Re: planet help


Tux Wonder-Dog wrote:
> S. Palmer wrote:
>
> > Hey all! Delurking after a very long time to pester y'all with questions
> > (-:
> >
> > I was hoping for some help figuring out some physics of my planetary
> > system, and I just don't have the math skills/knowledge to figure it out
> > myself (OTOH, I'm always happy to learn) and was hoping for some help.
> >
> > Here's what I've got (which is hopefully plausible) and what I'm hoping
> > to find out:
> > Two planets, A and B, tide-locked together (and stable) around a fairly
> > Sol-like sun. There are no moons or other natural orbiting bodies with
> > these two to complicate things.
> > A is larger, has maybe 110% Earth's gravity.
>
> Don't you mean Earth Mass = 1; A = 1.1
> > B is smaller, has maybe 80% Earth's gravity.
> B = .8
>
Perhaps it refers to the gravitational acceleration at surface rather
than mass?

> >
> > They should be about the right distance out from the sun so that A can
> > sustain an atmosphere, liquid oceans, and temperatures under which
> > people could live (I'm thinking sort of "canada").
>
> An Astronomical Unit (AU). Of what size is their sun? An F (Whitish Star;
> hotter than the sun) (on the Main Sequence) will have its habitable zone
> well outside the AU; a K (Yellowish-reddish; cooler than the sun) will have
> it well inside and as a consequence, planet in the habitable zone will run
> a greater risk of being tidally locked to the star.
> >
> > I'm assuming that because of the difference in mass, that the point of
> > rotation of the two planets around one another is closer to planet A
> > than to planet B. The angle of the plane of rotation should be about 30%
> > (if I can do that) to their rotation around the sun, Z. I'm assuming
> > that there is a fixed formula for determining how long it would take
> > them to complete one rotation around each other?

Indeed there is. The Third Law of Kepler, with corrections due to their
having comparable masses.


Around the sun?

Ditto, with negligible corrections.

How big
> > would each planet appear in the sky of the other, and will I get
> > eclipses of any sort?
> >
Depends on what you want the day length to be.

For a start, if you has the main planet exactly the size of the Earth,
and with the exact same day then for a small satellite, like
Moon-sized, just imagine the Moon on geostationary orbit. 42 000 km
between centres, about 36 000 km from undermoon point to Moon centre,
34 000 km between surfaces. The Moon covers around 6 degrees looked at
from Earth, the Earth would cover about 17-20 degrees from
geostationary orbit. Someone could offer better numbers.

What is 30 % as angle... If it means 0.3 radians - about 17 degrees -
then the Moon would pass about 13 000 km from Earth centreline at
maximum, and avoid eclipses. (they are inevitable if centrelines are
closer than 8000 km - the sum of radii). So, there would be eclipses in
spring ansd autumn, but not in summer and winter. Use geometry and
exact numbers for more precise dates.

> > Can I have A have an atmosphere but not B?
>
> At those sizes, both would have atmospheres. I can't see how B, only .2
> percent smaller than the Earth, would not have an atmosphere if Mars,
> considerably smaller, manages to hang on to its.

Mars also is way colder than Earth, so a planet the size of Mars or
slightly bigger, but near Earth, might lose atmosphere. But Mars has
just 0,38 gravity acceleration of Earth. So, with 0,8 I think both
would have atmospheres.

> >
> > Given the proximity of B, would it be reasonable to suppose a
> > substantial tidal effect on A? Enough for the oceans of A and storms and
> > the like to be pretty constant and wild?
>
> Accurate. Though if both were tidally locked to each other, it would be the
> solar tides that would be important.
> >
> > Can I put a station up in orbit around B that will stay fixed relative
> > to B and won't be constantly pulled out of its orbit by A? Would it have
> > to be on the far side of B to A?
>
> Same as Earth-Moon.

Therefore not on the far side - that is an unstable Lagrange point.

But stable Lagrange points only exist if the mass ratio of the
primaries is over 25! So, in this system, no Lagrange points. You might
have constantly perturbed orbits where the perturbations cancel out
over time, though.

> >
> > If I wanted to have a big ol' gas giant further out from the sun are
> > there rules governing how close such a thing can be or can I pretty much
> > put it anywhere I want (except right on top of A and B, of course) and
> > call it good?
>
> A planet acts like a giant broom, sweeping up all lesser matter in its path.
> If the gas giant is too close to the terrestrials, they'll get thrown out
> of their solar system.

Unless they wind up in a stable resonance.

> >
> > Again, I'd love answers that help me see how to figure this stuff out
> > for myself, but assume for the sake of this discussion that I've got an
> > art degree and haven't taken a math class since the mid-80's (and
> > nothing beyond pre-calc) :-/
> >
> > thanks for any help you can provide!
> >
> > -Suzanne
> "Habitable Planets for Man" by Dole, If I Remember Correctly. You might be
> able to interloan it from your local friendly University Science Library.
>
> Have a read of it; it has a lot more than I can remember offhand.
>
> Enjoy!
>
> Wesley Parish
> --
> "Good, late in to more rewarding well." "Well, you tonight. And I was
> lookintelligent woman of Ming home. I trust you with a tender silence." I
> get a word into my hands, a different and unbelike, probably - 'she
> fortunate fat woman', wrong word. I think to me, I justupid.
> Let not emacs meta-X dissociate-press write your romantic dialogs...!!!

.

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