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Durakken
2009-Nov-19, 04:27 AM
Ok.. gonna try to explain what I mean...

Is there any limit to how many satellites, moons, that a planet can have?
Can Earth like moons form around planets if so is there minimum size to the planet?
Can Earth like planets have multiple moons?

Why am I asking... because I am trying to create a game that creates a lot of planets and is fairly accurate...

I am dividing up planet sizes into classes that are pretty much like so...
Asteroid = 0-1,000km
Tiny = 1,000-10,000km
Small = 10,100-30,000km
Medium = 30,100-70,000km
Large = 70,100-150,000km
Gas Giant =36,000-1,400,000km

They are also each broken down into types of planets...
Icey (Pluto)
Metal (Mercury)
Rockey (Moon)
Ocean
Caustic (Venus like)
Terran (Earth like probably gonna change it to garden world)

So I need to know roughly how many moons each size range could support...It seems to me... that tiny planets can have 2+ asteroid moons and Small can have at least one tiny moon, but I also know Gas Giants can have 15+ so...can anyone help me figure some realistic numbers for these?

Asteroid = 0
Tiny = 3 Ast.
Small = 1 Tiny + 1 Ast. or 4+ Ast.
Medium
Large
Gas Giant 15+

WayneFrancis
2009-Nov-19, 04:58 AM
Earth is a bit of an odd ball. Our moon formed very differently then other planets moons. I think the number of moons that can be formed is dependant on a number of factors with the key factor being the size of the planet involved.

Earth could have many moons....just not many luna sized moons.

It also depends on what you mean by a "moon" I'll point you to
http://en.wikipedia.org/wiki/Natural_satellite

Durakken
2009-Nov-19, 05:24 AM
A moon for this purpose is any object larger than 100km and smaller than 150,000km that orbits around another object between those sizes that orbit around a stellar object and is not a stellar object.

As shown these sizes are split up into categories, asteroid, tiny, small, medium, large, and gas giant. This is how it will be represented in game. Basically I am trying to make it simple and fast while maintaining a level of believability.

I could just say large planets can have 8 moons... ok but what about terran planets? Can they have that many? Is that believable?

Also after looking at that image... are there no known moons bigger than Earth? So on my scale that would mean all moons are of the Tiny or Asteroid size

mugaliens
2009-Nov-19, 08:39 AM
Ok.. gonna try to explain what I mean...

Is there any limit to how many satellites, moons, that a planet can have?

Theoretically, yes, although it's probably in the thousands, if not tens of thousands, similar to the Sun's billions in the Oort cloud. On a more practical basis, however, Jupiter appears to have the most, with 63 named satellites, and thousands, if not millions of smaller bodies (Jupiter has rings).


Can Earth like moons form around planets if so is there minimum size to the planet?

Don't know! Perhaps someone else here does.


Can Earth like planets have multiple moons?

Jupiter is much larger than Earth, and has many. Meanwhile, Mars is smaller, and has two, so I'd say, "absolutely."


Why am I asking... because I am trying to create a game that creates a lot of planets and is fairly accurate...

I am dividing up planet sizes into classes that are pretty much like so...
Asteroid = 0-1,000km
Tiny = 1,000-10,000km
Small = 10,100-30,000km
Medium = 30,100-70,000km
Large = 70,100-150,000km
Gas Giant =36,000-1,400,000km

They are also each broken down into types of planets...
Icey (Pluto)
Metal (Mercury)
Rockey (Moon)
Ocean
Caustic (Venus like)
Terran (Earth like probably gonna change it to garden world)

So I need to know roughly how many moons each size range could support...It seems to me... that tiny planets can have 2+ asteroid moons and Small can have at least one tiny moon, but I also know Gas Giants can have 15+ so...can anyone help me figure some realistic numbers for these?

