# Orbital Motion Mechanics

#### Master J

Looking over past problems and these types of ones always bothered me. Really need the help here guys.

A particle moves in a plane, projected from an apse, with speed SQRT(t/b), at a distance b, under a repulsive force t(u)^2 + 2bt(u)^3.

Show the motion is u = (-1/3b) + (4/3b)COS(SQRT(3)O)

O is theta, the angular term. u = 1/r. t and b are constants.

So the orbit equation is:

second derivative (du/dO) + u = [-F(1/u)]/(h^2)(u^2) per unit mass

the right side I work out at the start as: (1/b) + 2u

There is a trick then to multiply across by 2(du/dO), which allows one to integrate. But after that I don't know where to go. I get a horrible integral!!!!

(du/dO)^2 - u^2 = (2/b)u - (3/b^2) Is this right first of all??<<<<<<<

Cheers

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