In this problem, we are given the astronaut's weight on Earth (We), and the distance the astronaut is from Earth (r). To solve, we will need to plug in the given values and solve for Ws.
r = [ sqrt((3960^2 x We) / Ws) ] - 3960
532 = [ sqrt((3960^2 x 148) / Ws) ] - 3960
---Add 3960 to both sides
4492 = sqrt((3960^2 x 148) / Ws)
---Simplify the numerical value under the radical
4492 = sqrt( 2320876800 / Ws )
---Square both sides
20178064 = 2320876800 / Ws
---Multiply both sides by Ws
20178064 x Ws = 2320876800
---Divide both sides by 20178064 to isolate Ws
Ws = 115.02 = 115 lbs
Answer: 115 lbs
Hope this helps!