What is the weight of a 2000 kg satellite in a geosynchronous orbit?

Refer to the diagram shown below.

In geosynchronous orbit, the satellite makes one circular revolution at the equator in 1 day.

From tables, obtain

r = 42,164 km = 4.2164 x 10⁷ m, the earth's radius

g = 9.8 m/s², acceleration due to gravity.

Note that 1 day = 86400 s

The angular velocity of rotation is

ω = (2π) / 86400 = 7.2722 x 10⁻⁵ rad/s

The centripetal acceleration on the satellite is

a = rω²

= (4.2164 x 10⁷ m) * (7.2722 X 10⁻⁵ rad/s) ²

= 0.223 m/s²

The weight of the 2000 kg satellite is

W = m (g - a)

= (2000 kg) * (9.8-0.223 m/s²)

= 19154 N

= 19.154 kN

Answer: 19 kN (nearest integer)