
The Sideways Tide - headalgorithm
https://www.solipsys.co.uk/new/TheSidewaysTide.html
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antognini
There's a (relatively) famous problem in astrodynamics called "Apples in a
Spacecraft". I wrote a blog post about it a little while back [1], but the
gist of the problem is this:

Suppose you're in a rectangular spacecraft orbiting around the Earth and you
release a bushel of apples so that they are uniformly distributed and
stationary relative to your spacecraft. If you don't disturb the apples, what
will their long-term distribution look like?

There was a bit of a debate in the literature as to the answer to this problem
and the physicist Alfvén (better known for Alfvén waves [2]) ended up getting
the wrong answer. The correct answer (due to Hénon, who is better known for
the Hénon map [3]). Hénon showed that half the apples would end up at the top
back corner, and the other half would end up at the bottom front corner of the
spacecraft.

The reason for this is that the apples at the top of the spacecraft are in a
slightly larger orbit and therefore have a slower velocity than the center of
mass of the spacecraft. This causes them to drift to the back of the
spacecraft. Similarly, the apples that start on the bottom of the spacecraft
have a higher velocity and start to drift towards the front of the spacecraft.

[1]: [https://joe-antognini.github.io/astronomy/apples-in-a-
spacec...](https://joe-antognini.github.io/astronomy/apples-in-a-spacecraft)

[2]:
[https://en.wikipedia.org/wiki/Alfv%C3%A9n_wave](https://en.wikipedia.org/wiki/Alfv%C3%A9n_wave)

[3]:
[https://en.wikipedia.org/wiki/H%C3%A9non_map](https://en.wikipedia.org/wiki/H%C3%A9non_map)

~~~
Doxin
Wouldn't the answer be a circulation of apples, depending on how many apples
we're talking? Half the apples would pile up in a top corner, which'd push
some of the apples into the bottom corner instead, making them traverse to the
other side of the spaceship.

This is of course ignoring that the spaceship itself might be bumped off-
course by the apples or start spinning because of them.

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GlenTheMachine
"What happens if we throw the ball forward or backward? Will we again have a
fictitious force?"

Yes, you will. Only that force will be in the plane of the orbit. Throw the
ball forward and you raise its orbit - so it will start going forward, end up
going "up" and then cycle back down exactly one orbital period later.

Throw it backwards and you will lower its orbit. It will go back, down, the up
again. Unless you throw it too hard, in which case it will re-enter and burn
up.

~~~
MaysonL
Yes, but in either case you will change its orbital period slightly.

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Terr_
Mildly related:
[https://en.wikipedia.org/wiki/Horseshoe_orbit](https://en.wikipedia.org/wiki/Horseshoe_orbit)

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amelius
> If you get the direction exactly right (and the tolerances are inhumanly
> small) then the ball will go away from you, yes, in a straight line (more-
> or-less), yes, but it will slow down. After about 23.2 minutes it will come
> to a complete stop, and start to come back.

Ok, this makes me wonder, in the movie "Gravity", when people accidentially
got separated from the space station, they were not forever lost?

~~~
B1FF_PSUVM
> when people accidentally got separated from the space station, they were not
> forever lost?

Only if going perfectly sideways, i.e. keeping the same distance from the
center of the gravity well ("and the tolerances are inhumanly small").

Go down, you'll spiral to the bottom; go up, you'll float away, maybe to the
Sun or Jupiter or just the Ooort cloud and beyond.

(I don't think you'll find another stable orbit without some sort of
maneuvering jets or very well tossed bits of spare mass you may have on you.
Even so your distance from the station is probably unrecoverable.)

~~~
FreeFull
If orbital mechanics were this unstable, we wouldn't ever manage to have any
sattellites up in orbit around the Earth (or have the Earth orbit the Sun, and
the Sun orbit the centre of the galaxy..). The important part of your orbit is
the sideways velocity (For example, the International Space Station orbits at
around 27,600 km/h). Let's say you're launched from the ISS (and that the
ISS's orbit is perfectly circular), straight down towards the Earth at about
30km/s. Initially, you'll get closer to the Earth, but at the same time your
orbital velocity will increase as you're going down, which eventually ends up
sending you back up to the same orbit as the ISS (although I'm not sure if
you'll end up ahead of the ISS, behind it or right back at it). You'll have an
upwards speed of 30km/s, and will keep going up at a decreasing speed until
you hit some maximum point, and start coming back down to repeat the cycle.
Your orbital path will end up tracing out an ellipse, and at no point will you
spiral in or away.

Ultimately, to actually come back down to Earth you have to burn off a lot of
sideways speed (especially if you don't want to be going too fast when you
enter the atmosphere). And, to leave Earth's gravity, it takes quite a lot of
acceleration too.

~~~
tomatotomato37
While your parent comment does have a ridiculous idea of how orbits
fundamentally work, orbital mechanics in near earth do end up being that
unstable, hence the orbital stationkeeping fuel budget all satellites in the
region have. It's just the toll of a faint atmosphere, solar radiation,
mountainous terrain. You'd have to go out to around the geostationary area for
a "clean" orbit, and even that one's still going to be tugged around by the
moon.

On the plus side all those weird interactions with real life allow you to do
fun things like change orbit with electronic tethers or orbit around nothing
by exploiting Lagrange points

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SimonPStevens
Perhaps I'm misunderstanding, but does this mean that the sci-fi cliche of
going for a spacewalk and accidentally being knocked off your ship and
drifting away forever is wrong? Actually, given a short wait you'll just stop
and drift right back to the ship again?

(Yes, in orbit only, I understand that freefall is different from zero gravity
scenarios)

~~~
marcosdumay
You'll pass through the ship's orbit again and again.

If you pushed in a direction exactly perpendicular to the orbit, you'll reach
the ship again. If you pushed somewhat into or against the orbit direction,
you will get in front or behind the ship.

~~~
zamalek
You'd have to have enough oxygen for one [edit: half] orbital period, mind
you. The unfortunate astronaut would likely still die.

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aetherson
If you wish to read this article in novel form, _Incandescence_ by Greg Egan.

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ak217
I would recommend _Seveneves_ by Neal Stephenson on this topic.

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crooked-v
That book has the major problem that it's three-quarters of a good book
stapled to half of a mediocre one, and the mediocre one is the one that the
author was apparently actually interested in.

~~~
ak217
That's fair to say, but I think it's true of most of Stephenson's books - and
he still manages to cover so much interesting ground that they turn out to be
good reads despite the long-winded plot holes.

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npmaile
I would absolutely recommend playing a game called Kerbal Space Program if you
have any questions on how orbital mechanics works.

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k_sze
I wonder if it can be simulated in Universe Sandbox (2).

