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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?
Question Date: 2017-06-20
Answer 1:

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.

Answer 2:

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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