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[10ebbor10]

Well, the problem is that the moon isn't an equatorial orbit. Your elevator would tear itself to pieces. ((Or if it's indestructible, will cut through the earth at several opportunities)).

As for the energy, you're probably going to get a profit out of it, due to the gravitational energy. After all, the moon is in an orbit, so there's no net force pulling it away from the Earth. There's merely the kinetic energy as the moon flies around in it's orbit, a force which will be located perpendicular(*) on our conveyor belt. Ie, it's not our fan that has to counteract the force, but the structural integrity of the conveyor belt.

*Maybe not always, but it does if you assume the moon to be in an equatorial orbit.

Edit: Assuming a circular orbit this will have interesting effects on the moons orbit.

1) Assuming the Earth end is freestanding pivot, the moon's rotation will increase significantly.
2) If it isn't, the earth's rotation and that of the moon will increase significantly.

Spoiler: sketch (click to show/hide)

[da_nang]

Instead of using the 100W engine, we can just plant a strong, sturdy pole somewhere between 70.811ºN and the North Pole and let gravity do the rest.

[Il Palazzo]

Well, the problem is that the moon isn't an equatorial orbit. Your elevator would tear itself to pieces. ((Or if it's indestructible, will cut through the earth at several opportunities)).

By "all that jazz" I really meant all that jazz. Equatorial orbit alingment, no nutation, libration, external perturbations. And before you start screaming "not realistic!" consider there's Santa in there.

As for the energy, you're probably going to get a profit out of it, due to the gravitational energy. After all, the moon is in an orbit, so there's no net force pulling it away from the Earth. There's merely the kinetic energy as the moon flies around in it's orbit, a force which will be located perpendicular(*) on our conveyor belt. Ie, it's not our fan that has to counteract the force, but the structural integrity of the conveyor belt.

You still need to lift the mass out of Moon's gravity well, don't you?

[Tarran]

Question: Would it be possible for two bodies, of equal mass and density, to both orbit at least partially within the other's Roche Limit (assuming they somehow manage to get into that position)? And if so, what kinds of weird things would happen to the two bodies over time?

[Gigaz]

Question: Would it be possible for two bodies, of equal mass and density, to both orbit at least partially within the other's Roche Limit (assuming they somehow manage to get into that position)? And if so, what kinds of weird things would happen to the two bodies over time?

Yes, because the Roche limit only applies to objects which are mostly held together by gravity. This is true for most planets, comets and some asteroids, but small bodies can keep their shape by electromagnetism. But the question you asked is too general for a complete answer. Are these bodies supposed to be spheres? Are they solid or elastic? Realistic density or higher?

[Tarran]

Yes, they'd be spheres. They can be solid or elastic--whichever one you think gives the more interesting answer (solid, failing that).

I'm not entirely sure of what you mean by "realistic density". If you mean realistic as in non-fantasy, then yes, we'll assume the density of these bodies are what you'd expect to see in real life. If you'd like a specific density, let's say some density akin to Mercury, Venus, or Earth.

[10ebbor10]

As for the energy, you're probably going to get a profit out of it, due to the gravitational energy. After all, the moon is in an orbit, so there's no net force pulling it away from the Earth. There's merely the kinetic energy as the moon flies around in it's orbit, a force which will be located perpendicular(*) on our conveyor belt. Ie, it's not our fan that has to counteract the force, but the structural integrity of the conveyor belt.

You still need to lift the mass out of Moon's gravity well, don't you?

Yes, but you'd get more energy out of the return to earth. And since this is a conveyor, once the first stuff starts dropping, it will keep going. Anyway, I might do this later, if I find the time somewhere. It's rather complicated.

[Silfurdreki]

I was meaning more like, it becomes gravitationally bound with a protostar, and starts orbiting the planetary accretion disc.

Just by guessing, without properly looking things up, I'd say it would just give enough angular momentum to the protoplanetary disk to completely dissolve it on a fairly short timescale (not that protoplanetary disks live very long on astronomical timescales anyway, something like 1-10 Myrs).

Of course, it very much depends on the separation of the new protostar-neutron star binary. A binary with a 1000+ AU separation would probably not do anything to the protoplanetary disk at all.

[Gigaz]

Yes, they'd be spheres. They can be solid or elastic--whichever one you think gives the more interesting answer (solid, failing that).

I'm not entirely sure of what you mean by "realistic density". If you mean realistic as in non-fantasy, then yes, we'll assume the density of these bodies are what you'd expect to see in real life. If you'd like a specific density, let's say some density akin to Mercury, Venus, or Earth.

So, if you take the usual Roche limit definition and two identical small (<1m) spheres, they can happily orbit each other with 1cm surface distance forever. Then they will be within each others Roche limit and if one of them would be just metal dust, it would fall apart in no time.
Now, if the spheres were made of liquid mercury, they would also fall apart quickly somewhere within the Roche limit, but the Roche limit would probably be a bit reduced. For usual Roche, you'd consider the derivative of the gravitation force, but if the objects are of the same size you'd have to take higher order derivatives into account.
The liquid spheres would be deformed a bit and the orbit energy would be transformed into thermal energy, up till the point where the spheres fall apart or fuse.

[wierd]

I was meaning more like, it becomes gravitationally bound with a protostar, and starts orbiting the planetary accretion disc.

Just by guessing, without properly looking things up, I'd say it would just give enough angular momentum to the protoplanetary disk to completely dissolve it on a fairly short timescale (not that protoplanetary disks live very long on astronomical timescales anyway, something like 1-10 Myrs).

Of course, it very much depends on the separation of the new protostar-neutron star binary. A binary with a 1000+ AU separation would probably not do anything to the protoplanetary disk at all.

