Can a Ringworld have a 'moon'?
The idea is to have a number of artificial, spherical satellite to have sort of a "spiral" orbit around a Ringworld, such that the inhabitants of each of a number of ring sections see a moon in the sky once every year or two. Is that theoretically possible for a sufficiently advanced civilization?
Edit: By 'Ringworld' I mean a Niven-Ring, I should've clarified that sooner and I will try to do better next time. Thank you all for your answers! I think I have a better idea of what I want to do now.
moons dyson-ring
JBH
AnkyriAnkyri
$\begingroup$ Welcome to WorldBuilding Ankyri! Interesting first question. And no need to apologize for your english. I think you would write languages with an uppercase letter in the beginning, but other than that I couldn't find any mistakes so I edited out the apology. If you have a moment please take the tour and visit the help center to learn more about the site. Have fun! $\endgroup$ – Secespitus Oct 1 '17 at 20:50
$\begingroup$ Welcome to World Building Ankyri. I suspect that the answer to your question might be yes, but it would be useful if you could clarify the question for us a little. A spiral orbit would bring the satellite crashing down onto the surface eventually. But an eccentric elliptical orbit might be what you are looking for. $\endgroup$ – Slarty Oct 1 '17 at 20:51
$\begingroup$ What is a ring world? Like Niven's Ringworld? $\endgroup$ – Willk Oct 1 '17 at 23:15
$\begingroup$ I think by spiral, Ankyri means a helical orbit wrapping around the ring world. $\endgroup$ – Lex Oct 2 '17 at 5:18
$\begingroup$ What's a "Dyson Ring" - I know of Dyson spheres, and Niven rings, but not Dyson rings. $\endgroup$ – Dewi Morgan Oct 2 '17 at 19:21
There are a few options. I'll assume a Niven-type ringworld with a radius of 1AU (i.e. the surface is the same distance from the sun as the Earth's surface).
If a ring this size were simply in orbit, rotating about the sun once per year, then its occupants wouldn't experience weight. So it actually rotates 41.6 times faster (once every 8.8 days), creating a centripetal force of 1g.
The following ignores the mass of the ring itself (it's made of carbon fiber or something), but at least the first two scenarios could probably be adjusted to account for that.
The "moon" (actually a planet) orbits the sun in a highly eccentric anecliptic orbit, meaning that its orbital plane M is at 90 degrees or so to the ringworld's orbital plane R (figure A). If you fix your camera to a point on the ringworld, the moon follows a helical path around the ring, as requested (figure B). However, this isn't really what you want, because most of the time it would be too far away to see, and when you could see it, it would be rapidly falling toward the horizon and then rapidly rising out of view on the other side of the ring.
You'd never see it pass right overhead. But you could time the orbits so that people in a given town only see it once every 5 or 10 or 50 years.
Orbits like this aren't seen much in nature, for a few reasons, but it's nothing that a ringworld engineer couldn't easily fix.
You have two (or more) moons orbiting each other in a "rosette" (Niven actually mentions this in Ringworld although his terminology is a bit wrong). The center of this system orbits the sun in a circular orbit of the exact size of the ringworld itself, so it looks as if the moons are orbiting the ring (figure C). The center point of the rosette goes round the sun once per year, while a point on the ring goes round the sun 42 times per year, so again, relative to the ring, the moons' path describes a helix (figure D). You will pass under the moons once every 9 days.
This one is a bit harder to visualize. First, let's forget for a moment that the ring is a centrifuge, and assume it's simply floating in orbit round the sun. If you have a single moon orbiting the sun in approximately the same orbit (figure E), then it's in geosynchronous (halosynchronous?) orbit and will appear stationary in the ring's sky.
Now, make that moon's orbit slightly eccentric, so that the apogee (strictly, the "aphelion") is outside the ring, while the perigee ("perihelion") is inside the ring (figure F). It's still sort of stationary, but it's bobbing above and below the ring – if you plot it out, its path looks like this:
It's not exactly a circle, but it does rise on one side of the ring and set on the other.
Now if you recall that the ring is spinning at an extra 40.6 revolutions per year, that shape becomes a distorted helix – I won't try to draw it, but it's the same type of situation as figures C and D.
