Lagrange Points

 

Lagrange Points - What makes them so special.

 

Lagrange Points, named in the honour of French-Italian mathematician Joseph Lagrange, are 5 equilibrium points located in the vicinity of two orbiting masses. These points are special, because an object dropped at any of these points, will have a constant orbit. This means the body needs less corrections, i.e., less fuel consumption. Joseph discovered these points while studying the restricted three body problem.

The 5 Lagrange Points in the Earth-Sun system

 

To understand why Lagrange Points are in equilibrium, look at the image below.

 

This is a contour map of a two-body system. The gravitational force due to the masses can be visualized by the holes. Since our spacecraft will be in rotatory motion, it will experience some outward fictional force, called the centrifugal force. This force can be visualized by the curvature of the space.

 

Now we can see five points that are relatively stable compared to any other point. These points are marked in the picture above. These five points are the Lagrange Points.

·        The first three points are collinear and meta-stable, which means any object on these points may drift out of orbit, hence requiring some corrections. In the image, we can clearly see that if a body is at any of these points, a little shift can make it fall into the holes.

1.      L1 point in the Earth-Sun system is home to the SOHO observatory as it provides an uninterrupted view of the sun.

2.      L2 point is home to the James Webb Space Telescope.

3.      L3 is home to no satellites because it is always hidden behind the sun.

 

·        The next two points, L4 and L5, form an equilateral triangle with the two masses and are very stable. This is due to the Coriolis force. Because of the stability of these points, dust and asteroids tend to accumulate in these regions. L4 and L5 are also possible points for a space colony due to their relative proximity to Earth, at least according to the writings of Gerard O'Neill and related thinkers.

 

These points act as a parking spot for the satellites to make observations without wasting a lot of fuel to stay in required orbit.