# Lagrangian Points

Lagrangian points, often referred to as “L-points,” are specific positions in space where the gravitational forces of two large celestial bodies, such as the Earth and the Moon or the Earth and the Sun, balance the centripetal force felt by a smaller object, like a spacecraft or a satellite. These points were named after Joseph-Louis Lagrange, an Italian-French mathematician who studied them in the late 18th century.

**Five Lagrangian points**

**There are five Lagrangian points in the Earth-Sun system, denoted as L1, L2, L3, L4, and L5. Each of these points has unique characteristics and applications:**

**1. L1 (Lagrange Point 1):**

– Located along the line connecting the two massive bodies, with the smaller object (e.g., a satellite) closer to the larger body (e.g., Earth).

– The gravitational forces from both bodies effectively cancel each other out at this point, allowing an object to stay relatively stationary with respect to them.

– L1 is commonly used for solar observatories like the SOHO (Solar and Heliospheric Observatory) because it provides an uninterrupted view of the Sun.

**2. L2 (Lagrange Point 2):**

– Also located along the line connecting the two massive bodies but on the opposite side of the larger body from L1.

– Objects at L2 can stay in a stable position with respect to the Earth and Sun.

– L2 is used for various astronomical observatories, such as the James Webb Space Telescope (JWST), which needs to observe distant objects with minimal interference from Earth’s atmosphere.

**3. L3 (Lagrange Point 3):**

– Situated directly opposite L1 along the same line.

– Objects at L3 are not stable and tend to drift away from this point, so it is not used for long-term missions.

**4. L4 and L5 (Lagrange Points 4 and 5):**

– Located at equal distances from both massive bodies in a 60-degree triangular configuration with them.

– Objects in these points form an equilateral triangle with the Earth and Sun (or another pair of massive bodies). L4 leads the smaller body in its orbit, while L5 follows it.

– L4 and L5 are considered stable points and are often used for the placement of satellites and objects like Trojan asteroids.

The stability of objects at Lagrangian points depends on their positions relative to the masses of the two primary bodies and any additional forces, such as solar radiation pressure. Objects at L4 and L5 are considered the most stable, followed by L1 and L2, while L3 is unstable. For long-term missions at these points, spacecraft may need to make occasional small adjustments to maintain their positions due to perturbations from other celestial bodies.

In summary, Lagrangian points are unique positions in space where the gravitational forces of two massive bodies allow for the stable placement of objects. They have important applications in space exploration, astronomy, and satellite deployment, enabling missions that require specific geometric relationships between celestial objects.

**Aditya L1**

Aditya-L1 is a satellite dedicated to the comprehensive study of the Sun. It has 7 distinct payloads developed, all developed indigenously. Five by ISRO and two by Indian academic institutes in collaboration with ISRO.

Aditya in Sanskrit means the Sun. L1 here refers to Lagrange Point 1 of the Sun-Earth system. For common understanding, L1 is a location in space where the gravitational forces of two celestial bodies, such as the Sun and Earth, are in equilibrium. This allows an object placed there to remain relatively stable with respect to both celestial bodies.

Following its scheduled launch on September 2, 2023, Aditya-L1 stays Earth-bound orbits for 16 days, during which it undergoes 5 maneuvres to gain the necessary velocity for its journey. Subsequently, Aditya-L1 undergoes a Trans-Lagrangian1 insertion maneuvre, marking the beginning of its 110-day trajectory to the destination around the L1 Lagrange point. Upon arrival at the L1 point, another maneuvre binds Aditya-L1 to an orbit around L1, a balanced gravitational location between the Earth and the Sun. The satellite spends its whole mission life orbiting around L1 in an irregularly shaped orbit in a plane roughly perpendicular to the line joining the Earth and the Sun.

The strategic placement at the L1 Lagrange point ensures that Aditya-L1 can maintain a constant, uninterrupted view of the Sun. This location also allows the satellite to access solar radiation and magnetic storms before they are influenced by Earth’s magnetic field and atmosphere. Additionally, the L1 point’s gravitational stability minimizes the need for frequent orbital maintenance efforts, optimizing the satellite’s operational efficiency.

Quick Facts: Aditya-L1 will stay approximately 1.5 million km away from Earth, directed towards the Sun, which is about 1% of the Earth-Sun distance. The Sun is a giant sphere of gas and Aditya-L1 would study the outer atmosphere of the Sun. Aditya-L1 will neither land on the Sun nor approach the Sun any closer.

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**Source: ISRO**