# Length of seasons on a planet with eliptical orbit

In my sci-fi story, I have a binary star system with two Sun-like stars orbiting each other in nearly circular orbits. The separation allows them to have planets in stable orbits, and their habitable zones slightly overlap, at least at the closest approach. (Or maybe the Primary, which has a few per cent more mass, can have planets in stable orbits while the Secondary can't.)

A planet orbits the Primary in a highly elliptical orbit that takes it from one edge of the habitable zone to another. And it has 45 degrees axial tilt. Water covers most of its surface, land mass is isles and archipelagoes, with the largest being slightly smaller than Australia. Adding some numbers: The closest approach to the star equals the smallest distance between Sun and Venus - 0,718 AU. The farthest distance from the star would be about 2 AU or a little more than the largest distance between Sun and Mars.

Thus, when the planet is on the closest approach to its star and its Southern hemisphere is pointed against the star, it has a short and severely hot summer, while the Northern hemisphere has a short and mild winter with average temperatures slightly below freezing and a lot of snow. In contrast, when the planet is farthest from the star (and travels in its orbit the slowest), the Northern hemisphere has a long and temperate Summer with bountiful agricultural harvests, while the southern hemisphere has a long and severely cold winter.

The question is: how long would each season be? What other circumstances should I consider?

• Would this planet be on S-type orbit? Jun 9 at 18:53
• @Alexander I didn't know this term before, but I think yes, it would be on S-type orbit, i.e., it orbits one of the stars. Jun 9 at 19:04
• You don't give any number that can help us get what you ask.
– L.Dutch
Jun 9 at 19:29
• @L.Dutch Thank you for the suggestion; I added some numbers I could think of. Jun 10 at 6:48

There are a few considerations for this kind of arrangement. The secondary star would have to be a great distance from the planet's orbit to avoid it performing a Lorenz orbit. At adequate distances, the other star would have negligible effects on the seasonal temperature shift.

There are a couple of arrangements for seasons, depending on whether the planet reached its apogee with the poles leaning towards the star. Whichever hemisphere was pointed at the star when it reached its nearest point would have more extreme summer/winter temperature shifts, and might be difficult to inhabit. Basically, it would contract the viable goldilocks zone for that hemisphere. Oceans would freeze in the winter and boil in the summer. You could call those seasons if you felt a need.

For the other hemisphere, I'm not sure if the eccentricity would contribute more to seasonal shifts than the tilt. I'm sure that it would depend upon just how eccentric you made the orbit. You'd still get massive winds from the other hemisphere during that hemisphere's summer, creating huge amounts of snow in this hemisphere's winter. The summers would likely be very dry, as much of the water would be locked up in ice on the other side. If you balanced the eccentricity and the tilt, you might have a wet spring and a dry autumn, with no summer and winter in between.

The second case is where the apogee is coincident with the equinox. For Earth, the seasons follow the tilt by about a month and a half. Just to make it easier to describe, let's say the north hemisphere points at the star before the equinox and the southern points at it after.

The northern hemisphere would pull out of winter early, have a very hot, long summer, and a relatively short winter, and vice-versa for the Southern. You could probably come up with an alignment where both hemispheres got the same treatment, but that would still be near-snowball planet cycling with 160 degree summers.

• "Whichever hemisphere was pointed at the star" - not necessarily. Periapsis/apoapsis does not need to match the solstice - it can be at the point of equinox just as well. Jun 9 at 20:46
• Ah, right, I forgot the second case. Jun 10 at 3:44
• @RobertRapplean Thank you for this informative answer! I have clarified that the Southern hemisphere is pointed towards the star when the planet is closest to it and added some numbers that I could think would be helpful. Jun 10 at 6:51