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Beemer

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Orbital Mechanics [Dec. 31st, 2009|12:48 am]
Beemer
If you have ever considered putting an Earth-like planet in orbit around a gas giant:

* It will become tidally-locked in a few tens of thousands of years, which is somewhat inconvenient if you wanted a particular rotation speed.

* But you can put it in an orbit close enough to its primary to have a 24-hour orbital period (and hence a 24-hour day) and come nowhere even close to the Roche limit. (Because the limit is probably near or below the top of the gas giant's atmosphere.)

* Being tidally-locked, your ocean tides aren't going to be affected by the primary (which is fixed in the sky), but will be due to the sun and any other moons the primary may have. (But that said, the inner and outer poles will probably be where the oceans are located.)

* At a distance of 300,000 km (roughly a 24-hour orbit), Jupiter has an angular width of around 13 degrees -- which is 25 times as big as the sun/moon from Earth. It will be REALLY BIG in the sky.

* And assuming a 24-hour day, the daily solar eclipse (as the moon passes through the primary's shadow) will last for a little under an hour.

* At the inner pole, lunchtime is the only time you'll get serious darkness. At the outer pole, the only obvious evidence of the gas giant's existence will be its effects on any other moons.
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Comments:
[User Picture]From: erik415
2009-12-31 10:18 am (UTC)
I like the way you think. It's kinda sexy.

And you must have seen Avatar.
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[User Picture]From: dr_tectonic
2009-12-31 02:49 pm (UTC)
Actually, I haven't seen it. Did they get this stuff right?
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[User Picture]From: erik415
2009-12-31 07:16 pm (UTC)
You know, I'm trying to think if there was a shot of Polyphemus, the primary, dominating the sky. I can't recall at the moment, so perhaps Pandora was tidally-locked and the hemisphere in which the story took place was facing opposite the primary. And there were no daily eclipses, which doesn't mean they didn't happen in Cameron's universe. I'd assume someone on their massive production team thought about those issues when creating the fictional world.

Either way, it was pretty. And what are you doing reading your LJ? You should go out and see the movie in 3D asap :)

Pandora
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[User Picture]From: ocschwar
2009-12-31 02:52 pm (UTC)
Planning a trip to Magrathea?
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[User Picture]From: flwyd
2009-12-31 03:29 pm (UTC)
I understand most of that, but what are inner and outer poles?
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[User Picture]From: dr_tectonic
2009-12-31 03:55 pm (UTC)
The inner pole is the spot where the primary is always at zenith; the outer pole is where it's at nadir.
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[User Picture]From: flwyd
2009-12-31 04:01 pm (UTC)
Ooh. A body with rotational axis aligned to inner/outer pole would have some neat celestial effects.
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[User Picture]From: dr_tectonic
2009-12-31 04:16 pm (UTC)
It would! Although I don't think you could get that naturally. You'd need some extra forcing to keep the rotational axis pointed at the primary.
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[User Picture]From: annlarimer
2009-12-31 06:01 pm (UTC)
Could it have its own satellite for tidallationing, or would that just make gas giant skee-ball?
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[User Picture]From: dr_tectonic
2009-12-31 07:42 pm (UTC)
Skee-ball! I think the only way you can have stable satellites of satellites is if there's a really big difference in the sizes & distances involved (e.g., Sun-Earth compared to Earth-Moon). A moon-of-a-moon that was be small and close enough to be stable would probably be too small to have any significant effect on the tides.

But if the gas giant has other moons, you can get plenty plenty of tidallation from them. Just look at Io, which is all volcano-riffic from tidal heating due to the 1:2:4 orbital resonance with Ganymede and Europa.
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[User Picture]From: annlarimer
2009-12-31 07:46 pm (UTC)
Just look at Io, which is all volcano-riffic from tidal heating due to the 1:2:4 orbital resonance with Ganymede and Europa.

The 1:2:4 resonance. Of course! If it had been a snake, it would have bitten me!
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[User Picture]From: goddessdster
2009-12-31 10:27 pm (UTC)
*nods*
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[User Picture]From: bluebear2
2009-12-31 11:10 pm (UTC)
I think my video camera does 1:2:4.
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[User Picture]From: dr_tectonic
2009-12-31 08:01 pm (UTC)
Oh, hey, lookie!

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

And the Hill sphere for an Earth orbiting Jupiter at 300,000 km would be about 30,000 km radius. (For comparison, the average distance from the Earth to the Moon is 380,000 km.)

Hmm... okay. Gravitational force is G M1 M2 / R^2, so if you wanted a moon that generated about the same size tides, but that was only 25,000 km away instead of 380,000, it would have to have 230 times as much mass. But then it would weigh about 3 times as much as the Earth does, making the earth the satellite and the moon the primary...

So yeah, I don't think you can do it.

Side note: Google calculator is pretty awesome.
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From: pocketbearwa
2010-01-14 05:37 pm (UTC)

Fortunately...

...Peter F. Hamilton got it exactly correct in "Fallen Dragon" - the protagonist's home planet is a tidally-locked moon of a gas giant.
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[User Picture]From: dr_tectonic
2010-01-14 05:48 pm (UTC)

Re: Fortunately...

Excellent! Is it worth reading otherwise?
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From: pocketbearwa
2010-01-14 05:51 pm (UTC)

Re: Fortunately...

It is...grim. He has a knack of painting interesting worlds in VERY LARGE BRUSHSTROKES, and them putting quirky characters in them - but this time, it seems to be drenched in unrelieved DARKNESS.

Massive corporations who use "asset realization" missions - piracy - to raid the colonial planets that were established centuries ago; apparently, it's the most cost-effective method of recouping the original development costs.

High-tech humans in battle suits raiding slightly-less-high-tech humans and holding them hostage while they raid the entire industrial output of the planet until their starship holds are full, then back to Earth they go!

(And there's a plot in there too - which, 300 pages in, I'm only STARTING to see...)

Interesting read; I'd HIGHLY recommend "Second Chance at Eden" first - his collection of short fiction. Then the Reality Dysfunction trilogy. Don't start *here*, or you'll never come back. :)
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[User Picture]From: dr_tectonic
2010-01-14 05:59 pm (UTC)

Re: Fortunately...

Ah, like THAT.

Thanks for the rec!
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