Force map of the Lagrange points

jaufrec · 03-04-2002, 04:13 AM

<img src="http://map.gsfc.nasa.gov/m_ig/990529/990529b.jpg" alt="picture of lagrange forces">
The Lagrange points are places between two heavenly bodies where small objects can orbit stably. L1, L2, and L3 are stable but precarious, and any random bump (like solar wind or the influence of the other planets) can dislodge you. But L4 and L5 are metastable - if you get close, you'll get gently sucked in and you'll stay put. There are actually clusters of asteriods at the L4/L5 points of the Sun/Jupiter system. Looking at this picture I thought I understood why 1-3 are stable and 4-5 aren't - 1-3 are at "saddles" whereas 4 and 5 are in depressions. But reading the <a href="http://map.gsfc.nasa.gov/m_mm/ob_techorbit1.html">text on the page</a>, it's even weirder. 4 and 5 really are hills - any bump and you should start to slide away. But in 4 and 5, Coriolis force pushes you back. That's the force that works in orbit like this (I think): going up makes you slower, going slower makes you go down, going down makes you go faster, going faster makes you go up. If you think that's confusing, well, orbital mechanics isn't rocket science; it's harder.

verbatim · 03-04-2002, 10:59 AM

We are just finished learning about this in physics. I think the reason L4 and L5 are stable because of the acceleration due to gravity. At L4 its gaining massive amount of speed because it is heading towards the two bodies of mass, and at L5 it looses most of the acceleration, so there is less of a chance to pull it into either of the planets/suns. L3 is percarious(sp?) cause at that point it has the least speed. Its something dealing with Kepler's laws. Its the one that deals with a line sweeps out equal areas in the same amount of time, and that the speed and gravity is greatest at the perihelion and least at the aphelion. Its some crazy shit like that. First person to make sense of it all gets $5.

Joe · 03-04-2002, 11:26 AM

Space can (if you want to anyway) be thought of as a somewhat flat surface with low spots caused by gravity. While not really accurate, the analogy works for thinking. The isobars shown in the image can be thought of as topographical lines (again if you want to).

Envision setting a sphere on our imaginary space plane. The sphere will roll downhill. No space is truly "flat", it all leans to some degree into a low. The degree of "steepness" will indicate whether the sphere will very slowly drift across a huge empty area, or get wickedly yanked into a black hole.

The Lagrange points are areas of space where the contour of the surface is such that a sphere could rest there without rolling toward a low. The gravity pulls equally in all directions.

The unstable points are the ones where something could stay, but the coutour drops off steeply nearby. If the object gets bumped, see ya. The stable ones are more like plateau areas. Objects would need more of a shove to get them to move to the sloping areas.

russotto · 03-04-2002, 01:20 PM

L1, L2, and L3 are unstable -- as you say, they're saddle points, which is to say they're stable in one direction but unstable in the other.

L4 and L5 are stable (metastable, because a large enough disturbance can toss you out of them).

As for orbital mechanics, it's easy:

East takes you out
Out takes you west
West takes you in
In takes you east
North and south bring you back
-- Larry Niven, _The Smoke Ring_

Undertoad · 03-04-2002, 02:50 PM

I don't understand why the moon doesn't screw up any of these points. Al Gore was gonna put a camera at L1 and show us all what we look like...

Joe · 03-04-2002, 02:53 PM

They blew off mapping the Moon. It also has a Lagrange point w/respect to the Earth.

Griff · 09-20-2002, 07:04 PM

Welcome back to Earth.

