As long as we’re hitting the Earth with baseball bats and dropping the moon into the Pacific, let’s stick to the theme.
How much larger could the moon be without destabilizing the orbital system? Is there a maximum, say up to the size of the Earth itself? Could you have two Earth-sized bodies, revolving around one another (I know, all bodies revolve around one another; you know what I’m getting at), and the paired bodies revolving together around their star? Would this be stable in the long term?
I assume they’d need to be some distance apart; if they were close together, a large orbital speed would be required, yes? And at some threshold, the high speed would create stresses greater than the ability of the planet to hold itself together.
Would the two Earths need to be tidally locked, for any reason?
If Earth is too big, could the pair be of Mars-size bodies? (Marses?)
This might seem to be an obvious question to people with backgrounds in physics, but I’m not one of those people. My lay knowledge is pretty much limited to the knowledge that our moon is extremely large relative to its “parent” body, compared to the other planetary systems orbiting our sun. Our moon-and-Earth is, obviously, stable, at least up until the extreme long term. But if per the above two Earth-size bodies need to have a larger separation than the gap between the Earth and the moon, does that required distance make the system any more unstable?
Um… and just to keep this in line with the other threads… what happens if the women decide they want one of the Earths to themselves, and they make all the men move to the other Earth, because the women are tired of the men’s snoring and they just want a decent night’s sleep?
I see no reason why you could not have two same-sized bodies in orbit around a common centre (which would be midway between them). Presumably those bodies could be any size you wanted; aren’t binary stars an example of this?
Robert L Forward (I think) wrote a science-fiction novel, Rocheworld, that took place on such a pair of worlds. They were close enough to be tidally locked and distorted in shape, I think they shared an atmosphere, and ISTR that at one point water sloshed from one to the other.
[sub]And we only snore to keep away the bears. You don’t see any bears around, do you? See? It worked![/sub]
Also, just for the record, I hadn’t seen this other thread when I started this one. Not the same question, but interesting bit of overlap. Must be something in the air.
There’s no celestial mechanical reason that you couldn’t have two Earth-sized bodies orbiting about their common center of mass, and while the presence of the Sun would perturb them somewhat it wouldn’t be enough (at Earth’s orbit) to destabilize an otherwise stable system. The main limitation is that the bodies can’t be any closer than their respective Roche limits. In the special case that the bodies are identical in size and density, this is about 1.26 times the radius of either body. Of course, to maintain orbit at that speed they’d be spinning about very rapidly; I get about 45,000km/hr or a period of roughly 54 minutes.
In reality, such a system coalescing seems highly unlikely. If they did at that distance, they’d almost certainly be tidally locked as a result. If they formed seperately and by some unlikely circumstance came together in that fashion, then there’s no reason that they’d be tidally locked by default, but they would (as eventually all bodies demonstrating hysteresis will) become tidally locked.
That would be the Roche limit. I’ve never done the calculations for two objects of comparable mass, but it’d be roughly a few times the radii of the planets. For comparison, the current Moon is about 80 Earth-radii away, which is plenty far.
Well, more generally there’s no need for the “moon” to be smaller than the Earth, except if it was larger then Earth would be the moon and the other body would be the planet. So you could have Earth orbiting Jupiter with no problem. Of course, most of the bodies orbiting Jupiter are tidally locked to Jupiter, where 1 rotation of the body is exactly equal in length to 1 revolution around Jupiter. But you can have other orbital resonances, IIRC some aren’t 1:1 tidal locks but 3:2 or some such. Anyone know of a reference that can give the resonances of known moons? I’m suddenly curious because if Earth orbited a larger body at a distance from the sun that permitted liquid water, I imagine you could have stupendous high and low tides…unless Earth was tidally locked 1:1.
Doh! Yeah, you’d need a radius of at least r=2R[sub]e[/sub], and in this case they’d actually be mechanically locked, rolling over each other like a couple of, if you’ll pardon the expression, planetary gears. This also assumes rigid body behavior (i.e. the planet is a solid body held together by its own gravity). If we assume it to be fluid, the Roche limit is about 2.4R[sub]e[/sub]. Reality is probably somewhere in between. Tidal stresses would be enormous, of course.
