- #1
cromata
Homework Statement
-Two objects of negligable radius and masses M and m are fixed in space at the distance R. Gravity is the only force acting between those two bodies. At some point in time, body of mass m is realized and starts moving due to gravity toward statical mass M.
Find v(x) and speed of body m when it collides with M [x is the distance between the objects]
Homework Equations
F=GMm/r2
The Attempt at a Solution
GMm/(R-x)^2=m dv/dt
GM/(R-x)^2 =dv*v/dx
GM ∫dx/(R-x)^2=∫v*dv [integral of dx goes from 0 to x, and v from 0 to v]
GM*[1/(R-x)-1/R]=½(v^2)
v(x)=sqrt(2GM/R) * sqrt[x/(R-x)]
and for this function, we get that the speed at the moment of impact (x=R) is infinity
-Same result is obtained using energy conservation law, but it doesn't make sense to me