# Halley's Comet Orbit

1. Oct 28, 2009

### 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)
(vx,vy,vz) = (-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

$$\alpha$$/r = 1 + $$\epsilon$$cos$$\theta$$

where $$\alpha$$ = l2/$$\mu$$k and $$\epsilon$$ = 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.

Last edited: Oct 28, 2009