ay45c4-page15 - The orbit in this case, is an ellipse. If...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The orbit in this case, is an ellipse. If we put x = r cos( 0) y = r sin( 0) and eliminate  and r, the equation of the orbit becomes   1 1 1+ x (x2 + y2)1=2 = r (x2 + y2)1=2 0 which simpli es to x + a 2 y2 + b2 = 1 a where a = 1 r0 2 ; b = (1 r02)1=2 are semi-major and semi-minor axes. y θ = θ 0 + π/2 b x = a(1 − ε ), r = r0 /(1 + ε), r0 εa y=0 θ=θ x a x = − a(1 + ε), y = 0 r = r0 /(1 − ε), θ = θ 0 + π The axial ratio of the ellipse is b=a = (1 2)1=2. The quantitiy r0 is called the \semi-latus rectum." Note that  < 1 implies, from the de nition 2EL2 2  1 + (GM )23 that E < 0, i.e. the total energy of a bound system is negative. 74 ...
View Full Document

Ask a homework question - tutors are online