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March 25, 2017

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At what altitude above the Earth's surface is the acceleration due to gravity equal to g/128?

i did

g/128=(G*Earth's mass)/r^2
then solved for r and got 72080960. its within 10% of the correct answer but not correct. what am i doing wrong? (ive already rounding differently,etc)

  • physics - ,

    you need to subtract earth radius from r, the question asked for altitude.

    There was a easier way to do this.

    g/128=g*(re/(re+alt))^2 notice the g's divide out, or

    (re+alt)^2/re^2=128

    or (1+alt/re )^2=128
    take the sqrt of each side...
    alt= re * (sqrt128 -1)

    Now you see why your answer was within ten percent, as the sqrt 128 is about 11.

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