Asteroid = 0
Tiny = 3 Ast.
Small = 1 Tiny + 1 Ast. or 4+ Ast.
Medium
Large
Gas Giant 15+

It's a function of both mass (more mass means more capability of having moons beyond the Roche limit), as well as distance from the Sun - the further away, the more nebulous the planets themselves, and the more scarce the material for solid moons.

Thus, the general equation would look something like this:

N = F ( G ( m ), H ( d ) ), where:

N is the number of moons
F is the function of the subfunctions G and H
G is the function involving the effect a planet's mass has on the number of moons
H is the function involving the effect a planet's distance from Sol has on the number of moons
m is the mass of the planet
d is the distance from Sol

Someone more knowledgeable than I will have to fill in the details with respect to what the functions F, G, and H look like.

Those equations will provide a mean number of moons for each m and d, about which, for the purposes of your game, you can distribute moons within a reasonable distribution curve.

Rounded to the nearest integer, of course!

Nick Theodorakis
2009-Nov-19, 01:31 PM
...
Also after looking at that image... are there no known moons bigger than Earth? ...

No. None are bigger than Mars, although Ganymede and Titan are bigger than Mercury.

See:

http://en.wikipedia.org/wiki/List_of_Solar_System_objects_by_size

Nick

slang
2009-Nov-19, 02:04 PM
I think the number of moons that can be formed [...]

Or captured. And then the question could become: how many moons can a planet capture without all moons disrupting the heck out of each others orbits.

Nick Theodorakis
2009-Nov-19, 02:08 PM
How does capture work? Does a wayward body have to hit something to slow down to orbital velocity?

Nick

AlexInOklahoma
2009-Nov-19, 04:00 PM
How does capture work? Does a wayward body have to hit something to slow down to orbital velocity?

Nick

Nope - just has to have the approximately correct initial velocity and 'nearness' (angle-of-approach, per se) when approaching. Too fast and it zips by with some angular change - too slow and it will eventually, if not immediately, be pulled inwards and 'crash'. Its super-rare that a ~perfect orbit will be obtained on first-pass of object; tidal locking/friction plays a big role in stabilized orbits, iirr.

It gets pretty complicated overall, but its all a matter of velocity/approach angle (forget actual terms used - sorry) and the stealing of angular momentum/energy from the larger to the smaller of the bodies...and I bet I am not saying it correctly ;)

HTH,
Alex

Argos
2009-Nov-19, 04:06 PM
Can Earth like moons form around planets if so is there minimum size to the planet?

Earth could have a satellite of its same size [and mass], in which case it would be a double planet, orbiting a common center of mass. The bottom line is, there is not a limit.

chornedsnorkack
2009-Nov-19, 05:27 PM
Let us count the real, physical limits on the number and location of satellites.

Generally, the distance to the sun and to the planet has modest relevance. It is better to compute with orbital period.

The maximum orbital period is limited by the Hill limit. It is sometimes called "Hill sphere", but this is misleading, because it is not a sphere, and depends on inclination, eccentricity and direction of satellite orbits.

Basically Sun perturbs satellites that orbit the planet, and this perturbation is stronger if the Sun is nearby, or the planet has small mass, or the satellite is far from planet. The orbit of Moon is perturbed by the Sun - Moon has a bit over 13 orbits a year.

Because the distance to the Sun defines length of the year of the planet, and the mass and distance define the orbital period of the satellite, we can cancel out all of those factors and have only the ratio. A satellite cannot have an orbital period which is bigger than the orbital period of the planet or a large fraction of it. Moon has 1/13. Jupiter has outer irregular satellites which have a larger fraction of orbital period. But note that the outermost orbit retrograde; this is supposed to be not a coincidence, because prograde orbits are more perturbed. High inclination orbits are especially easy to perturb, so polar satellites can only happen, e. g. near a planet with highly inclined rotation axis like Uranus.

Now the inside limit. This is the Roche limit. A satellite cannot orbit too close to planet either, because tides would tear it apart.

