While applying the Lagrange interpolation for a given set of points with unequal values, the functions coincide at each point. The L2 point is rapidly establishing itself as a pre-eminent location for advanced spaceprobes and ESA has a number of missions that will make use of this orbital 'sweet-spot' in the coming years. At those locations the two-body calculation based on the Earth and the Sun also predicts station-keeping (that is, equilibrium in a frame of reference rotating with the Earth). Lagrangian mechanics is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in 1788.. The other two Lagrangian points, L4 and L5, are on the Earth's orbit, with the lines linking them to the Sun making 60° angles with the Earth-Sun line. You may have to register before you can post: click the register link above to proceed. I wrote this calculator to be able to verify solutions for Lagrange's interpolation problems. L2 will become home to ESA missions such as Herschel, Planck, Eddington, Gaia, the James Webb Space Telescope and Darwin. Not only to 3-body systems; I’m trying to extend the calculation to n-body systems (consider, for example, Jupiter or Pluto systems, where the perturbations are very big). Calculating the location of a Lagrange Point such as L1 is an excellent way to see how difficult math problems can be solved by keeping Lagrange Points The Lagrange Points are the five locations near Earth's orbit which orbit the Sun with the exact same period as the Earth, due to the combined effect of the Sun and Earth's gravity. Lagrange points calculation If this is your first visit, be sure to check out the FAQ by clicking the link above. A reference is Cornish (pdf) . In these problems you are often asked to interpolate the value of the unknown function corresponding to certain x value, using Lagrange's interpolation formula from the given set of data, that is, set of points x, f(x).. Zero-Velocity Surfaces Up: The Three-Body Problem Previous: Co-Rotating Frame Lagrange Points Let us search for possible equilibrium points of the mass in the rotating reference frame. It is, thus, clear that these points are fixed in the rotating frame. Such points are termed Lagrange points.Thus, in the rotating frame, the mass would remain at rest if placed at one of the Lagrange points. Interpolation Calculator.Input the set of points, choose one of the following interpolation methods (Linear interpolation, Lagrange interpolation or Cubic Spline interpolation) and click "Interpolate".The interpolation calculator will return the function that best approximates the given points according to the method chosen. What are "Lagrange points", also known as "libration points" or "L-points"? It turns out that L1, L2, and L3 all have positive real natural frequencies and therefore are unstable. The calculator below can assist with the following: These are all jargon for places where a light third body can sit "motionless" relative to two heavier bodies that are orbiting each other thanks to the force of gravity. Lagrangian points L1 L2 L3 L4 L5: Lagrangian points, good place : Automatic translation : Category: probes and satellites Updated June 01, 2013: Lagrange point is a vantage point of space, described by Joseph-Louis Lagrange in 1772.