Question

An earth satellite moves in a circular orbit at a speed of 5,434 m/s. What is its distance from the center of the Earth? (Me = 5.98x1024 kg)

Answer 1

Explanation:

Given:

orbital speed(s) = 5,434m/s

mass(m)=5.98*10^24kg

radius of earth (R)= 6400 km=6.4*10^6m

acceleration due to gravity =9.8m/s

we know ,

s= R*(√(g/(R+h)))

or, 5434=6.4*10^6(√(9.8/(6.4*10^6+h)))

or, 5434/6.4*10^6=√(9.8/(6.4*10^6+h))

or, 8.49*10^-4=√(9.8/(6.4*10^6+h))

squaring both the sides,we get,

or, 7.20*10^-7=9.8/(6.4*10^6+h)

or, 6.4*10^6+h=9.8/7.2*10^-7

or, 6.4*10^6+h=1.35*10^7

or, h=1.35*10^7-6.4*10^6

or, h=7.19*10^6m

Therefore, the distance of satellite from centre of earth is 6400km+7.19*10^6m=1.35*10^7m.

If answer is correct inform me because I am little confused.