At what point (in km from Earth) between Earth and Saturn is the net force of gravity on a body by both Earth and Saturn exactly zero?
1 Answer
see below
Explanation:
Gravity force is never zero, but at a certain distance the two force can be the same:
When the two force are the same the force between earth and body, FG1:
where KG is the universal gravitational constant, ME and MG the mass of Earth and of the body and d the distance,
is equal at the force between Saturn and body FG2:
so you have:
simplifying the same terms, you have
(1)
Now you can early find on internet the mass of Earth and of Saturn, but not the distance d that changes continuosly.
In a certain instant you have
From this equation you can obtain