Question

Someone weighs 200 pounds on the surface of the Earth. If the radius of the Earth is 4000 miles, how much would that person weigh 1000 miles above the surface?

Answer 1

Person will weigh `128` pounds, `1000` miles above the surface.

Explanation:

Weight of an object is the force of gravitation on the object.

As force of gravitation `F` is directly proportional to the two objects, here `m_o`, mass of object and `m_E`, mass of Earth and inversely proportional to the square of the distance between them. Constant of proportionality being `G`m the gravitational constant.

In other words `F=Gxx(m_om_E)/r^2` and here

`200=Gxx(m_om_E)/4000^2`

i.e. `Gm_om_E=200xx4000^2`

When the person (the object in our case) moves `1000` `km.` above Earth i.e. the distance between them increases to `5000` `km.`, the weight (i.e. the force) becomes

`F=(Gm_om_E)/5000^2=(200xx4000^2)/5000^2`

= `200xx16/25=128` pounds