theoretical astrophysics questions

Factual Questions
1

Hi, folks!

This board has helped me out so many times I thought I’d return with a few more questions regarding my [post=7401127]aforementioned[/post] personal project (yup, it’s for a story).

[Note: I’m not quite sure if this belongs in G.D. or if it would be more appropriate elsewhere. I’m seeking factual answers, but the questions are entirely theoretical, so I’m not sure where that leaves us. The Moderators will, of course, move as they deem fit. Also, if there is a forum/website better suited to such questions, wherein I might be allowed to pester astrophysicists with such theoretical questions, I’d be much obliged for a link.]

Background: I’m writing a fantasy tale and am trying to explain scientifically how it’s possible (unless it isn’t, of course) to have a planetary system with four moons (from innermost orbit to outermost: X1, X2, X3, X4, all of which orbit Planet X which in turn orbits the sun) on one of which (X2) exists life (e.g., liquid water, Earth-like climate, etc.). Basically, I always thought it’d be cool to see three moons and a mother planet overhead but I don’t want to wind up with really nasty tidal situations or other scientific difficulties that would get in the way of my story. Going a bit further here, I wanted each of the planetoids to take up about ½ a degree of visual space in the sky (which, as I understand, is about the same as our moon). Is this all just wishful thinking on my part or could it be possible?

Second question: If our moon had liquid water, would the earth’s greater mass relative to the mass of the moon do more serious things to the moon’s tides than the moon does to the earth’s tides?

Third question (unrelated to those above, but pertinent to my tale): What would happen to our Earth-moon relationship if the moon’s mass were suddenly (instantly) increased to three-and-a-half times its current mass? I assume they would come together with a great bang and hasta luego to life as we know it—is that about right? And what if the moon’s orbit were farther away than it currently is? Could I come up with some work-around here?

Thanks, everyone, for your patience. As always, your help would be very much appreciated.

-Archer

2

First of all, minor & pedantic nitpick but your questions actually pertain to celestial mechanics and planetology rather than astrophysics, which is the study of stellar-class and larger phenomenon. (No charge for that one; it’s a freebie. :slight_smile: )

Back to your question: insofar as the little we know about planetology–since there’s only one solar system we can observe in any detail our emperical data set is naturally limited–there’s certainly nothing that prohibits the system you’ve proposed. A habitable moon would have to be large enough to retain an atmosphere, so we’d assume something at least roughly Titan-sized or larger with sufficient surface gravity to hold low molecular weight molecules like O[sub]2[/sub] and N[sub]2[/sub] orbiting in a habitable zone. For a G2 star like Sol that would require a much more massive inboard planet; a more luminescent star could have your hypothetical Planet X about a much more distant orbit (and in a presumably wider habitable range). We’ve seen supermassive planets in close orbit of nearby stars, so this isn’t entirely out of question. For the purposes of discussion we’ll assume that your Planet X is, like Jupiter, seriously more massive than the system it anchors so that we don’t have to place significant consideration on orbital couplets (as with the Pluto-Charon system).

The issue of other moons is somewhat more complex. Multiple moon systems fall into what are called orbital resonances, which can be fiendishly difficult problems to work out. This restricts the range of long-term stable orbits about a body. Having three moons big enough and close enough to take up 1/2 angle of arc slice of the sky is iffy, methinks, though perhaps not impossible, particularly if the moons are in a close orbit. However, orbital resonances are going to contribute to tidal locking (reducting and ultimate elimination of independent rotation as with The Moon) which would probably be detrimental to a stable climatological system on your forest moon. I’d guestimate that so many large bodies in close proximity a) probably wouldn’t develop naturally, though they might possibly be captured later, and b) would ultimately become unstable owing to their influence upon each other. But that’s just a total, back-of-the-gum-wrapper guess with no math behind it whatsoever.

This is more complex than a yes or no question; the force of gravity upon the Moon as imposed by the Earth is the same as that which is seen by the Earth from the Moon; nominally, the tidal forces are the same. (The tidal forces by the Sun on either body are minor, although not insignificant, in comparison.) The more significant factors are the depths of the ocean–a shallow ocean and larger littoral area (that is, the shallow coastal areas) are going to see vastly more effect from tides than a moon with deep oceans and small shelves–and the particularly fact that the Earth’s Moon, with its tidal locking, is going to see a more-or-less constant tide with only minor fluctuations in accordance with its orientation to the sun and tidal rocking.

