Question

How much would a 80kg astronaut weigh on Earth? How much would they weigh 500 km above the surface of the Earth?

Thank you!

Answer 1

on Earth, weight= mg
at the higher altitude,
weight= mg* (re/(re+800))^2 where re is the radius of earth in km.

Answer 2

80 * 9.81 = weight on surface where R = Rearth

weight * R^2 = constant = G m M

weight at Rearth +500,000 meters

weight*(Rearth+5*10^5)^2 = 80*9.81 * Rearth^2

so
weight up there = 80*9.81 (Rearth)^2/(Reart+5*10^5)^2