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

Question:

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

Apparent weight:

The weight of the satellite in the orbit is different and somewhat less than the weight at the surface of the earth. This is because the centripetal force acts on the satellite or we can say that the gravitational acceleration decreases as the altitude increases above the surface of the earth.

Given Data:

• Mass of the satellite {eq}\rm (m) = 2000 \ kg {/eq}
• Altitude of the orbit {eq}\rm (r) = 3.58 \times 10^{7} \ m \ \ [\text{missing value, assumed } ] {/eq}

The centripetal force on the satellite would be

{eq}\rm F = mrw^{2} {/eq}

where

• {eq}\rm w = \dfrac{2 \pi}{T} \\ w = \dfrac{2 \pi}{86400} \\ w = 7.27 \times 10^{-5} \ rad/ s {/eq} is the angular velocity of the satellite
• T is the time period of the rotation

Therefore, the apparent weight would be

{eq}\rm W' = mg - F \\ W' = (2000 \times 9.8) - [ 2000 \times 3.58 \times 10^{7} \ m \times (7.27 \times 10^{-5})^{2} ] \\ W' = 19.22 \ kN {/eq}