Halley's Comet Orbit

CaptainEvil

1. The problem statement, all variables and given/known data

Consider Comet Halley. At a particular instant in time, its position and velocity
are given below, in units of AU and AU/yr relative to the centre of the Sun.

(x,y,z) = 0.331060, -0.455488, 0.166180)
(v_x,v_y,v_z) = (-9.01154, -7.02645, -1.30645)

There are a number of questions attatched to this problem, all of which are dependent on the answer of part a, which is all I need.

a) What are the semi-major axis and eccentricity of this comet?

2. Relevant equations

[tex]\alpha[/tex]/r = 1 + [tex]\epsilon[/tex]cos[tex]\theta[/tex]

where [tex]\alpha[/tex] = l²/[tex]\mu[/tex]k and [tex]\epsilon[/tex] = sqrt(1 +2El^2/mu k^2)



3. The attempt at a solution

We've done a similar problem in two dimensions, given two components of speed, finding E, l and alpha, but in this case I'm not sure where to start.
Also, mass is not given so condensed mass mu cannot be found. Maybe an assumption since m << Mass of the Sun?

Should I find the radius by sqrt(x²+y²+z²)?
If I do, I'm left with 3 components of speed that I don't know how to start working with.

I'm stuck and think I just need a push, any help would be great thanks.