Question

From the gravitational law calculate the weight W (gravitational force with respect to the earth) of a 83-kg man in a spacecraft traveling in a circular orbit 291 km above the earth's surface. Express W in both newtons and pounds.

Answer 1

83 km. = 41.5 * 10^5 m.

Let:
G be the gravitational constant,
M be the mass of the earth,
m be the mass of the man,
R be the radius of the earth,
r be the height above the surface of the earth.

G = 6.674 * 10^(-11) N m^2 / kg^2
M = 5.976 * 10^24 kg.
R = 41.5 * 10^5 m.

mg = GMm / (R + r)^2
g = GM / (R + r)^2
= 6.674 * 10^(-11) * 5.976 * 10^24 / (6.378 + 0.25)^2 * 10^12
= 9.079 m/s^2

mg = 83 * 9.079 = 753.3 N
W = 753.3 / 9.81 kg
= 753.3* 2.205 / 9.81
= 168.9 lb.