Lagrange Point 2

JPL Horizons ephemeris:

Revised: Aug 29, 2013                SEMB-L2                                32

                      (Sun & Earth-Moon Barycenter Lagrange 2)

  #1) The Sun & Earth-Moon Barycenter Lagrange-2 (L2) point is a location where the Earth's gravitational field partially counters that of the Sun.

  #2) This L2 point is about 1.5 million km (~900,000 miles) away from the Earth, opposite the direction of the Sun, or slightly less than one percent of the Earth-Sun distance (four times the distance from Earth to the Moon) 

  #3) L2 has been selected as the location of the next generation James Webb Space Telescope, was used by the Genesis spacecraft on the return to Earth, and is (or will be) used for WMAP, Herschel, and Planck spacecraft. 

 Time-span available: 1900-Jan-01 to 2151-Jan-01

NASA web page on Lagrange Points

Wikipedia page on Lagrange Points

3D HTML Visualizations: 

• 52-week animation of the Webb Space Telescope (JWST) orbiting around L2 (File: 383 KB). 

• Static plot of L2 and the Sun, with the Earth's Hill Sphere (Large File: 5.3 MB)

• 52-week animation of L2 and the Sun from an Earth-centered perspective (File: 143 KB)

• 52-week animation of L2, the James Webb Space Telescope and the Sun from an Earth-centered perspective (File: 194 KB)

• 60-week animation of L1-L5 (Large File: 5 MB)

• Static plot of all the Solar-Earth and Earth-Moon Lagrange points (Large File: 7.2 MB)

The first image shows the Webb Space Telescope's orbit around L2:

The beautiful saddle-shaped pattern you're observing in JWST's orbit around the Sun-Earth L2 point is called a "halo orbit," and it's a fascinating example of celestial mechanics.

Three-Body Dynamics JWST orbits in a complex gravitational environment influenced by both the Sun and Earth. The L2 point itself isn't a fixed location but rather a dynamic equilibrium point where the gravitational forces of the Sun and Earth, combined with the centrifugal force of the orbital motion, balance out.

Why Not a Simple Circle? If JWST were simply "parked" at L2, it would be unstable - like balancing a ball on top of a hill. Any small perturbation would cause it to drift away. Instead, JWST follows a large periodic orbit around the L2 point, which is actually stable.

The regular saddle or figure-8 pattern:

1. Perpendicular Motion Components: JWST moves in all three dimensions around L2, creating loops that appear as a saddle when viewed from certain angles.

2. Coriolis Forces: As JWST orbits with Earth around the Sun, Coriolis forces create the characteristic twisting motion.

3. Gravitational Gradients: The varying strength of gravitational pull as JWST moves closer to or farther from Earth creates the regular oscillation.

Benefits of this orbit:

• Continuous Sunlight: The orbit keeps JWST out of Earth's shadow, ensuring constant solar power.

• Stable Temperature: Always facing away from Sun, Earth, and Moon for optimal infrared observations.

• Minimal Station-keeping: The orbit requires very little fuel to maintain (only small adjustments every ~21 days).

• Clear Communications: The orbit ensures JWST never goes behind the Sun from Earth's perspective.

The period of this orbit is approximately 6 months, which is why you see such a regular, repeating pattern in the animation. It's a beautiful example of how we can use complex gravitational dynamics to our advantage in space missions.

Coriolis force in space: 

The Coriolis force is an apparent force that appears when you're observing motion from within a rotating reference frame. For JWST at L2:

• JWST is in a reference frame that rotates with Earth around the Sun (one rotation per year).

• From this rotating viewpoint, objects appear to experience forces that aren't "real" in an inertial frame.

• If it moves "radially" (toward or away from the Sun), it appears to be deflected sideways

• If it moves "tangentially" (in the direction of Earth's orbit), it appears to be pushed inward or outward

In the rotating frame that keeps Earth-Sun-L2 aligned:

• Coriolis acceleration = -2Ω × v

• Where Ω is Earth's orbital angular velocity (one revolution/year)

• And v is JWST's velocity relative to L2

The Coriolis force contributes to the saddle shape by:

1. Coupling the motions: Movement in one direction automatically creates acceleration in a perpendicular direction.

2. Creating rotation: This coupling tends to turn straight-line motions into curved paths.

3. Stabilizing the orbit: It helps create the closed, periodic orbit instead of letting JWST drift away.

Think of it like this: As JWST tries to move in its orbit around L2, the fact that the whole system is spinning around the Sun causes JWST's path to curve in complex ways, contributing to that beautiful saddle pattern you observed.

It's not the only force creating the pattern (gravity gradients are crucial too), but it's an essential ingredient in the orbital dynamics recipe.

The second image shows L2 orbiting around Earth:

• You can see that L2 orbits around the Earth at the edge of the Earth's zone of gravitational influence, its Hill Sphere. This is the point where the gravitational influence of the Earth balances that of the Sun. This is a feature of Lagrange points. You can explore this view in 3D in the HTML visualization.

• In the HTML 3D animation of L2 and the Sun, you can see that as the year progresses over 52 weeks, the Sun appears to move around the Earth (the old geocentric perspective) and L2 also moves around the Earth in a position opposing the Sun's. Zoom in to see L2. 

• In the HTML 3D animation of L2, the James Webb Space Telescope and the Sun, you can see how JWSP follows the intricate "saddle" orbit around L2 as both orbit around the Earth and the Sun over a year.

The third image shows L1 through L2 orbiting around the Sun:

• L1 and L2 are much closer to Earth and harder to see. You can zoom in. 

The fourth image shows all the Lagrange points for both the Sun-Earth system and the Earth-Moon system. 

• You can also download the complete plot here.