Re: planet help
- From: chornedsnorkack@xxxxxxxxxxxx
- Date: 3 Oct 2005 09:26:54 -0700
brdavis@xxxxxxxx wrote:
> Suzanne Palmer wrote:
>
> For "Earth normal" climate on an Earth-sized planet around
> >> a Sun-like star, you'll probably want it, well... in an Earth-like
> >> (1 AU) orbit.
> >
> > I just wasn't sure if having two planets threw stuff off,
> > but I guess now that I think about it more it's pretty obvious.
>
> It's obvious only if you've spent some time thinking about this
> stuff (like waaaay to many of us on this forum have spent waaaay to
> much of our time doing). And actually, you have a reasonable point, in
> that if the twin planets are really really close ("Rocheworld") the
> mutual eclipses are significant enough to reduce the amount of solar
> energy falling in the surface, especially in certain parts, and *can*
> influence climate. Just to complicate matters ;-).
>
> > I seem to recall that there was a fixed range of distance
> > where the system would be stable -- any closer and they
> > smash together, any farther apart and they don't stay
> > together.
>
> As other have mentioned, usually a satellite will not orbit closer
> to the planet than Roche's limit, which usually works out to about 2.5
> R_planet - closer than that, the differential tidal force will pull
> apart a satellite that is held together only by its self-gravity. The
> "classical" Roche limit is when self-gravity of two touching spheres in
> orbit is equal to the tidal forces pulling them apart, for a circular
> orbit, when spheres have a very small mass relative to the primary:
>
> a_Roche = 16^(1/3) ( rho_M / rho_m )^(1/3) R
> a_Roche = Roche limit, in, say, kilometers
> rho_M, rho_m = density of the primary (planet; big_M) & satellite
> (little_m)
> R = radius of the primary, in, say, kilometers
>
> Notice that if you change the units on "R", you change the units on
> "a_Roche" - this type of equation, where dimensions cancel all over the
> place, is really very kind. The caution here is that I'm not sure how
> it works for elliptical orbits, exactly, and I'm not actually sure how
> it applies to equal-sized "primary" & "satellites" (for instance, it
> does *not* work this way for "Rocheworld" - and Forward was a good
> physicist, I'll trust his calculations over my gut feel on this).
> As others have mentioned, there *are* satellites that orbit inside
> the Roche limit (notably Phobos), but these bodies are being held
> together by more than their own self-gravity (we think; hard to see for
> Phobos, actually). And if you want to be technical, modeling a
> satellite as "two touching spheres" is a little bit of an idealization
> ;-). For more accurate assumptions, change the "16^(1/3)" in the above
> to about 2.44.
>
> As to how far apart a satellite can get from a planet, a good rule
> of thumb (as others have mentioned) is it can orbit no further out than
> about 1/3 a_hill, where a_hill is something called the Hill radius:
>
> a_hill = a (m/M)^(1/3)
> a = semi-major axis of the planet around the star, in AU
> a_hill = the Hill limit around the planet (again, in AU!)
> m, M = the masses of the primary (planet) and the central star
>
> Simple? Well, not in this case. The Hill radius is an approximation
> used in deriving the motion of the Moon around the Earth, and I
> strongly it should NOT be trusted for a situation where the "primary" &
> "secondary" are similar masses. *But*, the only people that would try
> to fault you on this are, realisticly, folks in this or similar forums
> (planetary science can be such a great battering ram ;-). Conclusion:
> don't put the two planets further apart than about 1/3 a_hill, but
> closer would be better.
>
> > The 30% [inclination] was sort of arbitrary on my part
>
> A 3 inclination would produce, generally, very few eclipses,
> depending on a lot of other things. The inclination of our Moon
> relative to the plane of the Earth's orbit is never more than about ,
> and we still only get (if we're lucky) two eclipses a month. The
> problem with a 3 inclination is that I'm not sure how tidal forces from
> the star will effect things. It will at least change the precession of
> the pair (result, the twin planet's "vernal equinox" will shift over
> time, probably faster than for the Earth, but again I'd have to crunch
> some numbers... which requires masses, orbital distances, etc.).
> Also, a 3 inclination for the twin planets mutual orbit will give
> significant seasonality on them (more than Earth's).
