Question

Using 6400 km as the radius of Earth, calculate how high above Earth’s surface you would have to be in order to weigh 1/16th of your current weight. Show all work leading to your answer OR describe your solution using 3 -4 complete sentences.

Answer 1

@leon549 help me master of wisdom hahha

Answer 2

Your weight it the force you experience due to gravity. It's given by the equation:
\[F = G\frac{m_1 m_2}{r^2}\]
We know that we want to weight 1/16 what we normally do, so we can set up the following relation:
\[\frac{F_2}{F_{surface}} = \frac{1}{16}\]
We then plug in for the two F's. All the variables are the same except for r in each of them, so they'll cancel:
\[\frac{F_2}{F_{surface}} = \frac{G\frac{m_1m_2}{r_2^2}}{G\frac{m_1m_2}{r_{surface}^2}} = \frac{r_{surface}^2}{r_2^2} = \frac{1}{16}\]
We can then use this to find r2.

Becareful! This is the distance from the CENTER of the earth. You need to subtract the radius of the earth to get the height above the ground!