Gravity earth's radius question

[physicshard22]

Homework Statement

The force of gravity on an astronaut is 600N at the Earth's surface. what is the force of gravity acting on him at a distance of 10 times the Earth's radius?

Homework Equations

F = Fm1m2/r^2

The Attempt at a Solution

F = Gm1m2/r^2
F = 600/11r^2
F = 4.96N

11r because its measured from the surface of the earth

 

[Stonebridge]

I think it means at a distance of 10 times R from the centre of the Earth. (not from the surface)

 

[kerimek]

to the astronaut, which is 10 times the Earth's radius, plus the radius of the Earth itself.This is incorrect. The correct approach to solving this problem would be to use the equation F = Gm1m2/r^2, where G is the gravitational constant (6.67x10^-11 Nm^2/kg^2), m1 is the mass of the astronaut (which we can assume to be 80 kg), m2 is the mass of the Earth (5.97x10^24 kg), and r is the distance from the center of the Earth to the astronaut (11 times the Earth's radius, or 11x6.37x10^6 m). Plugging in these values, we get:

F = (6.67x10^-11 Nm^2/kg^2)(80 kg)(5.97x10^24 kg)/(11x6.37x10^6 m)^2
F = 5.37x10^5 N

Therefore, the force of gravity acting on the astronaut at a distance of 10 times the Earth's radius is 5.37x10^5 N, significantly higher than the force of 600N at the Earth's surface. This is because the force of gravity decreases with distance according to the inverse square law.