Question

How far away from the earth must an orbiting spacecraft be for the astronauts inside to be weightless? Explain.

Short answer

It must be at half the radius of earth (R/2)

Step-by-step solution

Given

spacecraft orbiting earth with the astronauts inside to be weightless

Explanation

The gravitational force from in earth's orbit depends on the value of g.

The value of g varies with height as

$g^{\text{'}}=g\left(1-\frac{2h}{R}\right)$

Where h=height and R= radius of earth.

For g' to be zero

$$\begin{gathered} 1-\frac{2h}{R}=0 \\ \Rightarrow h=\frac{R}{2} \end{gathered}$$