# Lagrangepunt

##### Article

January 26, 2022

A Lagrange point (named after the Italian mathematician and astronomer Joseph-Louis Lagrange) is a specific form of orbital resonance. At a Lagrangian point, a small object such as a space station can maintain a fixed relative position to two celestial bodies orbiting a common center of gravity. This position is more or less stable, depending on the case. The mass of the object in the Lagrangian point must be negligible in relation to the two celestial bodies and this mass must have the correct speed and direction. Any two-body system that revolves around a common center of gravity has five Lagrangian points, three of which lie on the line connecting the two celestial bodies. Two-body systems to which this applies are, for example, sun and earth, the sun and another planet, and the earth and its moon. Instead of "standing still" at a Lagrangian point, the small object can also orbit around it. Lagrangian points have several advantages as a position for a space station, just as geostationary orbit has advantages for certain observation and communication purposes.

## Lagrangian points of the sun-earth system

The Lagrangian points are explained below for the Sun-Earth system, but this also applies mutatis mutandis to other two-body systems.

## Lagrangian point L1

The point L1 lies on the straight line between Earth and Sun. According to Kepler's Third Law, an object closer to the sun than the earth must have a shorter orbital period than the earth. However, if we get close enough to Earth on the straight line between Earth and Sun, Earth's gravity will counteract that of the Sun, and the orbital period of an object at that point will lengthen. This creates the point L1, in which the orbital period is equal to that of the Earth. Approximate applies to the distance from the earth X ( m a a r d e 3 m z O n ) 1 / 3 d {\displaystyle x\left({\frac {M_{earth}}{3M_{sun}}}\right)^{1/3}d} After filling in the mass of the earth: 5,972•1024 kg, mass of the sun: 1,989•1030 kg and the distance earth-sun: 149,600,000 km, we get a distance of 1.5 million km from the earth. Lagrange point L1 is therefore four times the distance from the moon, in the direction of the sun. Joseph-Louis Lagrange (1736-1813) first calculated this point. The solar observation satellite Solar and Heliospheric Observatory (SOHO) is located in L1, so it has a continuous view of the sun. The satellite orbits L1 so that it is not exactly in the direction of the sun. This would make communication difficult due to interference with solar radiation. Also, an orbit around L1 is only possible in the plane perpendicular to the earth-sun line, given the stability of L1. SOHO's orbit has a semimajor axis of about 660,000 km in the direction of orbit around the sun. With a distance of about 1.5 million kilometers from Earth, the maximum deviation from the sun's direction is several tens of degrees. The Deep Space Climate Observatory (DSCOVR) is also located here.

## Lagrangian point L2

Lagrange point L2, just like L1, lies on the axis between Earth and Sun, but this time further from the Sun than the Earth. An object orbiting outside of Earth normally has g

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