Question

Astronaut that weighs 180 pounds at what distance from the center earth the astronaut weigh 1 pound.

Answer 1

The height of the astronaut from the center of the Earth is 85865 km.

Explanation:

It is assumed that the astronaut will be going towards space, so we have to find out that at what height from the center of the earth would the value of g will be
`(g)/(180)`.

The weight of astronaut on the surface of Earth 180 pounds.

g=9.81
`m/s^(2)`

Required value of g'=
`(g)/(180)`

g'=
`(gR^(2) )/(h^(2) )`

where R=Radius of the Earth

h=Height of the point from the center of the earth

`(g)/(180) = (gR^(2) )/(h^(2) ) \\\\h^(2) =180R^(2) \\h=√(180)  R\\`

h=13.42

The value of R is approximately 6400 km.

So, h=85865 km.