Gravity is probably the most intriguing force and indeed really special, a gentile but relentless force. It subdue any two objects to mutually attract each other, either at close distance, or through the vastness of the cosmos.

### Gentile but relentless

We might not be aware of gravity all the time here on Earth, but we can surely notice its effects, when we see a falling object, or due the weight we feel as a result of Earth’s gravity acting on our body mass.

As we all might know, artificial satellites and other bodies like the International Space Station orbit Earth, and they maintain semi-stable trajectories as they go around earth, yet these satellites still the need trajectory correction considering that little by little, due the force of gravity, Earth pull these objects towards the planet’s surface, and this effect must be continuously counteracted by using propellant to correct their orbits.

But the Earth orbit option is not the only one we have there are similar locations to position bodies in space (mostly satellites or space probes), located in more distant locations from Earth. These are denominated Lagrange points.

### Lagrange and the three body problem.

Joseph-Louis Lagrange was an Italian Mathematician and astronomer that lived during the eighteen century’s “Age of Enlightenment”; he replaced Euler as the Mathematics director on the Prussian Science Academy in Berlin.

Among his multiple and relevant scientific contributions he published a paper in 1772 about the three-body problem, as part of his astronomy studies; he studying this problem focused mainly on the Earth, Sun and Moon’s interaction, creating a new branch of the Newtonian mechanics denominated, of course, Lagrangian mechanics, where he explaining the mentioned three body problem mechanics and the special case of the then called Lagrangian points.

This problem was formulated from classical mechanics, with the intent of predict the motion of three different bodies using Newton’s gravity laws; knowing only their initial conditions (position, mass and velocity).

### Lagrange points.

Lagrange points are locations where the combined gravitational force (pull or push), caused by two larger bodies over a smaller third body counteracts the centrifugal and gravitational force of it, leaving it in a state of equilibrium, the equivalent spatial of “being parked”. Due this fact these are also called libration points.

There are a total of five Lagrangian points; three of them in a line connecting the two larger bodies. For example, if we consider the Sun and the Earth masses, the first Lagrangian point “L1” is located between the Earth & Sun, the second, “L2”, is in the far side from both Earth and the Sun, and the third, “L3” in a similarly far side region but the opposite side, away from the Sun and Earth. Two additional Lagrange points, “L4” & “L5”, are in the apex of equilateral triangles formed with on side formed by the distance between the Sun and Earth.

The importance of these points is that given its gravitational effect, it allows a steady location for space probes that require to “maintain its distance” from Earth.

Not all these points are equal, the initial three points, L1, L2 and L3, aren’t perfectly stable, and objects located in these need to perform orbit corrections to stay in position; bodies in these points behave like if they were at the top of a mountain, where they potentially can slide through its slope in any direction. On the other hand, Points L4 and L5 have an opposite behavior, being very stable; like objects in a bowl, tending to stay at the bottom of it, bodies in L4 and L5 tend to return to the center of these gravity points if they start to distance themselves; due this reason these points tend to accumulate dust and asteroids, these are called Trojans, in honor to three major asteroids (Agamemnon, Achilles and Hector; characters Troy’s story), located in these Lagrange points between Jupiter and the Sun.

### Lagrange points in space exploration

Due its particular characteristics, Lagrange points are used in special space exploration missions, when its either inefficient to have these proves orbiting Earth or it’s the same Earth’s heat or radiation who make difficult to perform the intended measurements and observations.

Some examples are:

- The WMAP (Wilkinson Microwave Anisotropy Probe), who until 2010 stayed at the Sun-Earth L2 point, and then moved to a sun orbit outside L2 and who did the most detailed measurement of the temperature differences of the Cosmic Microwave background (CMB), basically taking a snapshot of the conditions at the beginning of the universe (the Big bang).
- The SOHO (Solar and Heliospheric Observatory), which is studying the Sun, currently maintains a semi-fixed orbit in L1 between the Sun and the Earth, making an elliptical movement around this point to regularly align with Earth and transmit its data.
- And probably one of the most interesting uses that will be given to these points will be for the location of the James Webb space telescope, which is considered the scientific replacement of the Hubble space telescope, which will be located in the Sun-Earth’s L2 point, to isolate it as much as possible from these bodies’ radiation, as this telescope will operate around bandwidth of infrared light; mission scheduled to be launched the coming 2019, enabling a new era of astronomical and cosmological investigations.

For a long time Lagrange points were just a mere physical and astronomical curiosity till the arrival of the space era and nowadays they are regular destination for space probes, taking advantage of the lower need for orbit adjustments and therefore making more efficient and extending the operational life of current space probes. Lagrange points are truly a a port to anchor our space exploration missions.

Regards, Alex – ScienceKindle.