Lagrangian Point: Overview, Questions, Preparation

Lagrangian Point can be understood as the paradigm in which the objects launched into space stay put in a region, primarily because of the repulsion and attraction of gravitational force created between two large bodies. The aircraft as an object here stay put between two large bodies like the earth and the sun. Aircraft can save up a lot of fuel consumption this way.

There are 5 Lagrangian points, and they are between L1 to L5. The first three Lagrangian points were invented by Leonhard Euler, i.e., L1, L2, and L3. Joseph Louis discovered the L4 and L5 Lagrangian Points.

Let us study the mathematical details of the Lagrange points.

1. L1 Point: The L1 point lies between M1 and M1 (two large masses) and the line made by the masses. Gravitational force partially cancels all the gravitational attraction of M1. It can be represented as follows:

M1 (R − r)2 = M2 / r2 + M1 / R2 – r (M1 + M2) / R3

Here, the distance between the two objects is denoted as R,

The distance of L1 point is represented by r

The masses of the large and small objects are denoted as M1 and M2, respectively.

2. L2 Point: The L2 point is defined as the line between two large masses and beyond the smaller one of the totals of two. The gravitational force manages and balances the centrifugal effect on the L2 by using two large masses. It can be written as:

M1 (R − r)2 + M2 / r2 = M1 / R2 + r (M1 + M2) / R3

Here, the distance of the L2 point from the smaller object is represented as r.

3. L3 Point: The L3 point is also defined by the two masses, M1 and M2 and beyond the larger of the two, unlike the L2 point. It can be written as:

M1 (R − r)2 + M2 / (2 R – r)2 = (M2 / M1 + M2 R + R – r) M1 + M2 / R3

4. L4 and L5 Points: The L4 and L5 points lie in the center of the two masses M1 and M2 to lie at the third part of the two equilateral triangles. It can be written as:

A = − GM1 / r2 sgn (r) + GM2 / (R − r)2 sgn (R − r) + G ((M1 + M2) r − M2 R) / R3

Lagrangian Point for Class 11

The chapter 'Gravitation' holds a weightage of only 4 marks. It includes 2 questions in total consisting of one very short question of 1 mark and one short question of 3 marks, giving a total of 4 marks.

Example 1: Name the Lagrangian Points.

Answer: L1, L2, L3, L4, and L5

Example 2: Write the equation of L1 point.

Answer: The equation can be written as:

M1 (R − r)2 = M2 / r2 + M1 / R2 – r (M1 + M2) / R3

Example 3: Write the representation of the distance between two objects.

Answer: The distance between two objects is denoted as R.

Q: What do you mean by Lagrangian Point?

Q: What is the other name of Lagrangian Point?

Q: How many types are there of Lagrangian Point?

Q: Who discovered the L1, L2, and L3?

Q: Who discovered L4 and L5?