Lagrange Points: How James Webb Orbits Around "NOTHING"?
The James Webb Space Telescope has finally arrived at the Sun-Earth L2 point after a 1.5
million kilometer voyage. After the dramatic unfolding of the telescope, it is finally in
its designated orbit. Webb had earlier spent the last 30 days gradually and carefully unfolding its
sunshield and other important instruments. A Mid-Course Correction burn, dubbed as
"MCC-2 placed the James Webb in an orbit around L2. In fact, it sent it into a very huge orbit,
more than double the size of the Moon's orbit around Earth! Webb will take around six months
to complete a single orbit around L2, and this initial phase will be totally packed with mirror
alignments, phasing, sensor calibrations, moving target tracking tests, verifications,
station maintaining maneuvers, and, eventually, the first science observations by the telescope.
But what precisely makes the L2 so unique? I mean, it's simply a point in space,
and an empty one at that. So, how can Webb orbit something that does not exist?
In this video we will talk about how James Webb orbits around nothing.
It is true that the L2 is empty, but circling empty spots in space is really rather common.
That's because anytime two heavy entities circle one another, they both orbit a shared center of
mass, or "barycenter." If the objects are large enough, the center of mass will be somewhere in
the middle. We only say the Moon circles the Earth because its center of mass is within the Earth.
However, because Pluto and Charon have comparable masses, their barycenter is located somewhere
in the space between them. So the idea that anything may circle an empty point space isn't
all that surprising, but it is a two-body system. It doesn't explain how Webb can orbit a location
that isn't in the orbit of another two-body system. The good news is that we can deconstruct
this problem and figure out what the L2 point is and how Webb can circle around it. In reality,
numerous spacecraft have previously orbited L2, including NASA's WMAP Satellite and ESA's Planck
and Herschel observatories, and both Russia's Spektr-RG and ESA's Gaia spacecraft are now
circling there. So what is L2? What are lagrange points and why are they so helpful for James webb.
When you ask an astronomer about the orbit of the James Webb Space Telescope, they'll tell you
something that sounds like it's straight out of a science-fiction novel. The Webb will not orbit the
Earth; instead, we will launch it almost a million miles into space to a location known as "L2."
L2 is short for the second Lagrange Point, a marvelous accident of gravity and
orbital mechanics that serves as the ideal location for the Webb telescope in space.
There are five "Lagrange Points" - locations where gravity from the sun
and Earth balances a satellite's orbital velocity.
Placing a spacecraft at any of these sites allows it to maintain a constant position relative to
the Earth and sun while using as little energy as possible for course adjustment. The acronym L2 may
sound futuristic and intriguing, but it really celebrates a 1736 Mathematician. The Lagrange
points are named after Joseph-Louis Lagrange, an Italian-born mathematician and astronomer. L2 is
one of the five Lagrangian points that connect the Sun to the Earth. Actually,
these five locations occur in the vicinity of any two-body system, therefore there are
Lagrangian points for the Earth-Moon system, a set of points for the Sun-Jupiter system, and so on.
If a third object is put at any of these sites, the gravitational forces of the two enormous
bodies cooperate to keep the third object stable in relation to the others. The practical result
is that the third body follows the system as it circles. As a result, the Sun-Earth L1 point is an
excellent location for both Sun-facing missions such as the Solar Heliospheric Observatory and
Earth-facing projects such as DISCOVR. Similarly, L2 is the location for astrophysics missions such
as Gaia and Webb. Even while Earth circles the Sun, spacecraft at both places retain
continual line-of-sight connection with Earth. Webb, on the other hand, places a premium on L2.
Because a single sun shield can block the heat of the Sun, Earth, and Moon. That's an ideal
location for infrared astronomy. However, there are a few crucial limitations. For one thing, the
third item must have a very, very little mass in comparison to the larger bodies. That, obviously,
is not an issue. Webb's mass is insignificant in comparison to Earth, let alone the Sun.
The other limitation is that the Lagrangian points, particularly the first three,
are better characterized as metastable. Imagine a flawlessly smooth and frictionless saddle to
get a sense of what I mean. Consider attempting to balance a marble in the saddle's precise center.
It is theoretically feasible, but it is incredibly difficult to do in practice. An object traveling
perpendicular to the Sun-Earth line falls toward the center, which is similar to the L2 point.
However, it then either falls toward or away from Earth. If Webb slips away from Earth,
it will be in serious jeopardy since the only way to get it back is to turn around and push back.
However, this will cause the telescope to rapidly warm up! The mission would be over
when all of the constructions expanded, glues and adhesives melted, and the mission would be done.
That's a negative thing. Webb's thrusters are only on the observatory's warm,
Sun-facing side.This is due to the fact that hot thrusters would contaminate the cool
telescope's side with heat or rocket exhaust that would otherwise condense on the optics.
