|There are 2 suns, both following a parallel path
through the universe at the exact same distance
apart, both of these stars are equal in mass to
the size of Earth's sun. A planet with equal mass
to Earth orbits both suns. How would I determine
the eccentricity, speed, and habitable zone of the
orbit? If the planet sits at a similar axial tilt
to Earth, and spins at the same speed, would the
two stars make a difference to the
ecology/climate/length of days on the planet?
Basically you want to know the eccentricity,
speed, etc. in your imagined Earth - Sun system.
The short answer is a lot of them can not be
determined given only the masses or under the
assumptions you made. For example:
Eccentricity: assume only the sun and
the earth, you still need to know the velocity and
orbit of Earth to the sun in order to calculate
the eccentricity. Things will get more complicated
if other factors are in consideration, for
example, other planets, the moon, etc. All of them
could affect the eccentricity.
Speed: it can not be calculated given the
masses only. It also depends on how the Earth-Sun
system is formed.
Habitable zone of the orbit: apparently, you
need to know a lot of other information, the power
of Sun, the distance of Earth to Sun etc..
Length of day: this one is relatively
simple, it is determined by the spin of Earth.
Ecology/climate: complicated! The power of
Sun, the orbit, the rotation of Earth, the axial
tilt of Earth, the Moon, the planet system, the
elements on Earth, the age of solar system, other
external factors, etc... A lot of those factors
could affect the ecology and climate. You know
even the ecology and climate is relatively stable,
still it could be very different compared to the
long history of our earth. One last thing I want
to mention, our human activity. The global
warming, the climate change is mainly because of
our human activity.
The stars cannot follow a parallel path because
they are going to be exerting gravitational force
on each-other. Either they will collide (and
bounce), or they will orbit one-another.
There are two ways that your planet can have
a stable orbit. It can either be (1) very
close to one of the stars, with the other far in
the distance. This is a similar situation that
exists in our solar system between the earth, sun,
and Jupiter, although Jupiter is much smaller and
much closer than the other star would be.
Alternatively, it can be (2) the two stars are
very close to each-other and the planet orbits
them at a greater distance.
In the case of (1), the planet would be
orbiting the closer star at the same orbit as the
earth orbits the sun, but the other star would be
much farther away. In the case of (2), the planet
would be at a distance of the square root of two
times that of the radius of the Earth's orbit. You
can then calculate the orbital speed based on
Newton's law of gravitation (the two suns simulate
a single sun with twice the mass).
There are other orbits that the planet could
have, but they aren't stable - the "figure-eight"
orbit, for example, would lead to the planet
eventually being either ejected from the binary
solar system or crashing into one of the two suns.
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