Math

The gravitational acceleration, g, on the Earth is proportional to the mass, M, of the Earth and inversely proportional to the square of the distance, r, from the Earth's center. If the gravitational acceleration on the center of the Earth is 9.8 m/s^2, what is the gravitational acceleration at a distance of 6,404,000km from the center of the Earth. The Earth has a radius of 6,378,000m and has a mass of 5.97 x 10^24kg. Give answer to two decimal places.

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  1. since F = GMm/r^2
    and we are changing only r, then if we change r by a factor of k, F changes by a factor of 1/k^2

    6,404,000/6,378,000 = 1.0040765, so
    F changes by a factor of 1/1.0081696 = 0.992

    so, F = 0.992 * 9.8 = 9.72 m/s^2

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