Pedantically speaking, that’s two questions, so I’m going to have to charge you double. :wink: If the Moon’s mass were “suddenly” increased by a substantial factor (ignoring the dynamic acceleration and jerk effects of said increase) the only significant change you’d see, at least immediately, is somewhat more exaggerated tides, which would be significant for low-lying coastal areas, but you wouldn’t significantly change the orbit of the Earth-Moon system. Kepler’s Laws don’t really care about mass; the characteristics of orbits are predicated upon period (or speed) and eccentricity. Of course, a much larger mass is going to force the barycenter–the common point about which the Earth-Moon (or whatever) system rotates–outside of the Earth’s surface. That’ll have some long-term impacts, and aside from that, the increased mass will exacerbate the effects of tidal locking and rocking, but it’s not going to cause worlds to collide or anysuch. In celestial mechanics, order of magnitude changes are required to seriously affect massy objects in orbit; these aren’t easily perturbed systems.

Sorry, that was kind of a disoganized glurge. I’d put it into a more formal order but I’m running late to attend a pointless meeting to explain the obvious to people regarding why they can’t stuff 170kip transporter onto a C-17 and fly it up to Alaska. Compared to that, orbital mechanics is a piece of cake. Anyway, I hope that helps some. A quick piece of advice for you regarding writing, though; don’t sweat the details. Heck, Niven had the Earth rotating the wrong direction in the first edition of Ringworld, and yet he still managed to crank out a sizeable volume of saleable novels after that. (Never mind the whole mess regarding the questionable stability of the Ringworld and his ad-hoc Engineers patch job.) It’s commendable that you desire techincal accuracy, but don’t get lost in the details.

Good luck to you,

Stranger

3

Dear Stranger,

Your response was even better than what I’d been hoping for. Thank you! And I appreciate the clarification about the terms–one of the problems of having been a Lit. major is the necessarily egregious amount of ignorance I have regarding subjects OTHER than literature. Then again, maybe that’s not a Lit. major thing as much as my own personal baggage… :dubious: I’m going to read through your answer several times as digestion is needed. Thanks again.

Man, I love this board.

-A

4

I see a problem here (or maybe an opportunity, depending on how you approach it). If I’m on Moon A and I’m looking at Moon B, both orbiting the same planet, the distance between me and Moon B is probably going to change significantly, depending on whether it’s on the same side of the planet as me or the opposite side. And if the distance changes significantly, then the apparent size is also going to change significantly. It wouldn’t be too hard to have all the other moons appear at about 1/2 degree at some time or another, but sometimes, they’ll be larger, and sometimes, smaller.

You didn’t ask, but there’s also the question of phases (crescent, full, etc.), which will be seen on all of these bodies (the parent planet and the other moons). Here, it makes a difference which moon you’re on: Any moon closer to the parent planet than you are will always be in about the same part of the sky as the parent planet, and will be closest to it at the time that it’s biggest or smallest. Any moon further away from the planet than you are will sometimes be near it in the sky, and sometimes far away, and will appear largest when it’s opposite the parent planet in the sky, and smallest when it’s near the parent planet. All objects which are near each other in the sky will have, at any given moment, approximately the same phase, and the lit side of a moon/planet will always point towards the Sun in the sky. Crescents are always close to the Sun in the sky; full phases are always far from the Sun in the sky.

So, in your example, we’re on X2. X1 will always be somewhat close to X in the sky, and since it’s close, it’ll have the same phase. When X1 and X are close to the Sun in the sky, they’ll both be crescents. When they’re both far from the Sun in the sky, they’ll both be full, or close to it. The distance between X1 and X in the sky will change with time, as will the apparent size of X1. If you watch it for a complete cycle, you’ll see it very close to X and very small, then move off to one side and get somewhat bigger, then move back towards X and get very big, then move off to the other side of X as it gets smaller again, and then move back towards X and get very small. All the while that this is happening, X and X1 are also moving relative to the Sun and therefore changing phase, but that’s happening on a different (slower) timescale (corresponding to the time it takes your own world, X2, to orbit X).

Meanwhile, X3 and X4 also have their cycles (slower than the X2 cycle). If you watch X3, say, at one time it’ll be near X and very small. It will then move all the way around the sky, relative to X, and grow larger as it does so. When it’s opposite X in the sky, it’ll appear at its largest. It will keep on moving around the sky, getting closer to X again, and shrinking again in the process. X4 will do the same thing, only slower, and its change in size won’t be as extreme as X3’s. X3 and X4 will also show phases, according to where they are in the sky relative to the Sun.

5

One small nitpick to Stranger’s excellent post: it’s not the size of the planet or moon that matters, it’s the mass. A very dense small object can exert the same gravity as a less dense but larger object. If this is the case then their mass is the same. The ultimate example would be a black hole - very small, very high density, very massive. In your story, a moon with large concentrations of iridium or osmium (the two densest elements) could be significantly smaller than otherwise expected - iron (a major component of the Earth) has a density of 7874 kg/m[sup]3[/sup], but iridium and osmium have densities over 22000 kg/m[sup]3[/sup].

