Question

GPS satellites orbit the earth about 20,000 km above the surface of the earth. The radius of the
earth is 6,371 km. What is the acceleration due to earth’s gravity on the GPS satellites?

i've tried fooling around with the A = V^2/ R and V = 2pir/T equations, but I cant seem to have it add up to the answer given: 0.573 m/s^2

Answer 1

We use the formula
g = GM / r^2

where
g = acceleration due to gravity (m/s^2)
G = gravitational constant = 6.673 x 10^-11 N-m^2-kg^2
M = mass of larger body (kg)
r = distance from center of mass of the body

Here, the total distance from the center of earth to the satellite is
20000 km + 6371 km = 26371 km = 26371000 m

The larger body between earth and satellite is earth. And the mass of the earth is approximately 5.98 x 10^24 kg.

Substituting,
g = (6.673 x 10^-11) * (5.98 x 10^24) / (26371000)^2
g = 3.990454 x 10^14 / 6.954296 x 10^14
g = 0.5738 m/s^2


hope this helps~ `u`