Question

Formula to calculate the lagrangian point where the forces acting from two bodies dissappear on a satellite

Answer 1

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. L4 and L5 each form an equilateral triangle with the centers of the 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.

Several planets have trojan satellites 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.[2] The Lagrangian points have been proposed for uses in space exploration.