You may also find the Aurora Sourcebook from the RPG Traveller 2300 useful - Aurora is a moon with gravity similar to Earth’s which orbits a gas giant.

6

The moons around a gas giant are usually tidally locked. Like the moon, they usually keep one face towards the primary. This means that the “day” and the “month” are the same length. So if it takes 17 days for X2 to travel around X, then a day on X2 will be 17 days.

This will mean that the tides on X2 won’t change. There will be tidal bulges, but they will always be in the same place. There will be solar tides, but these are going to be pretty small compared to the lunar tides on earth.

The complicating effect will be the tides caused by the other moons. As a rule of thumb, an object as dense as the moon that appears the same size as the moon will have the same gravitational effect as the moon. So if X1, X3 and X4 all sometimes appear as large as the moon, they’ll EACH cause tides as large as Earth’s lunar tides, although in different directions. So on occasions where the orbital periods of the moons line up, X2 will have tides 3 times as large as an Earth lunar tide.

If the other moons are more dense or less dense, or appear larger or smaller than Earth’s moon at their maximum, they’ll cause greater or lesser tides.

And there should be a couple of little moons out there too.

Note that if X2 has liquid water, there’s no reason X1, X3 or X4 couldn’t have liquid water too, since they will be the same distance from their sun as X2. However, there’s nothing saying that the moons should have the same composition.

7

True, but you’re unlikely to find planetary-sized masses of heavier elements than iron. Typically speaking, the Earth is about as dense as you can expect a naturally appearing planetary body to be. (A purely iron body would be rougly 25% denser but it’s unlikely that you’d form without bringing along some other, low mass garbage.) I was assuming, by the phrase “Titan-sized” to mean in both circumference and mass, but since I made such business of nitpicking its only fair that I get my nits picked in turn. :smiley:

Chronos went into volumous and useful detail on phases and aspects; I can’t really add anything to that except to note that the tidal effects on your X2 moon by the primary body are likely to predominate over any tidal effects by other moons for the purposes of the average bystander. They’ll certainly effect the other moons of the system per the discussion on orbital resonance, but their effects on ocean tides or whatnot are will be insigificant. (A body large enough, or moving slow enough relative to X2, to affect ocean tides will probably destabilize the system.)

Ah, another Traveller 2300/2300 AD refugee. There were really some great sourcebooks in that system.

Stranger

8

I’m not so sure about that… I think that the OP wants all of the celestial objects, including the parent planet, to appear about a half a degree in size (the other moons will all on average be smaller than the parent planet, but they could still appear this large or larger, at their largest). Tidal effects due to a body are proportional to the angular size of the object cubed times the density. If the other moons (at their closest) and the parent planet all have about the same apparent size, then it comes down to density, and gas giants generally have lower density than moons (especially if you’re in the liquid-water zone, so the moons would have to be made of minerals, not ice). So when the other moons are relatively close, they will in fact raise tides comparable to or greater than those from the parent planet.

9

A couple of clarifications, if you please.

Have you determined what sort of planet the primary is? Gas giant, rock ball, whatever? Are you thinking it will be populated?

I don’t quite understand this one. What moon is farther away from where? (Related to the moon increasing its mass.)

10

I’m not quite sure what my preference is at this point, considering the factors people have mentioned above. Initially, I’d been thinking that life might once have existed on Planet X and all its moons, and that they were therefore Earth-like, geo-structurally, if not exactly similar in size.

That question was related to Earth’s Moon and to my flawed knowledge of tidal systems and gravity. I had thought that, assuming the Moon had liquid water, Earth would exert a greater influence on it than does the Moon’s gravity on Earth’s tides, due simply to the size difference. So, I was wondering whether we couldn’t, for the purposes of that question, simply move the Moon farther from the Earth in order to decrease Earth’s influence.

After reading everyone’s responses, I seem to be moving further from the idea of making Planet X a gas giant or even a large terrestrial planet due to a number of factors, one of which is that it seems such a large planet would have to take up a huge chunk of sky on my life-carrying planet (X2). I’d rather my denizens only see the planetoids at periodic intervals BUT also have said planetoids orbit close enough so that their surface features can be seen from X2 with the naked eye. And while I had, for a while, enjoyed the idea of planting life in a destabilized system (e.g., maybe it was stable long enough for life to evolve, but it won’t be around much longer) I’m now thinking it’s a bit too problematic. I’m not totally convinced, but I’m realizing from what folks are saying that this would be quite a complex system. Not that complexity can’t be entertaining, too… :slight_smile:

Thank you again to everyone for your responses so far! Your assistance has proven invaluable.