Go Back   Physics Help Forum > College/University Physics Help > Advanced Mechanics

Advanced Mechanics Advanced Mechanics Physics Help Forum

LinkBack Thread Tools Display Modes
Old Apr 28th 2009, 02:20 PM   #1
Join Date: Apr 2009
Posts: 71
A conservation and Calculus question.

Hi, I was hoping someone could offer some guidance with the following, I don't even know how to start it.

The motion of a planet of mass m around the sun of mass M is governed by the following equation (note r is a vector):

d^2r = -k r
dt^2 ||r||^3

where K=Gm (G is the gravitational constant) and r(t) is the position of the planet relative to the sun.

1. Show the following quantities are conserved.

a. Total energy (the sum of the potential and kinetic energies of the planet).

b. The angular momentum of the planet J.

c.The lenz- Runge vector L= dr x J - mk r
dt ||r||
Hint: (a x b) x c = (a.c)b- (b.c)a (note a.c is scalar product of a and c similarly b.c is scalar product of b and c).

2. (a) Interpret the constancy of J geometrically.
(b). Assume the planet moves in an ellipse with one focus at the sun, show by considering the point when the planet is furthest from the sun that L points in the direction of the major axis of the ellipse.
C.E is offline   Reply With Quote

  Physics Help Forum > College/University Physics Help > Advanced Mechanics

calculus, conservation, question

Thread Tools
Display Modes

Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
calculus of gravitational force jjorg Kinematics and Dynamics 9 Dec 25th 2013 03:09 PM
Question about conservation of momentum!? muon321 Quantum Physics 0 Apr 13th 2013 01:48 PM
Conservation of momentum + Impulse question mikegh Kinematics and Dynamics 1 Oct 4th 2011 01:29 AM
Conservation of Energy Question Verbiski@hotmail.com Energy and Work 1 Feb 16th 2010 08:17 PM
conservation laws: A Spacecraft question C.E Advanced Mechanics 8 Apr 14th 2009 10:22 AM

Facebook Twitter Google+ RSS Feed