If it's important to have the moon pass overhead, then you want scenario 2 or 3; if it's more important to have the moon appear at long intervals, you want scenario 1. I don't think there's a way to have both using orbital mechanics, given that the moon needs to get close enough to actually be visible. If none of these options work, then perhaps instead of a real moon you could have a giant airship, or some sort of moon-shaped machine attached to the ring.
bobtatobobtato
$\begingroup$ Nice. A little bit more of actual math or references would be appreciated, but really nice none the less. $\endgroup$ – Mołot Oct 3 '17 at 9:52
$\begingroup$ Very ingenious well done. The moon would have to travel much slower than the ring in scenarios 2 and 3 as the ring is traveling 41.6 times faster than it should held in place by massively strong materials that can withstand 1g continuous acceleration across the whole ring and prevent it flying apart. So the moon would appear to be rapidly moving from the perspective of the ring and would be visible every 9 days or so. $\endgroup$ – Slarty Oct 3 '17 at 17:14
$\begingroup$ @Separatrix how so? None of the scenarios involves the gravitational attraction of the ring itself (the "moon" orbits the sun in all cases). $\endgroup$ – bobtato Dec 12 '17 at 10:24
$\begingroup$ @bobtato Sorry, it's taken me three attempts to work out what's going on. Time to stop for a cuppa I think. $\endgroup$ – Separatrix Dec 12 '17 at 10:31
Big problem.
Spiral orbits do not exist other than spiraling in in the very thin outer layers of the atmosphere. However, you could have a dwarf planet orbiting just inside the Ringworld's orbit. While it wouldn't actually be orbiting the Ringworld it would look like a moon. Beware that the Ringworld's rotational velocity is .4% of lightspeed, said "Moon" is going to flash by at that speed! Making it a gas giant a bit further out would help a bit in this regard but it's still going to be moving across the sky quickly.
The important problem--the Ringworld's year is just under 10 Earth days. It's going to come back to that "moon" every 10 days, not a year or two.
The designers aren't going to put up with something like this anyway. While a Ringworld requires attitude control systems anyway the presence of another body like that is going to make the orbital stability problem much worse.
Remember that it's always noon on a Ringworld. Moons come out at night!
If you're determined to have something in the sky you could make a fake moon, though. Build another ring at some distance inside the habitation ring. Your "moon" is merely a picture being carried on that ring. This avoids all the problems mentioned above. Why? There is some cultural importance to a moon that's enough to warrant the cost of making a fake one.
Mołot
Loren PechtelLoren Pechtel
$\begingroup$ I'm surprised your #3 isn't #1. I'd think that a significant mass moving around would rapidly destabilize the ring. $\endgroup$ – bgvaughan Oct 2 '17 at 15:56
$\begingroup$ A quick google search says that #4 is wrong. Mind, on a ringworld, with the moon directly between the observer and the sun, you're going to be in total solar eclipse territory (and a "new" moon, which is dark). But the way you've stated the point is wrong. $\endgroup$ – Draco18s Oct 2 '17 at 18:31
$\begingroup$ @Draco18s The Ringworld has shadow squares that block off the sun. The would also block off light off a nearby moon, though--you couldn't see it. Thus I stand by #4. $\endgroup$ – Loren Pechtel Oct 3 '17 at 18:58
$\begingroup$ Shadow squares cause night, which isn't noon. $\endgroup$ – Draco18s Oct 3 '17 at 22:04
$\begingroup$ @Draco18s They're a separate system and the night they cause would leave the moon dark, also. A shadow square "night" doesn't have a moon in the sky even if you put one there. $\endgroup$ – Loren Pechtel Oct 4 '17 at 2:57
You'll find some hard math here, but the short answer is: if you're moon is unpowered, you cannot have a spiral orbit. That's simply not the way the universe works. As mentioned by @Slarty, you could have a very long elliptical orbit, but there's a limit to how long the ellipsis can be before the moon walks away from lack of gravitational pull.
If you love physics & math (or simply want to learn something cool despite the headache it will give you), read Wiki's page on orbital mechanics. The basic truth is you can't get what you're looking for ... kinda. Let's examine some goods and bads.
