r^2  =  mv^2 / r

Here the little 'm's cancel, leaving us with:-

GM / r   =   v^2

So, r  =  GM / v^2

Plug these values in (remembering to convert the speed to m/s first), and looking up the values for 'G' (the universal gravitational constant) and 'M' (the mass of the earth), then you should get the distance between the earth and the satellite.

Answer 2

the orbital velocity is equal to the square root of G*M / r. And G is the universal gravitational constant and m is the mass of the earth which is 5.9742 × 10^ 24 kg and G is 6.67 x10^-11 and u know the velocity is 6300 m/s , therefore using the formula. radius is around 10039786.85 m. Radius is equal to the distance from the satellite to the center of the earth