20070902, 11:07  #1 
"Lucan"
Dec 2006
England
14512_{8} 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 20070902 at 11:21 
20070902, 19:57  #2 
"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 20070902 at 20:55 
20070902, 20:34  #3 
Jun 2003
The Texas Hill Country
3^{2}·11^{2} Posts 
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. 
20070902, 20:57  #4 
"Lucan"
Dec 2006
England
1100101001010_{2} Posts 
THX Wacky. I can't find where this sort of info is hiding ATM

20070903, 05:55  #5 
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 20070903 at 05:57 
20070903, 07:44  #6 
Bronze Medalist
Jan 2004
Mumbai,India
100000000100_{2} 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 
20070903, 20:13  #7 
"Lucan"
Dec 2006
England
194A_{16} Posts 
"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 20070903 at 20:18 
20070904, 12:50  #8  
"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:
Last fiddled with by davieddy on 20070904 at 13:08 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Basic Number Theory 15: Lagrange's theorem, cyclic groups and modular arithmetic  Nick  Number Theory Discussion Group  0  20170107 13:15 
Two points  devarajkandadai  Math  19  20121215 14:15 
My GHz and points are off as of today????  Unregistered  Information & Answers  14  20110927 05:34 
More points for PRP?  Mystwalker  Prime Sierpinski Project  6  20060103 23:32 
Lagrange's Theorem  Numbers  Math  2  20050907 15:22 