>
> > I need to use the [complete] formula to figure out how long
> > they take to [orbit, or revolve] around one another,
> > but I can use [a simplified version of the] formula to figure
> > out [the orbital period] around the sun...
>
> Exactly. The second is a simplified version of the first.
>
> > Now, since the orbit isn't around a point in the exact center,
> > I assume I can describe the orbit as an ellipse?
>
> Actually it could still be a circle as well - most planetary orbits
> are (in *our* solar system anyway).
>
> > What, then, is the semi-major axis? An average of the radius
> > from the point of rotation to object, or is it more specific than that?
>
> The semi-major axis is simply half ("semi") the largest ("major")
> axis (or diameter) of an ellipse. In practice, the average* distance
> from the star, or (as other mentioned) the average of the closest and
> furtherest approach. The thing is, it's a description of the size of
> the orbit, *not* what the other mass involved is doing. If one mass is
> much larger than the other, you can talk about it as if the smaller
> mass orbited the larger one (implicitly assuming the larger mass
> doesn't move). If the masses are similar, you more correctly talk about
> each following their own orbit around the barycenter, which is just a
> point in space (there's nothing there).
> Does that help?
>
> *note to the nit-pickers: I know it's the angular average, not the time
> average.
>
> >> have you ever read "Rocheworld"?).
> >
> > I haven't
>
> "Rocheworld" by Robert Forward is set on a "double planet", where
> the two planets (each about the size of our Moon) are so close that
> they share a common atmospheric envelope. The result is one is,
> gravitationally, "higher" than the other, so all the water and more of
> the atmosphere end up on that one, with the other being low-pressure
> and very dry. From the science standpoint, it is an *excellent* read
> (as are most of Forwards stories), with the details hammered out (and
> sometimes, bluntly hammered into the head of the reader by charecter
> exposition).
>
> > I want A to be life-sustaining but B not so much
>
> If you're worried about humans on an alien world, no problem. We're
> remarkably intolerant of a lot of common atmospheric constituents (too
> much CO2, or too little O2 partial pressure, temperature extremes,
> trace gases, etc. If one world is a "scum world" (ie- pre-oxygen
> producing biochemistry, but life-form wise probably just slime mats of
> algae), it could have nearly zero O2 and a wealth of other nasty things
> floating around (H2S, CH4, etc., some more likely than others).
>
> > I'd just like to have some very rough ocean weather
> > on A, and thought the tide thing might justify that.
>
> Not in this case. Try for very warm oceans to get high-energy
> hurricanes on a world that is mostly oceans with small continents or
> island arcs. If the world is low-gravity, thunderstorms can get a lot
> nastier... I'm not sure about hurricanes specificly, but I would
> strongly suspect this would be the case for them as well. Slightly
> higher planetary rotation would help hurricanes be more energetic (but
> smaller), but if you really want one world tide-locked to the other,
> this will be a low-rotation case, with almost no (almost certainly none
> at all) hurricanes.
> Speaking of tide-locked, if you want the two planets to be tidally
> locked to each other, they really should be close (I don't think i've
> seen this mentioned in this thread yet). The details are...
> complicated.
>
If they are close they must be a high-rotation case!
Actually, there is another constraint on the sizes and distances.
You want a stable synchronous rotation. And that puts a big constraint
on the masses. Lower bound on the satellite mass, depending on the
rotation period.
To understand it, compare Phobos, Deimos and Moon.
Phobos and Deimos are small satellites of Mars. One is faster than
Mars, the other slower.
Both are unstable. For example, take Phobos. It rotates faster than
Mars. Therefore, it is slowed by Mars and spirals inwards - therefore
revolving even faster. Whereas, because Phobos is so small, Mars is not
rotating much faster while Phobos spirals in.
Deimos is slower than Mars, therefore it moves ever farther from Mars
without slowing Mars a lot - until it escapes.
It follows that if you want tidal lock, you must have pretty massive
satellite - so that moving it out or in would impart significant
angular momentum to the primary and cause the primary rotation period
to change more than the satellite revolution period.
> >> To apply the formulas, you really don't need to get beyond algebra.
> >
> > Yes, but sometimes knowing the formulas is the tricky part of it (-:
>
> As well as knowning when to apply them... and when *not* to. I
> absolutely agree :-).
>
> --
> Brian Davis
.
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