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

Question

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)

Answer 1

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.