Welcome, Guest. Please Login.
Gravity Simulator
11/24/17 at 16:13:51
News: Registration for new users has been disabled to discourage spam. If you would like to join the forum please send me an email with your desired screen name to tony at gravitysimulator dot com.
Home Help Search Login


Pages: 1
Send Topic Print
Lagrange Points (Read 6801 times)
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1507
Gender: male
Lagrange Points
11/22/10 at 13:56:53
 
Ever wondered about lagrange points ?  
http://en.wikipedia.org/wiki/File:Lagrange_points2.svg gives a very good representation about this special points in space .  
Especially the L4 and L5 points are of interest as they harbour the Trojans in the Sun-Jupiter system .  
It's not easily to represent them in terms of gravitational potential  because the points in fact are at a maximum of the gravitational potential and the difference in gravitaional potential is hughe ( in fact infinite  as we go to the center of the sun ) . L4 and L5 represent a hill with small slope in potential while the Sun and Jupiter represent a hughe sink . So , very difficult to represent .  
The above picture adds the equipotential lines in order to represent the potential.
Back to top
 
 
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1507
Gender: male
Re: Lagrange Points
Reply #1 - 11/22/10 at 14:15:40
 
In fact the gravitational potential for a 1 kg mass ranges from -1.77e+11 to -2.66 e+8 Joules from the center of mass towards the L4 or L5 point .  
( energy represented in a rotating frame with Jupiter )  
This range is hard to represent by means of a colour plot .  One would hardly notice the hilltop.  
A way to work around this hughe "hill" is to work iteratively  and start with the small region on the top.  
Then gradually let increase the minimum value .  
The animation hereunder starts at an intermediate potential level and gradually goes op the hill , towards the L4 and L5 region .
Back to top
 

GravLagGlobal.gif
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1507
Gender: male
Re: Lagrange Points
Reply #2 - 11/22/10 at 14:21:17
 
"Zooming" in further , i.e starting at an intermediate level close to the Lagrange hill and raising the potential in small steps gives the following picture :  
 
The above animations were made with the following data : M1 = Msun ; M2 = 0.1 Msun ; Sma = SmaJup .
Back to top
 

LagPointsDetail.gif
Email View Profile   IP Logged
EDG
Ultimate Member
*****


oh, crumbs!!!

Posts: 611
Gender: male
Re: Lagrange Points
Reply #3 - 11/22/10 at 15:26:19
 
Cool! How are you making the animations?  
 
And can you add other bodies in interior/exterior orbits to see if those mess up the stability of a planet's lagrange points?
Back to top
 
 

(formerly known as Mal)
View Profile WWW   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1507
Gender: male
Re: Lagrange Points
Reply #4 - 11/22/10 at 15:37:02
 
Quote from Mal on 11/22/10 at 15:26:19:
Cool! How are you making the animations?
And can you add other bodies in interior/exterior orbits to see if those mess up the stability of a planet's lagrange points?

Euh .. with a lot of work and trial and error  embarrassed
I wrote a PBasic program to calculate the shapes , plotted tem and animated them /  
If you are interested I can provide the program here  
 
To second question : No , this isn't possible because the plots are in rotating frame . Other bodies , except from  those in coorbital motion cannot be represented because they move in such a frame
Back to top
 
 
Email View Profile   IP Logged
rsanchez
Uploader



I Love YaBB 2!

Posts: 6
Re: Lagrange Points
Reply #5 - 11/22/10 at 19:15:00
 
I'm interested in how you did it.  Smiley
Back to top
 
 
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1507
Gender: male
Re: Lagrange Points
Reply #6 - 11/23/10 at 10:44:57
 
Quote from rsanchez on 11/22/10 at 19:15:00:
I'm interested in how you did it.  Smiley

Here's the non compiled code , written in PowerBasic . It will generate some screenshots ( for k=1.....) representing the log of the effective potential .  
Feel free to ask if you run in trouble .  
If necessary I can make an executable in which the necessary parameters can be changed ...
Back to top
 
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1507
Gender: male
Re: Lagrange Points
Reply #7 - 11/23/10 at 10:59:59
 
The animation herunder shows the contours of effective potential .  
 
It starts at a low potential . Gradually the potential rises till the hills at the L4 and L5 points are reached .  
The animation halts at the L1, L2 and L3 points .  
It is noticable that all the points on the same contour can be reached by a body , as the effective potential is constant along the contour line .  
Given of course the body has zero velocity in this rotating frame.  
Animated is the case : M2=0.1 M1 , where M1=Msun and sma = SmaJup .  
Back to top
 

LagrangePointsContours.gif
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1507
Gender: male
Lagrange Points in 3D
Reply #8 - 11/27/10 at 05:24:50
 
I couldn't resist going one step further  Wink
For those who have anaglyph 3D glasses :  
The animation shows the gravitational potential , starting at the top at the L4 and L5 points and gradually decreasing towards the sink at the biggest mass.  
It may take some time before eyes are adapted , but one schould clearly see the slow bulbs around L4 and L5 and the sinks towards the two masses.  
Parameters were : M1=Msun ; M2=0.1M1 ; sma = 5AU .
Back to top
 

GravPotLagr3D_0p1_Mass.gif
Email View Profile   IP Logged
Pages: 1
Send Topic Print