What is the Formula for Determining Height in Newton's Law of Gravitation?

[science_rules]

Homework Statement

Starting with Newton's law of gravitation, determine the height h one person has to go from the surface of Earth in order for the person's weight to be reduced to 1/5 of their weight at the surface of the Earth. The only information you are given is that the radius of the Earth is 6400 km.

Homework Equations

GM_e/r^2, r = R_e + h

The Attempt at a Solution

i know that 4 times R_e at the center(of earth) is equal to 3 times R_e at the surface. I am not sure how to find the height using Newton's Law.

 

[arildno]

Well, what are you asked to actually compare?

Try to formulate an equation that incorporates this, what you have called equations are not that at all.

 

[lanedance]

hi science_rules

So the problem effectively says the gravitational force at the surface (r1=Re) is 5 times the force at (r2=Re+h). Equivalently you can consider the acceleration due to gravity (why?)

So try writing this out as an equation, then solving for h

 

[science_rules]

a person's weight is dependent on how far out you are from the surface, and the weight is reduced as the distance is increased. should it be some kind of ratio problem? could it be: GM_em/ r^2 = 1/5 (GM_em)/R_e^2

r^2 = 5R_e^2 where r = (squrrt5)R_e = 2.23R_e = 14272 km

 

[science_rules]

a_c = v^2 / r but what does that have to do with the height? you don't know the velocity, but you don't need the velocity to get the height.

 

[lanedance]

post #4 looked good, then h = r - Re

i'm not too sure about post #5, i don't think you need to look at centripetal acceleration in this problem