Question

An astronaut who weighs $162$ pounds on the surface of the earth is orbiting the earth at a height above the surface of the earth of two earth radii ($h=2R$ where R is the radius of the earth.)
How much does this astronaut weigh while in orbit at this height (With how much force is the earth pulling on him while he is in orbit at this height?)

• A. $81pounds$
• B. $40.5pounds$
• C. $18pounds$
• D. $54pounds$
• E. $0pounds$ (astronaut is weightless)

Answer 1

The correct option is C $18pounds$

Given : $h=2R$

Weight of astronaut on the earth surface $W_s=162$ pounds

Thus weight of astronaut at height h $W^{\prime }=W_s(\frac{R}{R+h}{)}^2$

$\therefore$ $W^{\prime }=162(\frac{R}{R+2R}{)}^2=\frac{162}{9}=18$ pounds