Ok Ok Ok - enough of the hard stuff, I want to chill out and relax a bit. Am just about to get stuck into a bit of quantum physics there (jeez I really look forward to Thursday nights!).... I've a little teaser there for ya though if you have 2-3 minutes to spare - before yez all go out and get wasted..... have fun...
Planets move in ellipses with the Sun at one focus. Ellipses can be described in terms of their semi-major axis, a, (basically the longest radius) and their eccentricity (basically how squashed the ellipse is: e=0 is a circle, a fully squashed ellipse looks like a line and has e=1).
r=a(1-e2)/(1+e cos()); rmin= a(1-e); rmax=a(1+e)
, the polar angle from closest approach is given the odd name: true anomaly. The timing of the motion (i.e., when the planet or electron has a particular ) is a bit complex. The game is to express the true anomaly () in terms of the eccentric anomaly (u) and then find an expression relating time and the eccentric anomaly.
Time starts now, you have 3 minutes.