mersenneforum.org Lagrange points L4 and L5
 User Name Remember Me? Password
 Register FAQ Search Today's Posts Mark Forums Read

 2007-09-02, 11:07 #1 davieddy     "Lucan" Dec 2006 England 145128 Posts Lagrange points L4 and L5 We have three different masses located at the vertices of an equilateral triangle. Show that their accelerations due to gravity are directed towards the centre of mass and inversely proportional to the square of their distances from it. If their initial velocities (relative to the c of m) are at 120 degrees to each other and proportional to their distance from the c of m, show that their elliptical orbits have identical periods. David Last fiddled with by davieddy on 2007-09-02 at 11:21
 2007-09-02, 19:57 #2 davieddy     "Lucan" Dec 2006 England 2×3×13×83 Posts A neater way of posing the problem is as follows: if L is the side of the equilateral triangle and r is the position of a mass relative to the C of M, show that acceleration = -k*r/L^3. What is k? (The similarity of orbits follows from this) PS where can I find out why [bold] isn't working? Last fiddled with by davieddy on 2007-09-02 at 20:55
2007-09-02, 20:34   #3
Wacky

Jun 2003
The Texas Hill Country

32·112 Posts

Quote:
 Originally Posted by davieddy PS where can I find out why [bold] isn't working?
Who says that it isn't working? Just because it doesn't do what you suggest it should ...

Now if you were looking to place a part of your response in boldface type, you should use "B" rather than "bold". That is much more likely to have the desired effect.

 2007-09-02, 20:57 #4 davieddy     "Lucan" Dec 2006 England 11001010010102 Posts THX Wacky. I can't find where this sort of info is hiding ATM
 2007-09-03, 05:55 #5 S485122     Sep 2006 Brussels, Belgium 17·89 Posts FAQ Reading and Posting Messages Are there any special codes/tags I can use to format my posts? vB Code List Last fiddled with by S485122 on 2007-09-03 at 05:57
 2007-09-03, 07:44 #6 mfgoode Bronze Medalist     Jan 2004 Mumbai,India 1000000001002 Posts THX S-----. I have not been aware of this and have never used this powerful code before. I must try a post in Tex. Mally
2007-09-03, 20:13   #7
davieddy

"Lucan"
Dec 2006
England

194A16 Posts

Quote:
 Originally Posted by S485122 FAQ
"Nobody bothers to read this"

BTW if you want to know what the three masses are called
they ar z1, p2 and j42.
I thought that went without saying

Last fiddled with by davieddy on 2007-09-03 at 20:18

2007-09-04, 12:50   #8
davieddy

"Lucan"
Dec 2006
England

2×3×13×83 Posts

Don't know whether this "puzzle" was too easy/hard/badly posed
but since there have been no takers, here is my solution which IMHO
is quite neat:

Quote:
 Originally Posted by davieddy Label the masses 1,2 and 3 and consider the acceleration of m1 due to the gravitational attraction of 2 and 3. This is (m2(r2 -r1)+ m3(r3 -r1))G/L3 We also have m1r1 + m2r2 + m3r3 = 0 by definition of centre of mass. It follows that the acceleration of m1 is -G(m1 + m2 + m3)r1/L3 David

Last fiddled with by davieddy on 2007-09-04 at 13:08

 Thread Tools

 Similar Threads Thread Thread Starter Forum Replies Last Post Nick Number Theory Discussion Group 0 2017-01-07 13:15 devarajkandadai Math 19 2012-12-15 14:15 Unregistered Information & Answers 14 2011-09-27 05:34 Mystwalker Prime Sierpinski Project 6 2006-01-03 23:32 Numbers Math 2 2005-09-07 15:22

All times are UTC. The time now is 13:38.

Fri May 29 13:38:25 UTC 2020 up 65 days, 11:11, 1 user, load averages: 2.45, 2.67, 2.77

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.