Recent content by Gregorski

Thanks haruspex, So, we have: $$\frac {dv} {dt} = -G\frac {M_1} {r^2} + G\frac {M_2} {(R-r)^2}$$ And using the standard trick: $$v\frac {dv} {dr} = -G\frac {M_1} {r^2} + G\frac {M_2} {(R-r)^2}$$ Now, separate the variables and integrate: $$\int v \,dv=-\int G \frac {M_1} {(R-r)^2}\,dr + \int G...

Aha! So, ##m_0##'s cancel, and we have: $$\ddot r=-G \frac {m_1} {r^2} + G\frac {m_2} {(R-r)^2}$$ I hope, this time it's correct.

Vela, I am not sure what you mean by the right hand side missing a factor of ##m_0##. Yes, the particle lies between the two masses.

Well, yes it wasn't clear to me either. But, I think now it is. So, I need the equation of motion for the test particle, and I hope it will look like this $$F=m_0\ddot r (t),$$ where ##m_0## is the mass of the test particle. Then the differential equation will be $$m_0\ddot r=-G \frac {m_1}...

Ray,mfb, Thanks for the input. I changed the equation for potential. And well, yes you both are probably right, let's assume that the system is not in equilibrium. Then the equations of motion would be F1 = m1d2r/dt2 and F2=m2d2(R-r)/dt2 ?

Homework Statement Statement of the problem (quoting from my assignment): a) write equations of motion b) try to solve analytically Given: m1, m2 - two masses R - distance between two masses Homework Equations V=-G(m1/r + m2/(R-r)) F=-dV/dr The Attempt at a Solution a) Equations of motion: v...

Andrew, Thank you for your input; you're absolutely right there are two frames. I managed to do the last step by applying Lambert W function. Greg

Homework Statement This is new for me, so forgive me my clumsiness. I am working on the following problem: A particle p is moving with a velocity v1 = c (speed of light) towards an object q, which is moving in the same direction with the speed v2, where v1>v2. Now, v2 is a function of the...