Question

The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object and the center of the Earth. If an astronaut weighs 193 pounds on the surface of the Earth, what will this astronaut weigh 1650 miles above the Earth? Assume that the radius of the Earth is 4000 miles Round your answer to one decimal place if necessary.

Answer 1

Notation

W1= represent the weight at Earth

W2= represent the weight outside

a= the redius of the Earth

b= height above the Earth

Solution

We can set up the following equation:

$\frac{W_2}{W_1}=\frac{a^2}{(a+b)^2}$

And if we solve for w2 we got:

$W_2=W_1\frac{a^2}{(a+b)^2}$

and replacing we got:

$W_2=193\cdot\frac{4000^2}{(1650+4000)^2}$

And solving we got:

$W_2=96.734pounds$