[TML] Planets in binary systems

[Jerry W Barrington]

On 3/3/08 6:27 AM, "Timothy Little" <tim at little-possums.net> wrote:

> On Mon, Mar 03, 2008 at 05:34:04AM -0500, Jerry W Barrington wrote:
>> Well, I couldn't quite follow some of your substitutions.  You said
>> "R = (1 - u) r1, so that u is the ratio between L1 distance from the
>> smaller body and that body's orbital radius", but that seems to call
>> for R=u*r1.
> 
> R is the distance between L1 and the barycentre of the system, not the
> distance between body 1 and L1.

Ah, Ok.  See, it's the little things that'll get you.  :)  I really should
have drawn this out on paper.

>> Since Goal Seek seems have a rather arbitrary precision, I found
>> that multiplying the entire formula by 100,000 made it find the
>> correct value for equal masses, .50..., instead of 0.50017933232343
>> or 0.499999986081074.
> 
> Yes, spreadsheets aren't exactly the best tools for precision
> mathematical analysis.

True, but I'll probably only use precision to *maybe* +/-.001 AU between
stars up to a few dozen AU apart, so it'll be good enough.  I just like to
start with a few more digits, because I'll also allow for eccentricity.
Although, I suppose I could add that to the spreadsheet at this point.

>> I suspect since the Hill formula is only an approximation anyway, my
>> values are better.  And they're smaller, and I'm only going to use
>> 2/3 to 1/2 of *that* value, so it's all good.  :)
> 
> Yes, extreme precision isn't really necessary when it's going to be
> divided by some rough factor later :-)

Well, it *is* just a game.  :P  The only reason I even started on this was
because it was obvious that a star that weighs 1/10 of it's companion
shouldn't equally split the available orbital space.