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21 September, 14:09

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

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  1. 21 September, 17:21
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    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)
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