# Seasons on a circumbinary planet

(I've tried to research this online but I'm a linguist, not a physicist, and most places that discuss this quickly get too technical for me. Simple answers will get tons of gratitude!)

I imagine two suns locked in a fairly tight orbit (for simplicity's sake let's say Sun 1 is the same size as our sun, while Sun 2 is twice the size of ours) with a planet that moves around both in a noticeable ellipse. In the absence of any tilt on the planet(?) my thoughts were that seasons would be determined by the distance of the planet from the suns, and I plotted out the course of one 'year' as follows.

Summer 1: Planet is at 3 o'clock, at one of the two points where it is nearest to both suns in its orbit. Days are long and the entire planet is warm.

Autumn/Fall 1: Planet is at 4-5 o'clock, moving further away from both suns (however Sun 1 is further away than Sun 2) Days steadily grow cooler as the season progresses.

Winter 1: Planet is at 6 o'clock, at its furthest point from Sun 1 and far from Sun 2 (in the sky Sun 2 eclipses Sun 1 at midwinter) The entire planet experiences mild winter.

Spring 1: Planet is at 7-8 o'clock, days lengthen and temperatures rise.

Summer 2: Planet is at 9 o'clock, at its other closest point to the two suns. The season is a mirror of Summer 1.

Autumn/Fall 2: Planet is at 10-11 o'clock, with Sun 2 further away than Sun 1. Days grow noticeably colder noticeably faster than in Autumn/Fall 1.

Winter 2: Planet is at 12 o'clock. This is the coldest winter, and the one where snow is likeliest to fall. Days will be dimmer and shorter than at any other time in the year.

Spring 2: Planet is at 1-2 o'clock, with days growing warmer again. A milder season than Spring 1.

...I'm sure I'm doing something wrong here, but I don't have the knowledge background necessary to figure out exactly what. If anyone could help me poke holes in this sequence and give any hints at what the actual order of seasons and variations might be, I would really appreciate it!!

• this system would probably be unstable May 24, 2015 at 21:23
• There a couple of flaws (or possible flaws) in your setting. First, your large star will have a much shorter lifespan than the smallest one. if it's twice the size and with the same density, it's 8 times the mass of the small star. That is a lifespan that is a lot shorter, maybe 100 million years only. I would recommend using smaller stars. May 24, 2015 at 21:27
• furthermore, the orbit will probably look like this : en.wikipedia.org/wiki/Binary_star#/media/File:Orbit2.gif I'm not sure if it's stable but the rotation is a lot quicker than what you described in the question. It could take a couple of days 1/2 weeks maybe. May 24, 2015 at 21:29
• @Xii precision in what you're asking will help in providing you with the answer you want. "Star 1 ~ Sol. Star 2 is twice Sol's (the Sun's) size." What do you mean by size? Mass, diameter, luminosity, or something else? Are we to assume both stars are main sequence like our Sun? May 24, 2015 at 22:27
• As @Vincent pointed out, your stars will rotate around the centre of mass. And your planet rotates (ellipse) around that system. To simplify, you could suppose that your planet orbit is a circle around the centre of mass of your binary system. But how do these two rotations combine? May 24, 2015 at 22:46

I'm afraid you've got a wrong picture in your mind about how an elliptical orbit works. It seems clear from your description that you think the ellipse can be centered on the center of the suns' mutual orbit (this is called the barycenter). So your seasons' description has the 3 o'clock and 9 o'clock as being the closest approach (perihelion), with 12 o'clock and 6 o'clock as the farthest away (aphelion).

Alas, this cannot be so. For an elliptical orbit, the barycenter must be at one of the foci of the ellipse, not the center.

Also, since the planet orbits well outside the mutual orbit of the two suns, those two must orbit each other much faster than the planet orbits them. This means that, although you do get a significant change in total radiation when the relative position of the suns changes, this varies much faster than the orbital distance. Let's say the suns orbit each other at 1/3 the distance of the planet, which is assumed to have a circular orbit around the barycenter. Note that I'm pretty sure such an orbit is grossly unstable, but I'm willing to suspend disbelief for the moment. We'll also assume that sun A has twice the luminosity as sun B, but both have equal mass. Set the total luminosity when the two suns are equidistant from the planet at 1. Then, just before A occults B, total luminosity will be about 1.6, and just before B occults A the total will be 1.07. For this configuration, when the two suns are equidistant their apparent separation will be 37 degrees. For this geometry, when the suns are equidistant their distance to the planet will be greater than the distance to the barycenter, which is why you get more heat at each occultation.

Roughly speaking, with the suns orbiting each other at 1/3 the distance of the planet, they will do so 9 times faster than the planet, so the rather large variation in heat will occur approximately monthly. Accounting for the fact that the two really ought to be rotating in the same direction as the planet orbits, you'll get 10 cycles per solar year.

If the planet has an even larger orbit two things happen. First, the relative intensity of the cycle will decrease. At longer overall distances the relative distance variations will decrease, which means the variations in total luminosity will also decrease. Second, the number of solar cycles per year will increase.

If you now change the planet's orbit from a circle to an ellipse, this will impose an annual luminosity cycle on the shorter solar cycles.

Finally, you should be aware that any major luminosity cycles will be catastrophic to the climate of the planet. The problem is that such temperature variation must be referenced to absolute zero. A variation of 2 to 1 in total insolation will produce an equilibrium temperature swing of 40%. With an average temperature of 27degrees C (300 K), this will have a total temperature swing of about 100 C. Although this will occur over a relatively short time period (think a month rather than a year) I think you'll agree that this will make for challenging conditions.

Your day length is dependent on axial tilt and orbital position of the planet.

Seasons will be dependent on axial tilt, orbital position of the planet and where the Suns are as they orbit each other.

So a couple of interesting effects here:

1. Day length will be related to seasons but not as tied to them as ours are. You could, for example, have short day summers. But not super hot short day summers.
2. Your basic cycle is correct but you'll get additional variation from the axial tilt. So sometimes the hot summer gets really hot, sometimes it's barely summer at all, etc. The exact pattern will depend on the exact dimensions of your solar system - rather than model it, you're probably free to just hand wave it. As long as it follows a pattern on a long enough basis, there should be some configuration that would do what you want.

Have you checked out the Helliconia trilogy by Brian Aldis? In that the planet orbits a fairly sunnish star, and that in turn is in a large eccentric orbit round a hotter one. Thus you get an Earthish short year from the first one but with a longer and stronger cycle from the second superimposed on it.