This depends on the distance and mass of the planet. But orbital period also depends on those same things, so it cancels out and Roche limit is best stated in terms of orbital period.

In short, satellites cannot orbit with periods shorter than 6 or 7 hours.

This depends on the density and nature of the satellite, slightly. A very dense, metal satellite can resist the tides at slightly closer orbits than a low density and weak pile of sand. Which could be expressed as dependence of minimum period on material.

Ring particles can orbit inside Roche limit, because they are small enough to resist the tides with their mechanical strength. The maximum size of a ring particle depends on both its strength and its location between Roche limit and planet surface. Particles small and strong enough can orbit right on surface or top of atmosphere.

And because of perturbations, you also cannot have dense rings outside Roche limits. You can have tenuous rings, like the outer Phoebe ring that blackened Iapetus; but if the ring is too dense, the particles would aggregate into satellites.

Then you have tidal effects with the planet.

There is a reason Moon is so far from Earth. Strong tides. Moon was once very much closer. But rotation of Earth pushed Moon outwards gradually over very long time till it has 27 day orbit, still increasing. If Earth had more satellites once, they were perturbed by Moon and collided with Moon or were pushed outside Hill limit and escaped.

There is a reason Mars´ 2 small satellites can be so much closer than Moon. The same tides.

The bigger a satellite, the faster the tidal evolution. This is because while the kinetic energy of a satellite on a given orbit is proportional to its mass, the tidal force is proportional to the square of its mass: the height of the tidal bulge on the planet is proportional to the mass of the satellite and thus the attraction of bulge to moon scales with square of the mass.

If Deimos were as massive as Moon, it would have spiralled outwards rapidly until it were perhaps as far from Mars as Moon is from Earth - or until Deimos managed to slow down the rotation of Mars to enter a mutual tidal lock, like Pluto and Charon are. Since Deimos is so small, however, its slowing on Mars is minimal, thus it spirals out till it crosses the Hill limit. But the mass of Deimos is so small that this outward spiral is slow, and it still is at 31 hour or so orbit.

Any satellite which orbits either faster or opposite to the rotation of planet is slowed rather than speeded, so it spirals in rather than out. Phobos orbits faster than Mars, so it spirals in. If it were more massive than it is, it would long ago have reached the Roche limit and broken into a ring. As it is, we are living in an interesting time because after 4 billions of years of tides Phobos is supposed to have less than 100 million years left.

mugaliens
2009-Nov-21, 03:50 PM
It gets pretty complicated overall, but its all a matter of velocity/approach angle (forget actual terms used - sorry) and the stealing of angular momentum/energy from the larger to the smaller of the bodies...and I bet I am not saying it correctly ;)

In English, the wayward body has to pass in front of the orbiting body which is to capture it. In so doing, it transfers a good deal of its energy to the orbiting body while settling into an elliptic orbit about that body. As Alex mentions, it's velocity vector much be within an appropriate range for capture.

chornedsnorkack
2009-Nov-21, 06:52 PM
If Deimos were as massive as Moon, it would have spiralled outwards rapidly until it were perhaps as far from Mars as Moon is from Earth - or until Deimos managed to slow down the rotation of Mars to enter a mutual tidal lock, like Pluto and Charon are. Since Deimos is so small, however, its slowing on Mars is minimal, thus it spirals out till it crosses the Hill limit.

This requirement of slowing effect means that there is a very simple and strict requirement about when a mutual tidal lock is stable. Namely, that the orbital angular momentum of satellite must be at least three times the rotational angular momentum of the planet. For example, Moon cannot be stable on 24 hour geostationary orbit, but two or more days would be stable, or twice Moon´s mass.

On the other hand, the speed of tidal evolution can vary within a wide range. Earth actually has more tidal dissipation than average over geologic history.

Gas giants, however, have very much weaker tidal dissipation.

Now, that goes for restraints on one satellite. But what about several satellites?

We have rather dense inner satellite systems of Jupiter, Saturn and Uranus...