Two objects each with mass \(M_1\) and \(M_2\) is presented in the space, given the following statements:
2.Both objects have initial velocity \(v=0\)
3.The distance between the two objects \(= D\)
4.Assume that both of their mass is concentrated at each of their own center of gravity, and both object's size \(=0\)
5.Gravity decreases with the inverse square of distance to an object.
Answer the following questions:
1.Find the point between \(M_1\) and \(M_2\) where the gravity from both of them are the same (\(L_1\)).
2.Find the point where they hit each other.
3.Find the center of mass of the system.
Gravitational forces etc:
Your answer to the 2nd and the 3rd question is correct, good job! (You must have read a lot of books about classical physics didn't you.)
But for the 1st question, the question states that \(M_1>M_2\), that means their first Lagrangian point won't be midway between the two objects, but closer to \(M_2\), like how the point between the Sun and the Earth is closer to Earth than Sun does :D
Actually, I gave answers for the first part for two cases; one when the two masses are not the same and one when they are (I could, of course, have left out the second possibility if I'd noticed that the question specified M1 > M2!)