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I have a fantasy world I'm making, with a planet and sun similar to our world, except the length of the seasons are significantly longer. Each of the seasons last two years, and the full seasonal cycle lasts eight years. Here's what I thought could explain it:

The planet has an orbital period similar to Earth's, but has a low axial tilt and a highly irregular orbit, so seasonal climate variation is primarily based on the distance to the sun,

Would this be a feasible way to have longer seasons, or would a planet like that not be able to support life? Also, would this have any other consequences besides longer seasons?

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  • $\begingroup$ If you want a plausible planet, you might want to check out my answer. $\endgroup$ Sep 3 at 0:36
  • $\begingroup$ On Sat. Sept. 4, 2021 I added a section at the end of my answer describing a situation as close as I ocld make to your requirements that would be scientifically plausible. $\endgroup$ Sep 4 at 17:45
  • $\begingroup$ In my answerto the question: worldbuilding.stackexchange.com/questions/213437/… I found a way to make a seaonal cycle longer than the planetary orbital period or year. You might find it useful. $\endgroup$ Sep 16 at 5:50
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Only with magic

An orbit can be "irregular" buts its "average" orbit radius will remain constant. It's almost the definition of an orbit. Which means that at times during each year it will be closer to the sun and at times it will be further away. This translates to "seasons" within each year.

In order to achieve what you want for the entire planet simultaneously (Willk's answer gives an alternative for local conditions but no longer allows "days") the planet actually needs to shift to an entirely different but very circular orbit every two years. For Earth it would mean:

  • Two years orbiting at 1 AU (spring)
  • Two years orbiting at 0.98 AU (summer)
  • Two years orbiting at 1 AU (autumn)
  • Two years orbiting at 1.02 AU (winter)

Note that I'm just making up numbers here - possibly the variation should only be 0.005 AU rather than 0.02 AU. Regardless, the energy required to shift orbits would be literally astronomical and any mechanism that could move the planet without obliterating all life would be magical - which may be OK on a fantasy world.

An alternative mechanism would be to have the planet maintain a constant orbit but have the star's energy output increase / decrease in a regular eight year cycle. I have no suggestions regarding a mechanism to achieve this, but given that this is for a fantasy world, just state it as a fact. (Anyone with a good idea how to scientifically achieve this, please chip in.)

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  • $\begingroup$ Given a low axial tilt you'd need a lot more than 0.02 AU of fluctuation, the summer and winter insolation on Earth varies by 50%, roughly the difference between Earth and Mars. $\endgroup$
    – Ash
    Sep 3 at 0:28
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You could definitely have a longer winter.

elliptical orbit

https://www.windows2universe.org/physical_science/physics/mechanics/orbit/ellipse.html

You mandate an orbital period similar to earth and also an irregular orbit, which I take to mean an elliptical orbit. Seasons would definitely depend on how close the planet was to the star. The planet is moving fastest when it is the closest, so the hot season would be the shortest. The planet is moving slowest when it is the farthest so the cold season would be the longest. Wikipedia has a fine gif showing various orbits with the same period.

https://en.wikipedia.org/wiki/Elliptic_orbit

What you ask for is super tricky. You want seasons that last more than a year. That means the planet does a circuit around the star and the season does not change.


Here is how to do it. It is not about how close the planet is to the sun. It is about which side is facing it.

summer and winter sun

Your long season world has an S type orbit around one of a pair of binary stars. https://en.wikipedia.org/wiki/Habitability_of_binary_star_systems

The planet rotates very slowly. It is almost tidally locked to its star. The side facing the star that this planet orbits (the Summer sun) has summer. The far side is in winter but it gets some light from the distant star (Winter sun) so it does not freeze. During the very slow change of seasons both stars will be in the sky.

Several years (orbits around the star) go by before the planet completes a single rotation. Thus the change of seasons is really the passing of a single day. The summer sun finally sets at the end of autumn.

This planet will not have night.

