Question

An astronaut in space is in orbit `250` `km` above the surface of Earth. What is the gravitational acceleration on the astronaut at this altitude?

Answer 1

The acceleration due to gravity is given by `a=(GM)/r^2` where G is the gravitational constant and M is the mass of Earth. The value at this altitude is `9.08` `ms^-2`.

Explanation:

Constants:

`G=6.67408xx10^-11` `m^3 kg^-1 s^-2`
`M=5.972xx10^24` `kg`

The radius of Earth is `r=6.371xx10^6` `m`

In this case, we need to add another `2.5xx10^5` `m` (250 km) to the radius, to give `r=6.621xx10^6` `m`

So:

`a=(GM)/r^2=(6.67xx10^-11xx5.97xx10^24)/(6.621xx10^6)^2=9.08` `ms^-2`

This makes sense, since the acceleration due to gravity is `9.81` `ms^-2`. The radius has been increased by only about 4%, but the acceleration due to gravity is inversely proportional to the square of the radius.