Wouldn't that depend heavily on the direction of rotation of the degenerate matter ball, how powerful its magnetosphere is, and what direction it is orbiting the protostar in relation to the direction of rotation of the protoplanetary disc?

Say for instance it is rotating and orbiting prograde, and not retrograde. It's influce would cause purterbations, but may not disrupt the disc.

If it is going retrograde, it will likely eventually collide with the protostar, and become one of those hypothetical stars with a neutron star fragment core, but not before seriously disrupting the protoplanetary disc.

It would also depend on how far out the degenerate matter clump was orbiting the protostar. (Is it orbiting the protostellar object's core mass, or the combined mass of the protostar and planetary disc?)

[Silfurdreki]

I think we need to establish the mass of the incoming neutron star. I was assuming a normal neutron star (NS), i.e. something like 1.5 M_solar. A less massive one would not be physically possible since the matter will not be degenerate any more and free neutrons decay very quickly (half-life of 15 minutes or so) into protons.

Such a significant short-term change in the matter distribution of the protostar system would likely have catastrophic consequences for the gas disk. These things are not very stable to begin with, being very turbulent due to a wide variety of gas interactions. A strong magnetic field might do something, but probably nothing good.

I don't think rotation will affect anything at all. Rotation only has an effect on gravity in extreme cases (see Kerr metric), but I haven't done any GR so I can't really comment. Since your average NS does not have much more mass than the sun, (and in fact, neither does it have more angular momentum) rotation would not have any effect on stuff orbiting it.

Orbiting retrograde would not really do much for the NS at all. A retrograde orbit around something else is perfectly stable, many of the solar system planets have smaller moons that orbit retrograde and they are on perfectly stable orbits. There's even one major moon, Triton, moon of Neptune on a retrograde orbit. Tidal effects are causing the orbit to decay due to being very close to Neptune, however, so on very long timescales (3.6 Gyrs) Triton will crash into be ripped apart as it enters Neptune's Roche lobe.

Anyway, even the gas will probably not slow down the NS enough to make it merge with the protostar, having a mass of only ~1% of the protostar itself. In astrophysics everything is a question of mass and time. When you have a large mass difference and a short time, the little guy is in for some serious changes to his way of life. So to speak.

The NS will at some point merge with the no-longer-a-protostar (at that point probably a white dwarf), at some point due to them emitting gravitational radiation. This takes a long time, however, quite probably longer than the current age of the universe, depending on their initial orbital separation and eccentricity.

It would also depend on how far out the degenerate matter clump was orbiting the protostar. (Is it orbiting the protostellar object's core mass, or the combined mass of the protostar and planetary disc?)

Finally, this piece is a bit weird. Something outside of the protoplanetary disk will always orbit their combined centre of mass. The combined centre of mass will be quite close to the protostar's centre of mass anyway due to the disk's low relative mass.


Heh, this got a bit ranty, sorry for that.

[wierd]

Depends on the disc. IIRC, some "interesting" ones have been observed with way more mass in them than they should have.

Remember, before fusion starts inside the protostar and blows the remaining gas away with solar wind and light pressures, there is a considerably greater amount of mass present than after the star ignites.

Two very massive objects will orbit each other around the system's barycenter. With a very small neutron star, and a massive protoplanetary disc, the mass difference between the two may be low enough for a stable barycentric orbit, but the gravitational effect of the neutron star companion would stretch the planetary gas disc, and make any bodies produced inside it have unusally eliptical orbits.

Even still, there might be stable configurations.

[HFS]

Hm. What would happen if, say, a hypervelocity (let's just say, oh, 2,000km/s) black hole of 5 solar masses approached our solar system, perpendicular to the plane of planetary orbits and slammed directly into the Sun (from "below")?

In particular, what would happen to the planets?

If we saw it coming (by, perhaps, looking in just the right direction), what would it look like?

[wierd]

In astronomical terms, that is slow. The sun is already traveling much faster than that in its orbit around the central black hole of the milky way.


As for what would happen?

The black hole's tradjectory would slightly change as a result of conservation of momentum, as the sun's currently existing momentum will have to merge with that of the black hole.

The sun will be ripped apart long before the black hole plows through it, and the resulting accretion disc would extinguish all life in our solar system from the immense amount of hard xrays and gamma rays produced.

The planets in the system will accellerate toward the new gravitational source, and the orbits will cease being harmonicaly stable. At 5 solar masses, it is unlikey that our planets will escape becoming part of the accretion disc. If they did, they would be thrown out of the solar system to become rogue planets.

The black hole will form 2 powerful jets of energy perpendicular to its axis of rotation as some of the infalling particles achieve angles of incident that cause them to miss the event horizon when they fall towards it.

The black hole will then be approximately 6 solar masses instead of 5.

[Il Palazzo]

In astronomical terms, that is slow. The sun is already traveling much faster than that in its orbit around the central black hole of the milky way.

No it isn't. You've probably read that as 2000km/h. It's per second, which is about four times the galactic escape velocity and nearly 1% of the speed of light.
Our Sun's orbital speed is closer to 250-ish km/s.

Also, it's not quite correct to say it's orbiting the central black hole. Sure, there is a black hole in the centre of the Galaxy, but at the estimated 1 million solar masses, it's gravitational pull mere 1000 ly away is the same as the Sun's at 1ly. We're 30000ly from it, and it's gravity is comparable to the gravity of the Sun 30 ly away. It'd be more plausible to say we're orbiting Alpha Centauri than the black hole.
It's the collective attraction of all the stars in the galaxy that gives rise to the orbital pattern we observe.