# A Giant Leap in Space Exploration

When you ask an astronomer about the James Webb Space Telescope’s orbit, they’ll tell you something that sounds like it came from a science-fiction novel. The Webb won’t be orbiting the Earth –instead we will send it almost a million miles out into space to a place called “L2.”

L2 is short-hand for the second Lagrange Point, a wonderful accident of gravity and orbital mechanics, and the perfect place to park the Webb telescope in space. There are five so-called “Lagrange Points” – areas where gravity from the sun and Earth balance the orbital motion of a satellite. Putting a spacecraft at any of these points allows it to stay in a fixed position relative to the Earth and sun with a minimal amount of energy needed for course correction.

The term L2 may sound futuristic and mysterious, but the name actually honors a Mathematician born in 1736. The Lagrange points were named after the Italian-born mathematician and astronomer Joseph-Louis Lagrange, who made important contributions to classical and celestial mechanics. Lagrange studied the “three-body problem” (so-called because three bodies are orbiting each other) for the Earth, sun, and moon in 1764, and by 1772 he had found the solution; there are five stable points at which you could put an object and have it stay fixed in place relative to the other two.

In the case of L2, this happens about 930,000 miles away from the Earth in the exact opposite direction from the sun. The Earth, as we know, orbits the sun once every year. Normally, an object almost a million miles farther out from the sun should move more slowly, taking more than a year to complete its orbit around the sun. However, at L2, exactly lined up with both the sun and Earth, the added gravity of the two large bodies pulling in the same direction gives a spacecraft an extra boost of energy, locking it into perfect unison with the Earth’s yearly orbit. The Webb telescope will be placed slightly off the true balance point, in a gentle orbit around L2.

[Image Detail: The James Webb Space Telescope (identified as “JWST” here) relative to the Hubble telescope’s orbit around the Earth. Credit: NASA]

Why send the Webb telescope all the way out to L2? When astronomers began to think about where the Webb telescope should be placed in space, there were several considerations to keep in mind. To begin with, the Webb telescope will view the universe entirely in infrared light, what we commonly think of as heat radiation. To give the telescope the best chance of detecting distant, dim objects in space, the coldest temperatures possible are needed.

The James Webb Space Telescope (JWST) is a large, infrared-optimized space telescope, scheduled for launch in 2014. JWST will find the first galaxies that formed in the early Universe, connecting the Big Bang to our own Milky Way Galaxy. JWST will peer through dusty clouds to see stars forming planetary systems, connecting the Milky Way to our own Solar System. JWST’s instruments will be designed to work primarily in the infrared range of the electromagnetic spectrum, with some capability in the visible range.

JWST will have a large mirror, 6.5 meters (21.3 feet) in diameter and a sunshield the size of a tennis court. Both the mirror and sunshade won’t fit onto the rocket fully open, so both will fold up and open once JWST is in outer space. JWST will reside in an orbit about 1.5 million km (1 million miles) from the Earth.[Source: JWST Homepage]

With the sun and the Earth in the same part of the sky, the Webb telescope will enjoy an open, unimpeded view of the universe. In comparison, the Hubble Space Telescope is in low-Earth orbit where it goes in and out of the Earth’s shadow every 90 minutes. Hubble’s view is blocked by the Earth for part of each orbit, limiting where the telescope can look at any given time.

The Spitzer Space Telescope, another infrared telescope, is in orbit around the sun and drifting away from the Earth. Spitzer is already more than 100 million kilometers (60 million miles) away from the Earth, and eventually its path will take it to the other side of the sun. Once we can no longer communicate with Spitzer that means it is at the end of its mission life.

In contrast, a major perk of parking at L2 is the ease of communications. Essentially, the Webb telescope will always be at the same point in space. “We can have continuous communications with Webb through the Deep Space Network (DSN),” Gardner said. “During routine operations, we will uplink command sequences and downlink data up to twice per day, through the DSN. The observatory can perform a sequence of commands (pointing and observations) autonomously. Typically, we will upload a full week’s worth of commands at a time, and make updates daily as needed.”

Even before the Webb telescope, L2 has been known to astronomers as a good spot for space-based observatories. There are already several satellites in the L2 orbit, including the Wilkinson Microwave Anisotropy Probe, and the Herschel and Planck space observatories. But there’s plenty of room for another neighbor, and the Webb telescope will be heading out to L2 in the near future.

The Lagrange Points

Lagrangian points are the stationary solutions of the circular restricted three-body problem. For example, given two massive bodies in circular orbits around their common center of mass, there are five positions in space where a third body, of comparatively negligible mass, could be placed which would then maintain its position relative to the two massive bodies. As seen in a rotating reference frame with the same period as the two co-orbiting bodies, the gravitational fields of two massive bodies combined with the satellite’s circular motion are in balance at the Lagrangian points, allowing the third body to be stationary with respect to the first two bodies.[Ref: Wikipedia]

Finding The Lagrangian Points

The easiest way to see how Lagrange made his discovery is to adopt a frame of reference that rotates with the system. The forces exerted on a body at rest in this frame can be derived from an effective potential in much the same way that wind speeds can be inferred from a weather map. The forces are strongest when the contours of the effective potential are closest together and weakest when the contours are far apart.

In the above contour plot we see that L4 and L5 correspond to hilltops and L1, L2 and L3 correspond to saddles (i.e. points where the potential is curving up in one direction and down in the other). This suggests that satellites placed at the Lagrange points will have a tendency to wander off (try sitting a marble on top of a watermelon or on top of a real saddle and you get the idea). A detailed analysis (PDF link) confirms our expectations for L1, L2 and L3, but not for L4 and L5. When a satellite parked at L4 or L5 starts to roll off the hill it picks up speed. At this point the Coriolis force comes into play – the same force that causes hurricanes to spin up on the earth – and sends the satellite into a stable orbit around the Lagrange point.

[Sources: NASA, WMAP and JWST Homepage]