Weight of an astronaut in motion and not

Question

Weight of an astronaut the weight W of an object caries inversely as the square of the distance d from the center of the earth, and at sea level (3978 mi. from the center of the earth), an astronaut weighs 118 lbs., so find her weight when she is 489 miles above the surface of the earth and the spacecraft is not in motion.

Answer 1

Very important:  The spacecraft is not orbiting the Earth (astronaut's weight would be 0).  It's just floating over one spot, 489 miles up.  Spacecraft don't normally do this.  It's possible, but the spacecraft would have to be firing its rockets continuously in order to not fall down.  If the rockets are turned off, then the rocket would be in free fall, like in orbit, and the astronaut's weight would be 0.

Question:  How much further up is the astronaut in this problem?

(3978+489) / 3978 = 1.12292609351 times further away from the Earth.

But the weight depends on the square of the distance so we have to square that number:

1.2292609351^2 = 1.2609630115

Divide the astronaut's normal weight by that number:

118 / 1.2609630115 = 93.5792714967

She would weigh about 94 pounds.

Very important:  Weight is not the same thing as mass.  The effort she would have to make in order to stand up would be about 94 pounds- it would take less effort.  The effort someone would have make in order to move her would be the same as on Earth- they would be moving a 118 pound person, not a 94 pound person.