Me = mass of Earth, Re = radius of Earth, G = universal Gravitational constant
d = distance between center of Earth and the object, m = mass of an object.
C = GMm
Force of gravitation = weight = C / d²
on the surface or above the surface of Earth, d >= Re.
Force of gravitation = K r , where K is a constant
inside the surface of Earth. Distance of object from center of Earth r <= Re.
On the surface weight = 81 pounds. Re = 4000 miles
Force at the surface according to both formulas is same.
C / Re² = K Re
So K = C / Re³
The force of gravitation below surface of Earth = weight = K r = (C / Re³ ) r
= [ C/Re² ] * r / Re
= 81 pounds * r / 4000 miles
= 0.02025 r units
Weight = (0.02025 * r) pounds, r distance of phoebe from center in miles.
(weight has to be multiplied by g in FPS units to get the value in units of force.)
Weight at 3000 miles is = 0.02025 * 3000 = 60.75 pounds
weight at surface = C / Re² = 81 pounds => C = 81 * 4000² units
Weight at 8000 miles = C / 8000² = 81 * 4000²/8000² = 20.25 pounds
Weight at 12000 miles = C / 12000² = 81 * 4000² /12000² = 9 pounds
C ) see diagram