03-04-2002, 04:13 AM	#1
jaufrec Neophyte-in-training Join Date: Mar 2002 Posts: 3	Force map of the Lagrange points <img src="http://map.gsfc.nasa.gov/m_ig/990529/990529b.jpg" alt="picture of lagrange forces"> <p>The Lagrange points are places between two heavenly bodies where small objects can orbit stably. <b>L1</b>, <b>L2</b>, and <b>L3</b> are stable but precarious, and any random bump (like solar wind or the influence of the other planets) can dislodge you. But <b>L4</b> and <b>L5</b> are <b>metastable</b> - if you get close, you'll get gently sucked in and you'll stay put. There are actually clusters of asteriods at the L4/L5 points of the Sun/Jupiter system. <p>Looking at this picture I thought I understood why 1-3 are stable and 4-5 aren't - 1-3 are at "saddles" whereas 4 and 5 are in depressions. But reading the <b><a href="http://map.gsfc.nasa.gov/m_mm/ob_techorbit1.html">text on the page</a></b>, it's even weirder. 4 and 5 really are hills - any bump and you should start to slide away. But in 4 and 5, Coriolis force pushes you back. That's the force that works in orbit like this (I think): going up makes you slower, going slower makes you go down, going down makes you go faster, going faster makes you go up. If you think that's confusing, well, orbital mechanics isn't rocket science; it's harder.

03-04-2002, 10:59 AM	#2
verbatim Vice-President of Resentment Join Date: Jun 2001 Location: Pennsultucky Posts: 199	We are just finished learning about this in physics. I think the reason L4 and L5 are stable because of the acceleration due to gravity. At L4 its gaining massive amount of speed because it is heading towards the two bodies of mass, and at L5 it looses most of the acceleration, so there is less of a chance to pull it into either of the planets/suns. L3 is percarious(sp?) cause at that point it has the least speed. Its something dealing with Kepler's laws. Its the one that deals with a line sweeps out equal areas in the same amount of time, and that the speed and gravity is greatest at the perihelion and least at the aphelion. Its some crazy shit like that. First person to make sense of it all gets $5. __________________ <-- I'm with stupid

03-04-2002, 11:26 AM	#3
Joe Master of the Domain Join Date: Sep 2001 Location: AZ Posts: 221	Here's my guess: Space can (if you want to anyway) be thought of as a somewhat flat surface with low spots caused by gravity. While not really accurate, the analogy works for thinking. The isobars shown in the image can be thought of as topographical lines (again if you want to). Envision setting a sphere on our imaginary space plane. The sphere will roll downhill. No space is truly "flat", it all leans to some degree into a low. The degree of "steepness" will indicate whether the sphere will very slowly drift across a huge empty area, or get wickedly yanked into a black hole. The Lagrange points are areas of space where the contour of the surface is such that a sphere could rest there without rolling toward a low. The gravity pulls equally in all directions. The unstable points are the ones where something could stay, but the coutour drops off steeply nearby. If the object gets bumped, see ya. The stable ones are more like plateau areas. Objects would need more of a shove to get them to move to the sloping areas.

03-04-2002, 02:53 PM	#6
Joe Master of the Domain Join Date: Sep 2001 Location: AZ Posts: 221	Yeah They blew off mapping the Moon. It also has a Lagrange point w/respect to the Earth.

09-20-2002, 07:04 PM	#7
Griff still says videotape Join Date: Feb 2001 Posts: 26,813	Welcome back to Earth. __________________ If you would only recognize that life is hard, things would be so much easier for you. - Louis D. Brandeis

03-04-2002, 01:20 PM	#4
russotto Professor Join Date: Jan 2001 Posts: 1,788	L1, L2, and L3 are unstable -- as you say, they're saddle points, which is to say they're stable in one direction but unstable in the other. L4 and L5 are stable (metastable, because a large enough disturbance can toss you out of them). As for orbital mechanics, it's easy: East takes you out Out takes you west West takes you in In takes you east North and south bring you back -- Larry Niven, _The Smoke Ring_

03-04-2002, 02:50 PM	#5
Undertoad Radical Centrist Join Date: Jan 2001 Location: Cottage of Prussia Posts: 31,423	I don't understand why the moon doesn't screw up any of these points. Al Gore was gonna put a camera at L1 and show us all what we look like...

Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)