The earth has radius R. A satellite of mass 100 kg is in orbit at an altitude of 3R above the earth's surface. What is the satellite's weight at the altitude of its orbit

W = 61.3 N

Explanation:

The only force acting on the satellite is the one due to the attraction from Earth, which obeys the Newton's Universal Law of Gravitation, as follows:

Fg = G*ms*me / (res) ²

This force, also obeys the Newton's 2nd Law, so we can write the following equation:

G*ms*me* / (res) ² = ms * a = ms*g

We call to the product of the mass times the acceleration caused by gravity (g), the weight of this mass, so we can write as follows:

G*ms*me / (res) ² = ms*g = W (1)

where G = 6.67*10⁻11 N*m²/kg², ms = 100 kg, me = 5.97*10²⁴ kg, and

res = 4 * re = 4*6.37*10⁶ m.

Replacing all these known values in (1), we get the value of W:

W = ((6.67*5.97 / (4*6.37) ²) * (10⁻¹¹ * 10²⁴ / 10¹²)) * 100 N = 61.3 N