This too would be bad for the Webb telescope. A safer approach for placing Webb, is to place it
very near to L2, but not quite at L2. As a result, Webb is never at risk of dropping below L2,
where it cannot be retrieved. That's why the Ariane 5 launch was purposefully intended to
slightly undershoot, allowing the spacecraft to do a sequence of Mid Course Correction burns.
The first two, MCC-1a and MCC-1b, were carried out on the route to L2. However, coming even slightly
short of L2 introduces a new issue. The Sun is permanently eclipsed by Earth at that distance.
Webb is fueled by the sun. It could now employ nuclear power, but that is both expensive and
difficult to implement. Another issue is that Coriolis forces might lead Webb to
break free near L2. In other words, Webb would be trapped in a small orbit around
L2 that would need even more engine fires. Oh, and the Moon's gravity on Webb is still a thing,
and it changes all the time as it circles Earth. These real-world problems can be handled by simply
establishing a big orbit around L2. But how can you orbit something that doesn't exist?
To understand this better we need to take into account the various forces acting on Webb.
If Webb were at L2, it would be subjected to gravitational pulls from both the Sun
and Earth. Now that Webb is circling the Sun, we can think of a centrifugal force dragging Webb
in the other direction. The amazing thing about L2 is that the centrifugal force is precisely
balanced by the gravity of the Earth and Sun at this distance. You may have heard that there is
no such thing as a centrifugal force, which is right, but since we are dealing with a rotating
non inertial frame, centrifugal forces are still a handy means of summarizing all of the real effects
that are taking place. Also to keep it simple we won’t take into account the effects by the
gravitation of the moon. Now if we move Webb up some distance away from L2 horizontally,
let's call it L2 prime for our understanding, it will send it farther away from the Earth and
its gravitational pull gets weaker. It's also no longer parallel with the Sun's direction, either.
To compensate this, Webb is not totally placed at the L2 point aws we mentioned earlier.
It is near to the L2, so that it doesn’t slip away into space.
But there’s another problem now, Webb might get pulled towards the earth. However, when
it approaches the Sun-Earth line, Earth's gravity becomes greater and it travels closer to Earth.
We can't let it happen because the heat load would be too much for the sunshield to bear.
We can, however, offset this downward force by pushing Webb sideways into a circular orbit,
just like the one you can see in the image on the screen. . This creates a fresh centrifugal force
that balances the downward force of gravity on Earth. When combined with the sideways motion,
Webb takes up a new circular halo orbit around L2-prime. That means Webb is simply being pulled
by the Y component of Earth's gravitational force. This explanation might seem a bit overwhelming at
first but it's a very oversimplified version. The actual calculations the scientists at NASA
did is way too complicated, taking into accounts all kinds of forces.
To make matters easier, Webb was not really launched to L2. It was instead launched to a
location around the edge of L2. Webb performed its MCC-2 burn to settle into its orbit as
it began to fall away and is now into an orbit that is tilted by about 33 degrees.
The orbit is also not exactly round, but rather has an elliptical form. As a result, the distance
between Webb and the L2 point ranges between 250,000 and 832,000 kilometers. For comparison,
the Moon's semi-major axis is around 400,000 kilometers, therefore Webb's orbit around L2
is massive! This big orbit was chosen because it makes it much easier to arrive at L2. The further
something is from its orbital focus, the slower it moves and the less energy it takes to manipulate.
Because of the wider orbit, Webb will never be in the shadow of the Earth or the Moon during
its mission. Larger orbits, on the other hand, may allow stray light from the Earth
or Moon to get through the sunshield and reach the primary or secondary mirrors.
Furthermore, a larger orbit may limit the number of connection possibilities with the Deep Space
Network. As a result, Webb will have to vary its orientation during its orbit to keep stray
light off the mirrors at all times, as well as plan the communication downlinks properly.
Webb completes one orbit around L2 in around six months. Although it occasionally flies out
a little bit past this point. The geometric center of the orbit remains the L2-prime point on Earth's
side. Remember, we don't want that ball in the center of the saddle. As a result,
Webb will perform tiny stationkeeping burns every now and again to keep its orbit stable.
Every year, missions like Gaia only require three to four of these burns. Webb, on the other hand,
will require significantly more frequent burns for a variety of reasons. For one thing,
its sunshield is constantly subjected to a torque caused by solar radiation pressure.
By spinning up its response wheels, Webb can counteract this rotating force. However,
because the solar radiation pressure is constant, the reaction wheels must spin faster with time.
A station-keeping burn is eventually necessary to spin Webb back into position and allow the
wheels to throttle down. Webb's orientation also shifts as it points from one location to the next.
All of these movements significantly disrupt Webb's orbit, necessitating more station-keeping
burns to sustain. That is why Webb does a burn once every 21 days. The Flight Dynamics Team at
NASA's Goddard Space Flight Center calculates the exact time and duration of such burns.
So Hats off to these scientists for doing such precise calculations and allowing us to look
into the questions of our origins. So What did you learn about the Orbit of James webb?
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