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
Andrea B.
Jun 5, 2018

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:
#F_(G1)= K_G xx (M_E xx M_B)/ d_(EB)^2#
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:
#F_(G2)= K_G xx (M_S xx M_B)/ d_(SB)^2#

so you have:
# K_G xx (M_E xx M_B)/ d_(EB)^2=K_G xx (M_S xx M_B)/ d_(SB)^2#
simplifying the same terms, you have
(1) # (M_E )/ d_(EB)^2= (M_S )/ d_(SB)^2#
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
#d_EB+ d_SB = D#
From this equation you can obtain #d_EB = D- d_SB# and put it in equation (1) solving your problem

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