Lagrange points

Lagrange points are locations in space where the combined gravitational forces of two large bodies, such as Earth and the sun or Earth and the moon, equal the centrifugal force felt by a much smaller third body.

There are five Lagrange points known as L1, L2 and L3 that are unstable equilibrium points while L4 and L5 are stable.

The five Lagrange points rotate with the system as it revolves.

Lagrange points are named in honor of the 18th century Italian-French mathematician Joseph-Louis Lagrange

Earth Sun lagrange points L1-L5

Sun-Earth system. In this case, the Sun is the center, and the Earth revolves around this. There are corresponding L1-5 points for the Sun-Earth system. Because the Sun is so massive, the L1 point for the Sun-Earth system is just 1.5 million km from the Earth.

Lagrange Points: Space Parking Spots

Unstable Lagrange Points L1, L2 and L3

Objects placed there will drift, and the more they drift, the stronger the forces will be to move them further away. Satellites placed in these locations need assistance to remain on station using "halo orbits".

Stable Lagrange Points L4 and L5

objects placed there will tend to remain there. These regions of stability are slightly 'kidney' shaped.

sun-earth lagrange regions

Earth Moon Lagrange points

Earth-Moon L4 and L5 might make good locations for man-made space colonies, but unfortunately these regions live outside the protection of the Earth's magnetosphere and so get bombarded with cosmic rays.

They could make useful locations for communicating with deep space probes when the sun is in opposition with Earth with respect to the probe.

Sun Mars Lagrange points

Placing a communications satellite in Mar's L4 or L5 points could be very useful for when the Mars is in Opposition (behind the Sun) when there is no direct communications available.

Sun Jupiter Lagrange points

Jupiter's L4 and L5 points are interesting for the large number of what are called 'Trojan asteroids' nesteds at these two points in Jupiter's orbit (L4 and L5).

L1, or Lagrange Point 1 (sometimes a Libration point) is unstable

L1 is the nearest point in a straight line between two masses where the mass attraction on a third object will balance between the two points.

Earth/Sun: L1 is located about 1.5 million km from Earth, between the sun and Earth, along a line from the sun to Earth.

L2 , or Lagrange Point 2 is unstable

Earth/Sun: L2 is located about 1.5 million km from Earth along the same line, opposite side of Earth from the Sun.

Earth/Moon: L2 is on the opposite side of the Moon from the Earth.

L3, or Lagrange Point 3 is also unstable

Earth/Sun: L3 is on the opposite side of the Earth from the Sun, so is not so easy to use.

Earth/Sun: L3 also cannot direct directly to Earth.

L4 , or Lagrange Point 4 is stable

L4 'Trojan asteroids follow behind a planet in its orbit around the Sun

L5 , or Lagrange Point 5 is stable

L5 'Trojan asteroids proceed the planet in its orbit around the Sun.

Lissajous orbits

Lissajous orbit is a path around the L1 or L2 Lagrangian points of a two-body system, in a quasi-periodic orbital trajectory that an object can follow around a Lagrangian point of a three-body system without requiring any propulsion.

In a Lissajous orbit the spacecraft follows a natural (but complex) motion that requires the minimum amount of energy for station-keeping, unlike a halo orbit, in which the craft follows a simple circular or elliptical path.

Lissajous orbit is named after Jules Antoine Lissajous.