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12 February, 20:15

A satellite would have a mass of 270 kg on the surface of Mars. Determine the weight of the satellite in pounds if it is in orbit 15,000 miles above the surface of the Earth.

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  1. 12 February, 23:56
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    26 lbf

    Explanation:

    The mass of the satellite is the same regardless of where it is.

    The weight however, depends on the acceleration of gravity.

    The universal gravitation equation:

    g = G * M / d^2

    Where

    G: universal gravitation constant (6.67*10^-11 m^3 / (kg*s))

    M: mass of the body causing the gravitational field (mass of Earth = 6*10^24 kg)

    d: distance to that body

    15000 miles = 24140 km

    The distance is to the center of Earth.

    Earth radius = 6371 km

    Then:

    d = 24140 + 6371 = 30511 km

    g = 6.67*10^-11 * 6*10^24 / 30511000^2 = 0.43 m/s^2

    Then we calculate the weight:

    w = m * a

    w = 270 * 0.43 = 116 N

    116 N is 26 lbf
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