newtons law of gravitation says that the magnitude F of the force exerted by a body of mass m on a body of mass M is: F=(GmM)/r^2 where G is the gravita

Question

newtons law of gravitation says that the magnitude F of the force exerted by a body of mass m on a body of mass M is:         F=(GmM)/r^2

where G is the gravitational constant and r is the distance between bodies 

 

(a) find df/dr and explain its meaning. what does the minus sign indicate?

 

(b) suppose it is known that the earth attracts an object with a force that decreases at the rate of 2N/km when r=20,000 km. how fast does this force change when r= 10,00 km?

 

 

for the derivative i got F'= [r^2(GmM)'-GmM(2r)]/r^4 but i don't know if thats right and don't know where to go from there

 

Answer 1

F(r) = GMm/r²

 

GMm is constant, so you only need to differentiate 1/r².

 

dF/dr = -2GMm/r³

 

The minus sign means that F(r) is decreasing with increasing distance.

 

Can you work the rest of the problem from here?