|Oct28-09, 12:43 PM||#1|
Halley's Comet Orbit
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
[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.
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