However, you're writing a story. Maybe the planet and the moon have higher than Earth-standard gravity, which would allow a longer ellipsis. Perhaps the moon is made of very dense material, which would also allow a longer ellipsis. Or maybe you just make it that way.
High declination
Another possibility is to put the moon's orbit on a high declination, such as the orbit of Pluto or the orbit of some asteroids around the Sun. This won't give you years, but it would make the moon appear aperiodically from the perspective of the planet's surface.
Its orbit must be outside/inside (not within) the rings
A gotcha you need to worry about is that the moon's orbit must not be within the rings, otherwise the rings will slowly pulverize the moon. An elliptical orbit with a high declination would allow it to move inside the orbit of the rings, but without the declination, it would need to be completely outside the rings (meaning from the right place on the planet you would always see a line across the moon as the rings cast a shadow).
But, it's artificial, so it can be what you want
But, everything I've been telling you is from the point of view of using gravity to keep everything in order. If you give the moon power then you can have it do what you want. That's really the question you need to answer: does my moon have the ability to apply force to correct/control its orbit? If yes, then it does what you want when you want. If no, then it doesn't matter if it's artificial or not, it must obey the laws of celestial mechanics (with a little literary license thrown in to keep astronomers on their toes).
JBHJBH
For a "ringworld" meaning a planet like Saturn
A spiral orbit would not be ideal for a long term satellite as it would eventually crash into the planet or fly off into space. However an eccentric elliptical orbit would allow a satellite to make relatively close flybys of the planet from time to time and depending on the exact orbital period it could easily pass over a different "section" of the planet each time. Here are some example eccentric orbits. The satellite would be moving fastest at its closest approach to the planet in each case.
Edit For a Ringworld like niven's ring world:
I suspect the stable orbit of a moon around the ring world would follow a figure of eight pattern or a linear motion perpendicular to the axis of the ring world in a pendulum motion like this:
See this link for the alternative:two possible orbits Although this would obviously not be possible with a central star.
However I think the geometry that the OP was asking for would be best described as a spiral ring similar to this (the closest that I could find being the electrical equivalent):
But the calculations are atypical and a little complex. So I stand to be corrected if anyone knows better. I should also point out that any ring world orbits would be highly unstable if any other large astronomical objects were in the vicinity (with catastrophic results).
SlartySlarty
$\begingroup$ As to first sentence - I'm not saying you are wrong, but could you show why would something like this have to happen? $\endgroup$ – Mołot Oct 1 '17 at 21:06
$\begingroup$ Imagine the planet was at the centre of a spiral pathway. If the satellite was following the orbit one way it would eventually hit the planet. If the satellite was following the orbit the other way it would eventually escape into space. Did you realy mean a spiral orbit? Or were you thinking of a more complex spiral orbit relative to the sun? $\endgroup$ – Slarty Oct 1 '17 at 21:19
$\begingroup$ @Molot Look at the second diagram in this link to see a spiral orbit:quora.com/Why-are-orbits-not-spiral-shaped $\endgroup$ – Slarty Oct 1 '17 at 21:25
$\begingroup$ OK Niven's Ringworld! Answer edited for this case $\endgroup$ – Slarty Oct 2 '17 at 8:45
$\begingroup$ Nice ringworld illustration. $\endgroup$ – Willk Oct 3 '17 at 13:43
You may be able to have an orbiting body that is moon-esque in its relationship to a Niven Ring but you don't want to. Ringworlds are unstable in their "orbit" of their primary, and the orbits of Moons are not stable over geological time. As such any object that shares a star system with a Niven Ringworld will either get too close and destabilise the structure or actually hit the ring and make a hole, holes are bad. In Ringworld the system is empty of everything except a few Oort Cloud distance objects left behind to "top-up" the biosphere at a later date, also it uses the star as an anti-impact defense particle weapon system because that's how much of a problem the ring getting hit is.
You could make a second ring structure "orbiting" the big ring(the truth would be it's orbiting the sun) structure which would hold a moon like artificial body and for good measure make it simulate night time on the ringworld segment it's on at that particular moment. Not having a night cycle could prove bad for the psychological aspect of the inhabitants.
KaotisKaotis
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