19
Hmmm no, it wouldn't be cluttered with debris, and yes, it's a good idea to park the JWST (James Webb Space Telescope) at the Sun-Earth L2 point.
The five Lagrange points are unstable, for one because of the gravitational anomalies of the two massive bodies of the Lagrange system, eccentric orbits, and there are many other factors to their instability. At ...
15
Hubble was in low earth orbit, and was always intended to be serviceable. In fact, the original plan for Hubble was to have the space shuttle carry it down from orbit and take it back up, but they decided that was too risky compared to servicing in orbit.
JWST, on the other hand, will be at the Earth/Sun L2 Lagrange point, like WMAP and Planck before it. ...
12
The L1, L2, and L3 points are unstable in any orbital system. (source)
The L4 and L5 points of a pair of bodies are only stable if the larger of the bodies is at least 25 times as massive than the smaller (source). The ratio of the Pluto/Charon system is only 8.7. Because of this, none of the Lagrange points are stable, and an object orbiting at any of ...
9
Gaia's original science and technology report (see page 221, see also the summary) gives an analysis of the Lissajous orbit. From what I understand Gaia will be placed in a small amplitude Lissajous orbit, giving it an orbital radius of $\sim400000$ km away from $\sim100000$ km along the Sun-Earth axis.
In addition to the fact that this orbit is ...
7
No. Such an arrangement is at best "metastable". That is, although there are periodic solutions to the three body problem (stable orbits) an infintesimal perturbation (eg the proverbial butterfly flapping its wings) will push the system off the stable orbit and into chaos. Getting a planet to remain at the barycentre is like trying to balance a ...
6
My question: is there a way to determine the "stable" region in each Lagrange location? Particularly in the L4 and L5 regions.
tl;dr: Yes but it's usually a fancy version of "trial and error".
We are sometimes wrongly told that this abominable zero-velocity potential diagram show areas that are "bound" or "unbound" to Lagrange points, but it does not and ...
6
The stability of this system depends the ratio of masses of the two stars. If the larger star is more than 25 times more massive than the smaller star, then L5 is potentially stable, and this remains the case even if the planet does not have negligible mass
The calculation of the value is done in detail on physics.stackexchange and there you can establish ...
4
The Lagrangian point $L_2$ is very close to the most distant point from Earth with an umbra.
$L_2$ is like the radius of the Hill sphere at $r=a\sqrt[3]{\frac{m}{3M}}$ for circular orbits, with $m$ the mass of Earth, $M$ the mass of the Sun, and $a$ the distance Earth-Sun. The ratio $\frac{m}{3M}$ of the Earth and the triple mass of the Sun is almost exactly ...
4
It does indeed seem counterintuitive that $L_4$ and $L_5$ would be at the same time both high points of potential as well as stable points in the system. In fact, a quick look at an example contour plot with all five Lagrangian points demonstrated would also suggest that $L_4$ and $L_5$ would be unstable:
In the picture you can see that $L_1 - L_3$ are ...
4
Objects are not place at the Sun-Earth L1 or L2 Lagrange points. They are instead placed in pseudo orbits about these points. These pseudo orbits intentionally avoid being directly in line with the Earth and the Sun for two key reasons. One reason is that these points are directly in the line between the Sun and the Earth. An object at the Sun-Earth L1 would ...
3
For this answer, I'll consider space telescopes to be telescopes that operate in space and that are intended to look at objects at the extremes of the solar system and beyond. This excludes Earth observation satellites, satellites that monitor the Sun, and satellites sent to another planet to observe that other planet as "space telescopes".
Every space ...
3
tldr;
L2 is a very stable thermal environment as well as good instantaneous sky visibility and high observing efficiency.
The main reason space telescopes are placed in an L2 orbit is because L2 is a stable thermal environment. Telescopes in Earth orbit can receive sunlight and earthlight in different directions, meaning that the telescope would have to ...
3
From this source I get:
The size of these islands varies. Each planet in the solar system has
its own Lagrangian points. The islands of stability get bigger farther
from the Sun and also for more massive planets. The ones associated
with Earth are roughly 500,000 miles (800,000 kilometers) wide. The
biggest zones (at least in the solar system) ...
3
The Wikipedia article cites "Zdeněk (1962)" for the statement that the dust responsible for the Gegenschein has a possible concentration at L2. I haven't been able to obtain that paper, but I can't really see why that would be the case, since L2 is not dynamically stable.
However, the dust consists of millimeter-sized grain (see e.g. this APOD image), which ...
3
The L1, L2, L3 points are not stable. (full stop) Small deviations grow exponentially, even in the perfectly circular restricted three-body problem. In reality, we have a non-circular many-body problem, when (1) these points are not strictly well-defined and (2) deviations from the simple case have to be accounted for to obtain the exact trajectories (and to ...
