
Kathleen Howell is developing potential orbits around a Lagrange point - montalbano
https://www.bloomberg.com/news/features/2018-07-25/one-woman-s-math-could-help-nasa-put-people-on-mars
======
Latteland
This article just teases interesting details. I want to see a simulator I can
play with an move and rotate in 3d.

~~~
troymc
I wasn't able to find an interactive simulator online, but this video has a
nice visualization:
[https://www.youtube.com/watch?v=X5O77OV9_ek](https://www.youtube.com/watch?v=X5O77OV9_ek)

------
rocqua
> 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.

~~~
troymc
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.

~~~
rocqua
" 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.

[1] [https://en.wikipedia.org/wiki/Three-
body_problem#Gravitation...](https://en.wikipedia.org/wiki/Three-
body_problem#Gravitational_systems)

~~~
privong
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.

~~~
rocqua
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?

~~~
privong
I don't have more than a cursory knowledge of the solution, but the Three-body
problem wikipedia page should have enough info to get you set in the right
direction: [https://en.wikipedia.org/wiki/Three-
body_problem#Sundman's_t...](https://en.wikipedia.org/wiki/Three-
body_problem#Sundman's_theorem)

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

------
valuearb
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.

~~~
johndunne
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.'

~~~
valuearb
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.

------
acobster
Why L2 and not L1? Isn't L1 supposed to be more stable?

~~~
tqkxzugoaupvwqr
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.

~~~
greglindahl
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.

