Really basic question but I wanted to just double check something. Im trying to work out where to place a point particle between two objects (one has a mass 4 times the other).
Now ive used very basic approximations as its just a rough idea I need so ive taken the mass of one object M1=10kg and the second M2=40kg and the point particle to be mp=1kg.
Ive worked out the force between the point particle and each of M1 and M2 individually assuming the distance between the Mass and the mp is 1m.
I have then rearranged the equation f=-gmm/r^2 for r.
After doing all this I have come to the following conclusions, the force that a 1kg point particle feels due to the force of gravity from the larger M2 acts at nearly half the distance as the smaller M1.
So would I be putting the particle closer to the larger mass? Because that seems incorrect.
no, 1/3 of distance from little one, 2/3 from 4M
1/(1/3)^2 = 4/(2/3)^2
9 = 4 /(4/9)