3
In short, most of the trojans stay orbiting arround L4 or L5. These can be called tad-pole orbit asteroids.
There are some trojan asteroids, however, that their orbit never get's too close to L4 nor L5 to get trapped and have a tad-pole orbit, or they do but they have too much energy to get trapped.
These trojan asteroids have larger orbits, following a ...
3
Yes, provided the star is big enough, the "Jupiter" is big enough and the planet is small enough.
The details are discussed herein: "Is there a ceiling for stable L4 or L5 masses?"
To summarise: The sun needs to be 25 times more massive than the giant planet, and the small planet needs to have negligible mass.
It is worth noting that the minor body could ...
3
No
Near-Earth objects (NEOs) may be temporarily captured to oribt Earth as discussed in the reference quoted in the question. Such a capture must invariably involve the NEO to pass by the L1 or L2 points, which are the saddle points in the co-rotating binary potential of the Earth-Sun system.
Thus, these objects have just high enough co-rotating energy (...
3
Yes.
Detection of inner Solar System Trojan Asteroids by Gaia (pdf):
The Gaia satellite, planned for launch by the European Space Agency (ESA) in 2013, is the next generation astrometry mission following Hipparcos. While mapping the whole sky, the Gaia space mission is expected to discover thousands of Solar System Objects. The se will include Near-Earth ...
3
Could there be a planet at the barycenter between two or more stars revolving around each other?
No.
The best case two star scenario is two stars of equal mass. In that case, the barycenter is midway between the two stars and coincides with the L1 Lagrange point. The L1 Lagrange point is metastable. Another name for metastable is unstable. Think of it as a ...
3
"What" is straightforward: L4 and L5 are two points on an orbit that are 60 degrees ahead and 60 degrees behind the planet, and so move as the planet orbits. If the planet is less than about 1/25 of the mass of the central object, then a combination of centrifugal and Coriolis forces will cause the L4 and L5 points to be places where a third body ...
2
The orbit is around L2 at a vast distance from it, perhas > 10,000 km around it.
This is a map of the stability of the lagrangian points:
L2 is unstable, like balancing a pencil on it's tip, but l4 and l5 have a force restoring a deprating object back onto L4.
There is a lot les space debris at L2 that orbiting the earth, JWST has less chance of a hit ...
2
You asked
L3 is obscured by the Sun, so is that true for our viewpoint of the other planets?
No. Each planet orbits with it's own period because each planet is at a different distance from the sun. So most of the time we can see the L3 point of each planet's orbit from Earth. Occasionally it goes behind the sun from our point of view.
For the Hilda's ...
2
All five Lagrange points are unstable
L1, 2, and 3 are "saddle points" in the effective potential formed from the combination of gravity and the centrifugal force of a rotating frame of reference. An object which is in front or behind in the orbit would tend to approach the Lagrange point, and then move away, either towards or away from the sun, following ...
2
Are their orbits circular as Neptune's (in this case) or highly
eccentrical?
L4 and L5 stability is rather narrow
Source: http://ccar.colorado.edu/asen5050/projects/projects_2010/singh/
A more elliptical or eccentric orbit in resonance with a planet with a circular orbit would reach well outside of L4 and L5 and wouldn't be an L4 or L5 object. (though ...
2
Not likely. The sun shade will always be pointed towards Earth and the sun. Thinking about the design, that means the telescope will never be pointed in a direction where it will have gegeschein in its field of view, because otherwise the heating from IR radiation from Earth would cause it problems. The term for the angle between where you're looking and ...
2
Since the question is about inequalities and ratios, I took the script from this answer and made it better by normalizing it, now $a=1, M1=1$ and $m \equiv M2/M1$
For physical situations in the spirit of Hill spheres and Lagrange points, I think the answer is always going to be:
$$r_1 < r_H < r_2$$
but I can't prove it, that would need math and it's ...
2
Bad news, this type of SPK file has a different sort of interpolation that is not supported by the jplephem package (Hermite interpolation vs Chebyshev polynomials). You can find this out by doing:
In [1]: print(len(kernel.segments))
1
In [2]: print(kernel.segments[0]....
2
The angle between the inner and outer edges of the penumbra is the same as the Sun's apparent angular diameter.
At 1.0 au from the Sun, that's 32 arcmin or 0.0093 radian.
At the distance from the Moon to EM-L2, this angle spans 0.0093 * 64700 km = 602 km.
The Moon's diameter is 3474 km, so the umbra diameter would be 2872 km and the penumbra diameter would ...
2
Satellites positioned at L2 has the sun, earth, and moon all behind it so it gets a continuous view of deep space. The Webb Space Telescope will be positioned there. A telescope at L1 would have a continuous view of the Sun and the SOHO satellite is currently there. This link explains some of the benefits in general terms.
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