Question

An astronaut orbits the earth in a space capsule whose height above the earth is equal to the earth's radius. How does the mass of the astronaut in the capsule compare to her mass on the earth?

Answer 1

The weight will be
`(1)/(4)` of its weight on earth surface. A further explanation is provided below.

Step-by-step explanation:

According to the question,

h = R

The value of gravitational acceleration at height equivalent to radius of earth R.

⇒
`g=(g_0)/((1+(h)/(R) )^2)`

or,

⇒
`g=(g_0)/((1+(R)/(R) )^2) =(g_0)/(4)`

here,

`g_0` = gravitational acceleration earth's surface

then,

⇒
`mg=(mg_0)/(4)`

Thus, the above is the appropriate solution.