A satellite is in a circular orbit around the Earth with a s

A satellite is in a circular orbit around the Earth with a speed of 6.3 km/s. What is the distance from the satellite to the center of the Earth? a. 1,000 km b. 6,000 km c. 10,000 km d. 60,000 km e. 100,000 km

Solution

C) 10000 km is the correct answer.

given

vo = 6.3 km/s = 6300 m/s

we know, Me = 5.98*10^24 kg

we know, orbital speed of a satellite, vo = sqrt(G*Me/r)

Me --> mass of the Earth
r ---> radius of the orbit of the satellite

vo^2 = G*M/r

==> r = G*M/vo^2

= 6.67*10^-11*5.98*10^24/(6300)^2

= 10^7 m

= 10000 km