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Lagrange Points Applet (1)

 The Lagrangian points are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be stationary relative to two larger objects (such as a satellite with respect to the Sun and Earth):

Lagrange Applet (2)

An article of N. Treitz inspired me to write this applet.

 A circular orbit around the common center of mass bc of the two bodies is assumed (circular restricted three body problem). The distance of the bodies M and m is a = rM + rm. The barycenter bc of the masses M and m is at distance rM = a·m/(M+m) from the center of M. The three curves of my applet represent the accelerations (positive to the right, negative to the left). At the position x=r of the Lagrange point L1 we have: aM (red) by the mass M (red), at distance r+rM from the center of M am (blue) by the mass m (blue), at distance a-rM-r from the center of m a (green) the resulting sum of the accelerations.

 Select from the view options of the menu. You may use the key "r", or "R" (shift key and "r", faster) to rotate the system around the center of mass. Click the applet first ! Select "Reset" to return.

Select "Data Sun-Earth" from the menu:

The solutions of my simple iteration method agree within 10-6 % with those by a series (Th. Münch)

Select "Data Earth-Moon" from the menu:

The solutions of my simple iteration method agree within 10-2 % with those by a series (Th. Münch)

For the Earth-Moon system (M/m=81.3) the point L1 is at a distance of 0.163·a from the Moon

 Web Links N. Treitz:  am Himmel, Spektrum der Wissenschaft, Oktober 2006 The Lagrange Points (NASA) Gaia's Lissajous Type Orbit Klemperer Rosettes Satellite in the triangular libration point (example 7) Lagrange points for two similar masses Satellites Click, drag and release to set location, speed and direction. Try to manage a Lagrange point! Orrery: Solar System Simulator lagrange points Th. Münch: The Three-Body Problem and the Lagrangian Points system Determination of Lagrange Points

Updated: 2023, Oct 06