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I've found the a general form of equation for the explicit integration of the shape, [itex]r(\theta)[/itex], of a one-body-problem (a particle rotating about a set point, O) for arbitrary [itex]\mathbf{f} = -f(r)\hat{\mathbf{r}}[/itex], and used it to find [itex]r(\theta)[/itex] for an inverse square law [itex]f(r) = \mu / r^2[/itex]. Where [itex]u = (1/r)[/itex].

I was able to get [tex]r = r(\theta(t)) => \dot{r} = {{dr} \over {d\theta}} {{d\theta} \over {dt}} = {{dr} \over {d\theta}} \left({{h_0} \over {r^2}}\right)[/tex]

Where [itex]h_0 \neq 0[/itex] is the constant angular momentum.

Can anyone help me to figure out the shape under an inverse cube law of force, [itex]f(r) = {{\nu} / {r^3}}[/itex], and show that if [itex]\nu \le h^2[/itex], the orbit is unbounded?

I know that this solution will depend on the relative sizes of [itex]\nu[/itex] and [itex]h[/itex], but I can't seem to get this to work.

EDIT:: Got LaTex to work

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# Homework Help: Orbital Dynamics problem help

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