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19

You are most likely seeing an artifact of how JPL represents its ephemerides for fast numerical computation. JPL integrates the equations of motion over time. This inevitably results in mismatches between the integrated state and observations. These errors are used to adjust initial states and the integration is then re-performed. The cycle stops when the ...


18

In a two body system the total energy, the sum of kinetic energy and potential energy is constant for each body. If the total energy is constant for each body, the total energy for the whole system is also constant. So energy conservation is valid for each body alone as well as the system. In a three body system energy may be exchanged between the bodys. ...


16

According to Wikipedia, the delta-v requirements to stay at L1 or L2 are about 30-100 m/s per year. That seems quite high, however, more likely is around 5-16 m/s. The sun shield has an area of about 300 m^2. The thrust possible is about 0.00279664 N, assuming purely reflective. Mass of JWST is about 6200 kg. Putting all of that together, the possible ...


15

Halo orbits and their cousins Lissajous orbits (like the one DSCOVR is in) around the Sun-Earth L1 and L2 have periods of about a half-year. They are not generally stable and they want to "unwind" along what's called an unstable manifold. In Is this what station keeping maneuvers look like, or just glitches in data? (SOHO via Horizons) I link to ...


15

Halo orbit families exist near the L1, L2, and L3 librations points. This video focuses on the L1 and L2 halo families. There are northern and southern families at each of the libration points. The northern family is identical to the southern family but mirrored across the x-y plane. At each point, the family bifurcates from the planar Lyapunov family of ...


14

This Northrop Grumman video (starting at 09:31) illustrates JWST's orbit in a non-rotating (normal) frame. It's really in an orbit around the Sun about 1% farther than Earth's, but the weak tug of Earth pulls it along a bit faster so that it remains in 1:1 resonance with the Earth. The orbit is called a "Halo orbit" because in a rotating frame it looks like ...


10

What is the required burn to keep a satellite at a Lagrangian point? tl;dr: typical station keeping delta-v for a halo orbit around Sun-Earth L1 or L2 points are of the order of 2 to 4 meters/sec per year based on a very old spacecraft (SOHO) and a future spacecraft (JWST). I'll address the two closest and most used Lagrange points; L1 and L2. Generally ...


9

There are several reasons why spacecraft are sent into pseudo-orbits (they aren't actually "orbits") about the unstable Lagrange points. The least important reason is that only one spacecraft can be at one of those Lagrange points. Wide pseudo-orbits allow multiple spacecraft to simultaneously operate in the vicinity of one of those Lagrange points. More ...


8

This paper by Heiligers et al. explores Earth-moon libration point orbits with the addition of solar sail thrusting. While it is of course not directly translateable to Sun-Earth L2 (JWST) the dynamics of libration point orbits in both systems are at least comparable. The study shows that an increase in stability can be acquired for some orbits (lunar L2 ...


7

I don't have too much time to research as I'm about to head off to work, but a quick investigation of the JWST doesn't show anything that could be used for Astrogation. Curiosity can do its own pathfinding in part because of the programming genius of its creators, and also because of how easily detectable the obstacles are. A camera can easily detect a ...


7

eRosita is on its way to an elliptical orbit around L2 (with L2 in the centre of the ellipse). (image source: https://www.slideshare.net/esaops/wilms, p. 19) According to Merloni et al. (2012, https://arxiv.org/abs/1209.3114), the semi-major axis is planed with about 1,000,000 km and the orbital period should be about 6 months. Taking a look into the ...


7

In fact, they are the preferred option among other staging orbits by analizing multiple factors: EARTH ACCESS: A study considering NASA SLS and Orion performances was carried out. Since SLS places Orion in a trans-lunar trajectory, Orion vehicle has to carried out orbital maneuvers to reach a orbit near the Moon, so the limiting factor will Orion's ...


7

Sorry that I'm so late to this, but I worked with the butterfly family quite a lot when I was a student in Professor Howell's group so I feel compelled to answer! It looks like you found some good resources already, but I can expand a bit and show some more of the family :) I have quite a few visualizations of the L2 southern butterfly family in the Earth-...


6

tl;dr: I think there could be room to do this. However, I don't think a conclusive answer can be had through analyses of magnitudes on envelope-backs. A real answer would only come from even more detailed Monte Carlo calculations than those already outlined in Stationkeeping Monte Carlo Simulation for the James Webb Space Telescope. Sounds like a fun project!...


6

The State Transition Matrix (STM) The STM is a linearization procedure of a dynamical system. It can be used for any non-linear dynamical system and is used to approximate the dynamics of a system over short period of times. In astrodynamics, it is used especially for statistical orbit determination (stat OD) and the circular restricted third body problem (...


