Re: Two suns

On 11 Nov 2007, Tina Hall wrote:

FennelGiraffe <sraarytvenssr@xxxxxxxxxxxxxxxxx> wrote:

[discussion of solar system with second sun in place of Jupiter]


On the other hand, if you put a sun-sized mass where Jupiter is,
it would orbit faster than Jupiter does (by a factor of the
square root of two, I think).

How many times bigger (massive, whatever matters) is the sun than
Jupiter?

Mass is the relevant measure here and the Sun is about 1000 times the
mass of Jupiter. (A very small, dim star could be as small as 13 times
the mass of Jupiter. One that small wouldn't provide noticeable heat
as far away as Earth, though.)

So Sun2 will have moved farther along its orbit during the 365
days Earth took to make one complete orbit, so it will take Earth
longer than 35 days to catch up.

It won't catch up at all if the Sun2's faster, it will be
overtaken by it.

Sun2 will be moving faster than Jupiter does, not faster than Earth.
Jupiter takes 4334 days to make one complete orbit; Sun2 would take
about 3062 days.

Look at a clock. Imagine a blue dot on the minute hand, way in near the
center, and a yellow dot on the hour hand, all of the way out at the
tip. The center of the clock is Sun1, the blue dot is Earth, and the
yellow dot is Sun2. At 12:00 both hands are lined up together, pointing
to the twelve. 60 minutes later, the minute hand has gone all the way
around and is back on twelve again. But the hour hand isn't on twelve
anymore. It didn't go all the way around, but it did move from twelve
to one. After five more minutes, the minute hand will catch up with
the hour hand, and they will both be pointing to one. It takes the
minute hand 60 minutes to go around once and come back to where it
started, but it takes it 65 minutes to go around once and come back to
be lined up with the hour hand. That's important because, when they are
lined up together, that's when the yellow dot and the blue dot are
closest to one another.

[snip]

Really, this is going in a completely unintuitive (for me)
direction. How about something straightforward?

Sun2 takes n planet-days a year at X orbit radius around Sun1,
with n and X shifting at <whatever ratio>. The X orbit radius in
AU is fine (multiples of planet distance to Sun1). If n (how long
it takes for a full circle) depends on its size (mass, whatever),
then that's just another variable. A Jupiter sun where it is is a
small star, fine, a sun sized sun where Jupiter is is (IIRC you
said) a quarter its size, also fine. What I don't know is the
rate at which it shifts, and how the length of its orbit shifts
with that (or even just its orbit at all).

With that data I can find a suitable orbit. (Perhaps I'll have to
look up the appearance of suns different size, but that's it.
Unless you tell me.)

Here are the formulas so you can do your own calculations. (Oh yeah,
they only apply to Main Sequence stars. I don't have a clue for the
other types.)

Distance is measured in AU
Mass is measured in Solar Masses
Time is measured in Earth Years
The amount of radiation is measured relative to the amount Earth
receives from our Sun.
The apparent size of Sun2 is measured relative to the apparant size of
our Sun.

A = the distance from Sun1 to Sun2
D = the distance from the planet to Sun2. This will vary depending on
where in their orbits Earth and Sun2 are, with a minimum value of A - 1
and a maximum value of A + 1
M1 = the mass of Sun1 (1, if Sun1 is our Sun)
M2 = the mass of Sun2 (Also 1, if Sun2 is the same as our Sun)
I = the amount of total radiation Earth receives from Sun2
P = the time for Sun2 to complete one orbit
S = the size Sun2 looks in the Earth sky

P = square root of (A^3 / (M1+M2))
I = M2^3.5 / D^2
S = [((M2*0.43)^2) * (M2^1.75)] / D

A few values to start with, so you don't have to look them up
If Sun2 replaces Jupiter, A = 5.20
If Sun2 replaces Saturn, A = 9.58
If Sun2 replaces Uranus, A = 19.23
If Sun2 replaces Neptune, A = 29.77
It doesn't have to be the same as one of the existing planets -- you
could pick any particular distance you like. I think putting the second
sun any closer than Jupiter would be extremely questionable, though.



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