1. The problem statement, all variables and given/known data The figure illustrates a Keplerian orbit, with Cartesian coordinates (x,y) and plane polar coordinates (r,φ). F = -(G*M*m)/r^2 The parametric equations for the orbit: r(ψ) = a ( 1 − e cos ψ) tan(φ/2) = [(1+e)/(1-e)]^(1/2)* tan(ψ/2) t(ψ) = (T/2π) ( ψ − e sin ψ) where ψ is the independent, parametric variable; a, e, and T are constants. Prove, directly from the parametric equations, that the angular momentum L is constant. Express L in terms of the constants of the orbit (and any other relevant parameters). 2. Relevant equations L = r x p τnet = r x F 3. The attempt at a solution I know that in order for L to be constant, its derivative (net torque) must be 0, but this isn't really getting me anywhere. I know torque = rxF and L = rmv, but quite frankly I can't seem to figure out how to do this using the parametric equations. What I have done using the parametric equations is this: L = m*r(ψ)*v(t) = m*(a*(1-e*cos(ψ)))*v(t) From here I'm having a difficult time finding an expression for v(t). I tried using the relations ω=((2*π)/T) and v = ω*r for the following work: t(ψ) = (1/ω)*(ψ-esin(ψ)) ==> ω = (ψ-esin(ψ))/t(ψ) ==> ω = (ψ-esin(ψ))/((T/(2π))*(ψ-esin(ψ)) ==> ω = (2π/T) (this obviously backtracked) ==> v = r*(2π/T) ∴L = m*(a*(1-e*cos(ψ)))*(a*(1-e*cos(ψ)))*(2π/T) or L = m*a2*(1-e*cos(ψ))2*(2π/T) I'm pretty sure this isn't right because it isn't going to be constant for different r values. Any help would be appreciated.