6

As the halo orbits grow out of plane, their orbital periods generally decrease. You can see a plot of the period (in days) of the L1 and L2 halo families at the Moon as a function of the closest approach distance from the Moon (rp) in Figure 2 of this paper: https://engineering.purdue.edu/people/kathleen.howell.1/Publications/Conferences/2017_AAS_DavPhiHow....


6

There are really two questions here: Do there exist $n$-body systems with long-term stability? Can a third body (massive or not) be shown, a-priori, to be bounded or to escape—without resorting to numerical simulation? 1. Stability of $n$-body systems It is widely known that $n$-body systems are "chaotic" when $n>2$. However, this must be unpacked ...


5

Basically, it would not be orbiting L2 in a Keplerian orbit sense. There is no mass at L2 for the spacecraft to orbit, you are correct in that sense. The JWST would be in a solar orbit in that would normally be a little longer than one year and would use the contours of the gravitational fields from the Earth and the Sun around the Earth-Sun L2 point to ...


5

Halo orbits are a sub-class of Lissajous orbits. So that image showing a simple circular-ish orbit is just showing a 1:1 Lissajous pattern. These Lagrange-point orbits are really orbiting around the larger body, in a way that's resonant with the smaller body. If we talk about the Earth-Sun system, then satellites like DSCOVR, SOHO (L1) and the (hopefully) ...


5

For those Lagrangian points which are unstable, L1, L2 and L3, there is no equilibrium, and any movement off the point will accelerate further away, towards the Sun or Earth. For them, you would need to counteract v1 (and any gravitational forces undergone along the way) in order to reach a rest velocity with respect to the Lagrangian point plus you would ...


5

What the pseudo-potential surface is: A plot of a 3D function. What the pseudo-potential surface is not: A hill to make a marble roll around on. All confusion around this thing comes from making the assumption that it is a regular 3D surface, which will behave just as you expect it to if you were to drop a marble on it. You can make the same nonsensical ...


5

You are likely looking for "KoLoMaRo". http://www.cds.caltech.edu/~koon/book/KoLoMaRo_DMissionBk.pdf Wang Sang Koon, Martin W. Lo, Jerrold E. Marsden and Shane D. Ross "Dynamical Systems, the Three-Body Problem, and Space Mission Design"


4

No. The gateway is not bound to Earth, if we interpret "bound to Earth if the Moon disappears" as not drifting into interplanetary space regardless of what instance the Moon's gravitational influence is disregarded. There's a neat property of zero-gain flybys: At the point of closest approach, the velocity vector of the spacecraft is parallel to ...


4

tl;dr: For a given pair of bodies in circular orbits around their center of mass, there are two symmetric families ("Northern" and "Southern") of proper halo orbits associated with each of the Lagrangian points L1, L2, and L3. We usually only talk about those with L1 and L2 because L3 is so far away from the secondary body (Earth in the case of Sun-Earth ...


4

The Earth-Moon L2 is located about 1.16 times as far from the Earth as the centre of the Moon (wikipedia, so the Earth is about 7 times as from L2 as the Moon is. Since the Earth is less than 7 times the Moon's diameter the Moon would protect a telescope at L2 (or in any small halo orbit around it) from all radio noise directly from the Earth and from LEO. ...


4

We want to find NEOs that are inside Earth's orbit, like Atens, and telescopes don't like looking close to the Sun. So the more inside the orbit of the Earth you can get, the more new NEOs you will find without having to look at the Sun. Ideally you'd like a NEOCAM near the orbit of Venus. Then you'd be able to catch 'em all. But at E-S L1, you'll find most ...


4

The pseudo-potential/effective potential for the circular restricted 3-body problem is the sum of the gravitational and the centrifugal potential, cf. Fig. 1. $\uparrow$ Fig. 1: The 2D orbital plane with equipotential lines and the 5 Lagrange points. (From Wikipedia.) The main shortcoming of the linked video is that it fails to mention the role of the ...


3

One thought is traffic collisions. Once you put the first satellite exactly at the L point in question no other satellites can occupy that position. And because that are gravitationally stable points shifting them out again at the end of their life time is relatively expensive. So to be good neighbors to the other missions in the neighborhood you will prefer ...


3

If you haven't looked there before, the starting place for all NASA data is the NASA Space Science Data Coordinated Archive (NSSDC). Back in the day when I used to work with ISEE-3/ICE data, they were the place were you went to get your data or you sent it to archive your data. I'm not familiar with the data format you are asking about, but the orbital ...


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