What is Lagrange points: Definition and 18 Discussions

In celestial mechanics, the Lagrange points (also Lagrangian points, L-points, or libration points) are points near two large orbiting bodies. Normally, the two objects exert an unbalanced gravitational force at a point, altering the orbit of whatever is at that point. At the Lagrange points, the gravitational forces of the two large bodies and the centrifugal force balance each other. This can make Lagrange points an excellent location for satellites, as few orbit corrections are needed to maintain the desired orbit. Small objects placed in orbit at Lagrange points are in equilibrium in at least two directions relative to the center of mass of the large bodies.
There are five such points, labeled L1 to L5, all in the orbital plane of the two large bodies, for each given combination of two orbital bodies. For instance, there are five Lagrangian points L1 to L5 for the Sun–Earth system, and in a similar way there are five different Lagrangian points for the Earth–Moon system. L1, L2, and L3 are on the line through the centers of the two large bodies, while L4 and L5 each act as the third vertex of an equilateral triangle formed with the centers of the two large bodies. L4 and L5 are stable, which implies that objects can orbit around them in a rotating coordinate system tied to the two large bodies.
The L4 and L5 points are stable gravity wells and have a tendency to pull objects into them. Several planets have trojan asteroids near their L4 and L5 points with respect to the Sun. Jupiter has more than a million of these trojans. Artificial satellites have been placed at L1 and L2 with respect to the Sun and Earth, and with respect to the Earth and the Moon. The Lagrangian points have been proposed for uses in space exploration.

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  1. Cerenkov

    B Is the barycentre of the Pluto - Charon system also the L1 point?

    Hello. I've been reading about the Lagrange points... https://en.wikipedia.org/wiki/Lagrange_point ...and also about Pluto and its moons. Having discovered that the barycentre of the Pluto - Charon system lies at a point in space between the dwarf planet and its major moon Charon a number of...
  2. S

    I Working model to demonstrate Lagrange points L4 & L5 -- possible?

    If we fabricate a surface like this... (source:www.youtube.com/watch?v=7PHvDj4TDfM) ... and rotate it around the appropriate vertical axis at the appropriate speed, would it be possible to get a bead to roll in an "orbit" around L4 or L5. (a) Possible at all in principle? (b) Practical...
  3. Mukhtar

    I Is it possible to build a Telescope the Size of Half the Solar System size using all Lagrange Points?

    If all the Lagrange Points(L1, L2, L3 and L4) are utilized to depart telescopes like JWST, Luvoir and Habex then is it possible to have a Telescope aperture with a half size of Solar System?
  4. Cerenkov

    B Questions about Lagrange points in the Pluto / Charon system

    Hello. With the recent interest in the JWST orbiting at the L2 Lagrange point of the Earth - Moon system, I was wondering about the dynamics of the Pluto - Charon system. Specifically, the barycentre of that system. This barycentre lies at a point in space between these two bodies. Does...
  5. T

    B Delta-v from Lagrange points to lunar surface?

    What is the delta-v requirements from each of the Earth-Moon lagrange points to landing on the lunar surface? What would be the best software I could use to visualise and calculate that kind of thing? Thanks.
  6. Dr Wu

    B Earth-Sun Lagrange Points Distance Query

    Hi Does anyone know what the straight line distances of L4 and L5 are from Earth? Many thanks.
  7. nomadreid

    I Why are Lagrange points called libration points, and....

    Two questions about Lagrange points. (1) According to Wikipedia, "libration is a perceived oscillating motion of orbiting bodies relative to each other," whereas the Lagrange points are, with respect to two bodies, null points for a (real or hypothetical) third body with respect to the sum...
  8. Dr Wu

    Do Mars' Lagrange Points Exist Near Phobos and Deimos?

    I'm trying to find out if Mars has any Lagrange Points - L1 and L2 specifically. A lengthy trawl through Google's webpages suggest that they may exist, although if so they would be extremely close to Mars, being gravitationally bound by Phobos and Deimos. Is this true? PS. Should Mars indeed...
  9. Imager

    B Understanding the Lagrange Points: What's Going Wrong with L2 and L3?

    The Wiki article shows 5 Lagrange points. I can “see” how the points L1, L4 and L5 points would be balanced by the gravitation of the two bodies, but not the L2 and L3. For L2 and L3, it looks to me like the combination of the Sun’s and Earth’s gravity increase pull and make less stable. So...
  10. H

    Help with contour plots of effective potential in R3BP.

    Hello everyone! I'm currently trying to plot the effective potential for Sun-Jupiter system, to show the lagrangian points in this system. I've converted to a system of units where G=1, m_sun+m_jupiter=1 and R=1, whereby I get the following equation describing the effective potential of a third...
  11. S

    Lagrange Points Calculation Work

    (Sorry text is hard to read, please see attached document for an easier read) I am having trouble with #6, I'm not sure if what I have going on is entirely correct. Also #7 is a little confusing. Problem Statement & work done: For an object in orbit around a second, there are five LaGrange...
  12. C

    What is the width of the Lagrange points?

    Hello everyone! I just finishexd reading Death By Black Hole and I was interested in the Lagrange points. Neil talks about how if you placed objects inside of them you could use the points as place holders for objects while building in space. I couldn't seem to find anything about the width of...
  13. G

    Orbiting around Lagrange points

    Physics gurus: I understood from Newton's Law that a 2 bodies would rotate around their common center of mass. Should one body disappear (Harry Potter invoked here), the other would go flying off at a tangent... like a 'David's Sling" releasing a missile. The mass of the bodies was crucial to...
  14. C

    Lagrange Points, Maximum mass and their effects

    So, I'm working through some ideas dealing with Lagrange points. I understand that, the rotation and mass of 2 objects in space create stable areas where an object of "insignificant Mass" compared to the objects it's balancing against, allows for the placement of an object in a stable area...
  15. C

    Force needed to reach Lagrange Points

    I'm trying to figure out how much force, over what period of time, is necessary to reach an earth-moon Lagrange point. L1 is about 323110 kilometers from earth, and an object there could remain (more or less) stationary relative to the Earth and the moon. Earth gravity is working against the...
  16. M

    Help Me Solve a Physics Homework Problem - Lagrange Points

    Hey a friend asked me for help on his physics homework, and I found this place and was wondering if you guys could help me out. 2: In 1772, the famed Italian-French mathematician Joseph Louis Lagrange was working on the infamous three-body problem when he discovered an intersting quirk in the...
  17. M

    Calculating Escape Speed, Lagrange Points, & Stress/Strain of Rope

    1: Determine the escape speed of a rocket on the far side of Ganymede, the largest of Jupiter's moons. The radius of Ganymede is 2.64 X 10^6m, and its mass is 1.495 X 10^23 kg. The mass of Jupiter is 1.90 x 10^27 kg, and the distance between Jupiter and Ganymede is 1.071 X 10^9m. Be sure to...
  18. Greg Bernhardt

    How many LaGrange points does the Earth/Moon system have?

    A)How many LaGrange points does the Earth/Moon system have? B) How many are stable (no stationkeeping neccessary)? C) Roughly where are the stable points located? 1/2 point point for each answered correctly