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.

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.

anonymous · Answer

Weight if the Force of Gravity. So you need to find a ratio of forces of gravity (a fraction) that gives you 1/16th. Therefore, there will be 2 weights:$\ w_1$ and$\ w_2$.

By Newton's Universal Law of Gravitation you have that: 

$$\ F = G\frac{mM}{r^2_1}$$

And the ratio: 
$$\ \frac{w1}{w_2} = \frac{G\frac{mM}{r^2_1}}{G\frac{mM}{r^2_2}}$$

$\ G,\ m $ and$\ M$re the same in both cases, and so they cancel out, giving you with:

$$\ \frac{w1}{w_2} = \frac{r^2_1}{r^2_2} = \left(\frac{r_1}{r_2}\right)^2 $$ 

Since it is a relationship to the second power if you ingrease $\ r_2$ 4 times, the strength will decrease $\ 4^2 = 16$ times.

anonymous · Answer

Ok, I am very lost.

anonymous · Answer

What is the part where you get lost?