410ahw5soln - HW#5Solutions Phys410Fall 2011 Prof. Ted...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
HW#5—Solutions —Phys410—Fall 2011 Prof. Ted Jacobson Room 4115, (301)405-6020 www.physics.umd.edu/grt/taj/410a/ jacobson@umd.edu 8.2 ( two bodies in an external field )) (a) The only new terms that were not in the analysis of (8.13) are the contributions to the potential energy due to the external field, U g = - m 1 g · r 1 - m 2 g · r 2 = - M g · R . This containts only R and not r , hence the Lagrangian still separates into two terms. (b) The R equation describes the center of mass motion in the external field, and the r equation describes the relative motion which is decoupled from the external field. This decoupling is in a sense accidental: the external field certainly breaks the symmetry in spatial directions, but since it is proportional to both the masses and the positions, the terms just happen to combine to involve only the center of mass position. (c) If instead of a uniform external field we take the field of a point mass m 0 , and use that mass as the origin of coordinates, then the extra contributions to the potential energy are U g ( r 1 ,r 2 ) = - Gm 0 m 1 | r 1 | - Gm 0 m 2 | r 2 | . The Lagrangian for the earth-moon system in the field of the sun is thus L = 1 2 M ˙ R 2 + 1 2 μ ˙ r 2 + Gm e m m r + Gm s ± m e r e + m m r m ² , where M = m e + m m is the sum of the earth and moon masses, μ = m e m m /M , r e = | R - ( m m /M ) r | , and r m = | R + ( m e /M ) r | . (d)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

410ahw5soln - HW#5Solutions Phys410Fall 2011 Prof. Ted...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online