A force of 5.25 newtons acts on an object of unknown mass at a distance of 6.9..*.108 meters from the center of Earth. To increase the force to 2.5 times its original value, how far should the object be from the center of Earth?

Question

anonymous · Answer

The formula for gravitational force is:$$F=G \frac{ m _{E}m _{2} }{ r ^{2}}$$where G is the gravitational constant; mE is the mass of Earth; m2 is the unknown object; and r is the distance between the center of Earth and the unknown object.

The problem asks you to find what the distance has to be for:$$F _{2}=2.5*F _{1}$$where F2 is the gravitational force at the new distance; and F1 is the gravitational force at the original distance.  So, set up the problem like this:$$\frac{ F _{2} }{ F _{1} }=\frac{ 2.5F _{1} }{ F _{1} }=\frac{ G \frac{ m _{E}m _{2} }{ r _{2}^{2} } }{ G \frac{ m _{E}m _{2} }{ r _{1}^{2} } }$$

anonymous · Answer

Note that a lot of simplification of that last equation will make the solution very simple.

anonymous · Answer

huh