Kerbal Space Program [0] (available on Steam) is a good simulator for lots of space things, but by default does not support multi-body physics (which are necessary for simulation of Lagrange points).
There is a mod called Principia [1] that adds this functionality, though I've not used it personally.
Probably not exactly the type of simulator you were looking for, but could be something!
If you get good at Kerbal Space Program, you can install the RSS (Real Solar System) mod that is a 1:1 scale of our solar system, and is correspondingly harder. You'll need to build things with about 7800-8000 m/s of delta-V to get to LEO.
It doesn't simulate more than two bodies at a time, so gravitation influence of multiple planets and moons on an orbit are not simulated, however, you can do multiply sequential gravity assist missions.
> perfect prediction is in principle impossible. “You can’t include everything in the universe in your calculation,”
The issue is even worse. Even if you just include the Earth, Moon and sun, the actual orbit is impossible to calculate. That is, we do not have an exact solution, and approximate solutions diverge quickly, and require a lot more computation to remain accurate for a bit longer. This is all related to the fact that it is very hard to establish whether a 3 body system of bodies is even 'stable'. That is, whether one of the bodies reaches escape velocity and just shoots off.
The belief that there's no exact solution to the three-body problem is common but wrong. There is one, and it was found about a hundred years ago. The history of the problem, and its solution, are all described in the book Poincare and the Three Body Problem, published by the American Mathematical Society. It includes a section about potential reasons for the pervasive belief that no solution exists.
" A complete solution for a particular three-body problem would provide the positions for all three particles for all time, given three initial positions and initial velocities. In general, no closed-form solution for such a problem exists, and the time evolution of the system is believed to be chaotic. " from wikipedia [1]. Not a fool-proof source, but it seems to disagree with you.
It does seem the case that whether the system is chaotic isn't yet determined.
There is a series solution to the 3-body problem, which can in principle be computed to an arbitrary level of precision. So while there's no closed-form solution (as the wikipedia article notes), there is a solution. However, my understanding is that this series solution converges slowly enough as to not be useful in practice.
Ah, that is interesting. I figure Numerical ODE solvers might be faster. But there is philosophical value in a series that is proven to converge for any time t. Do you happen to recall whether it is uniform convergence?
It says that the series should converge for all t, except for systems which begin with zero angular momentum.
It additionally states that:
> in 1930, David Beloriszky calculated that if Sundman’s series were to be used for astronomical observations, then the computations would involve at least 10^8000000 terms
In principle, orbits in a 3-body system are unstable when extrapolated arbitrarily far into the future. But in the case of the Earth-Moon system, it's easy to find orbits where the "instability" grows on a timescale of years or decades, and therefore can be easily dealt with by active course corrections.
This isn’t true. We have very reliable libraries for simulating N-body problems to sufficient detail to know the answers to such questions with great certainty. Not having an “exact solution” Does not bound whether solutions exist or whether they are computable, or how easy they are to compute. In this case, quite easy.
What she does sounds fascinating, but it’s application in this case is a waste. The Lunar Gateway is just a unnecessary expensive jobs program, that’s going to retard, not help, future exploration of both the moon and Mars.
From what I understand, the Lunar Gateway is more the result of an expanding business interest in space. The space tug sounds like it could cheaply ferry experiments to the moon at a fraction of the cost; sounds like a boom for innovation. I expect the highly specialised space exploration will continue regardless if countries want to remain at the bleeding edge of 'space tech.'
NASA is going to spend over $3B per launch for the SLS, which has similar lift capacity to a $130M Falcon Heavy.
You really think the space tug is going to be cheap?
And no commercial company wants to stick anything in a lunar parking orbit, because its a huge waste of energy that makes zero sense for any missions. The only commercial companies that are interested are SLS contractors who want more free money in their government pig trough.
The lunar gateway has nothing to do with the expanding new space sector, which frankly doesn’t know what to do with it. It’s a politically justified solution in need of a problem.
The L1, L2 and L3 points are all unstable, but there are nearby orbits that are neutrally stable, e.g. the halo orbits and the orbits described in the article. A spacecraft on one of those orbits will still need to use some propellant to get it back on track from time to time (for "station keeping"), but it's typically not very much propellant. Such orbits have already been used for other missions, such as the Solar and Heliospheric Observatory (SOHO).
I can only speculate, but the article alludes to establishing permanent communication with the moon’s backside:
> A satellite or spacecraft in a halo orbit [around L2] can be constantly in Earth’s sight and can therefore maintain communication between astronauts on the far side of the moon and control rooms back home.
China currently has a relay satellite at the Earth-Moon L2 for exactly this reason, they're going to launch a mission to land on the back side of the moon.
I would guess the reason is that while L1 is not stable it is still easy to maintain with minimal thrust and the instability of the point means that things 'passing through' do not need to work hard to leave the orbit. The unstable Lagrange points are not places that will collect unpowered/unguided objects or debris but they provide easy station-keeping opportunities.
