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how long did it take james webb to get to l2?

The James Webb Space Telescope is not in orbit around the Earth, like the Hubble Space Telescope is - it actually orbits the Sun, 1.5 million kilometers (1 million miles) away from the Earth at what is called the second Lagrange point or L2. What is special about this orbit is that it lets the telescope stay in line with the Earth as it moves around the Sun. This allows the satellite's large sunshield to protect the telescope from the light and heat of the Sun and Earth (and Moon).

What Is L2?
Joseph-Louis Lagrange was an 18th century mathematician who found the solution to what is called the “three-body problem.” That is, is there any stable configuration, in which three bodies could orbit each other, yet stay in the same position relative to each other? As it turns out, there are five solutions to this problem - and they are called the five Lagrange points, after their discoverer. At Lagrange points, the gravitational pull of two large masses precisely equals the centripetal force required for a small object to move with them. The L1, L2, and L3 points are all in line with each other - and L4 and L5 are at the points of equilateral triangles.

It took roughly 30 days for Webb to reach the start of its orbit at L2, but it took only 3 days to get as far away as the Moon’s orbit, which is about a quarter of the way there. Getting Webb to its orbit around L2 is like reaching the top of a hill by pedaling a bicycle vigorously only at the very beginning of the climb, generating enough energy and speed to spend most of the way coasting up the hill so as to slow to a stop and barely arrive at the top.

In the first hour: The ride to space, solar array deployment, and “free flight.” The Ariane 5 launch vehicle provided thrust for roughly 26 minutes after a morning liftoff from French Guiana. Moments after second stage engine cut-off, Webb separated from the Ariane, which triggered the solar array to deploy within minutes so that Webb could start making electricity from sunshine and stop draining its battery. Webb quickly established its ability to orient itself and “fly” in space.

In the first day: Mid-course correction to L2. Ariane sent Webb on a direct route to L2, without first orbiting Earth. During the first day, we executed the first and most important trajectory correction maneuver using small rocket engines aboard Webb itself. We also released and deployed the high gain antenna to enable the highest available rates of data communication as early as practical.

In the first week: Sunshield deployment. Shortly after we executed a second trajectory correction maneuver, we started the sequence of major deployments, beginning with the fore and aft sunshield pallets. The next step was separation of the spacecraft bus and telescope by extending the telescoping tower between them. The tower extended about 2 meters, which was necessary at this point in the sequence so that the rest of the sunshield deployment could proceed. Next, the sunshield membranes were unpinned and the telescoping sunshield midbooms were extended – first the port side and then the starboard side – pulling the membranes out with them. The last sunshield deployment step was the tensioning of the membranes. In the meantime, other things like radiators were released and deployed.
In the first month: Telescope deployment, cooldown, instrument turn-on, and insertion into orbit around L2. During the second week after launch, we finished deploying the telescope structures by unfolding and latching the secondary mirror tripod and rotating and latching the two primary mirror wings. Note that the telescope and scientific instruments started to cool rapidly in the shade of the sunshield, but it took several weeks for them to cool all the way down and reach stable temperatures. This cooldown was carefully controlled with strategically-placed electric heater strips so that everything shrinks carefully and so that water trapped inside parts of the observatory can escape as gas to the vacuum of space and not freeze as ice onto mirrors or detectors, which would degrade scientific performance. We unlocked all the primary mirror segments and the secondary mirror and verified that we can move them. Near the end of the first month, we executed the last mid-course maneuver to insert into the optimum orbit around L2. During this time we also powered-up the scientific instrument systems. The remaining five months of commissioning were all about aligning the optics and calibrating the scientific instruments.
In the second, third and fourth months: Initial optics checkouts, and telescope alignment. Using the Fine Guidance Sensor, we pointed Webb at a single bright star and demonstrated that the observatory could acquire and lock onto targets, and we took data mainly with NIRCam. But because the primary mirror segments had yet to be aligned to work as a single mirror, there were distorted images of the same single target star. We then embarked on the long process of aligning all the telescope optics, beginning with identifying which primary mirror segment went with which image by moving each segment one at a time and ended a few months later with all the segments aligned as one and the secondary mirror aligned optimally. Cooldown effectively ended and the cryocooler started running at its lowest temperature and MIRI started taking good data too.

In the fifth and sixth months: Calibration and completion of commissioning. We meticulously calibrated all of the scientific instruments’ many modes of operation while observing representative targets, and we demonstrated the ability to track “moving” targets, which were nearby objects like asteroids, comets, moons, and planets in our own solar system. We made “Early Release Observations,” to be revealed right after commissioning was over, that showcased the capabilities of the observatory.
After six months: “Science operations!” Webb began its science mission and started to conduct routine science operations. 

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