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  • $\begingroup$ I think that the question asks for seasons which are longer than Earth years, not for seasons which are longer than the years of the planet. The question asks for 4 seasons each 2 earth years long, in a planetary year that is 8 Earth years long. $\endgroup$ Sep 2 at 17:04
  • $\begingroup$ @M.A.Golding from the OP: /Each of the seasons last two years, and the full seasonal cycle lasts eight years. / The term "earth years" does not appear. But regardless, this planet must have a year that is the same length as an earth year because /The planet has an orbital period similar to Earth's,/ and 1 orbital period is a year. $\endgroup$
    – Willk
    Sep 2 at 21:53
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You can't have everything.

The question specifies

  • planet similar to earth
  • star similar to the sun
  • orbital period similar to earth's
  • 2-year seasons / 8-year cycle

There's no good way to get all of that. So, let's look at what we can sacrifice to get you close.

Binary stars: As suggested by others (Willk and Ash), there are binary arrangements that would get your seasons right. Both involve orbiting a star that gets really close to another star on its orbit. That poses a lot of orbital stability challenges and might end up tossing your planet into interstellar space -- probably not your goal. Still with enough tweaking (or handwaving) you could make it work but your planet wouldn't be all that earthlike.

Long orbit: You could move your planet into an 8-year (2292-day) orbit. Each season would still only last approximately 1/4 of a year but the year would be 8 times longer. This would require moving to something like a 4 AU average distance. That's well outside the habitable zone for a G-type star like the sun. Instead you'd need something nearly twice the size of the sun (pale blue to white A-type). An A-type star introduces some issues with high-energy radiation and stellar longevity. That would require some serious explaining in hard SF but could maybe be handwaved in soft SF and maybe ignored in fantasy.

Highly eccentric planetary orbit: You could create an orbit that takes the planet to wildly different distances from its star: from one edge or the habitable zone to the other. This would get you seasons without axial tilt but it wouldn't really change their duration.

Different average distances on each orbit: Here you have a planet that orbits in a normal near-circular orbit but changes its orbital distance on a cyclic basis (e.g., 2 orbits at inner habitable distance, 2 at mid habitable distance, 2 at outer habitable distance, then back to 2 at mid). This gets you mostly what you want with two problems. (1) Years will not be the same length. The "winter orbit" will be much longer than the "summer orbit". (2) Basically, you need magic to make it happen. Theoretically you could achieve it with enough correctly placed massive objects but you'd need such a complex system that you might as well call it magic anyway. But you said this was a fantasy world so maybe that's ok?

A variable star: There are stars out there that change in energy output on a cyclic basis that might meet your requirements. Most of them are cycling on much shorter periods than you want (minutes to days with a few reaching to months) but there is one class that has a sufficiently long period to meet your needs, cleverly named "long-period variable stars". They're not very similar to our sun. We're talking about really big orange monsters but maybe with some handwaving?

Finally, about axial tilt: Changing the axial tilt to near zero is going to have major climate impacts. Most notable, your poles are going to get a lot colder. Assuming similar conditions to earth, expect ice caps to stretch down to cover much of Europe and North America (similarly high in the southern hemisphere). Maybe this is useful for your setting, maybe not. Just be aware that axial tilt does more than cause seasons.

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  • $\begingroup$ The binary solutions actually Require a large separation (on the order of at least 5 local AU) between the two stars and thus between the planet and the companion star at closest approach. $\endgroup$
    – Ash
    Sep 2 at 22:45
  • $\begingroup$ They have to be close enough for the planet to get into the non-primary's habitable zone, otherwise there's no point. A decently large separation gives you stability but doesn't provide much energy. $\endgroup$
    – legio1
    Sep 2 at 23:10
  • $\begingroup$ For an Earthlike seasonal variation the insolation budget needs to shift by roughly 50%, on earth that is almost entirely due to variation in daylight hours. To create that difference the companion star would, at closest approach, be supplying roughly half the amount of energy the primary does, if it were the same class as the primary it would need to be half again as far away and have a commensurately less gravitational effect, gravity decreasing by the square of the distance between objects. The orbital behaviour needed means a larger, hotter, companion being much farther away. $\endgroup$
    – Ash
    Sep 2 at 23:38
  • $\begingroup$ When I thought thru the binary option I tried to keep as much of the system matching the conditions stated in the question as possible, so I assumed sun-like stars. That would lead to close orbits and instability. I didn't consider replacing one of the stars with something bigger. If you do that, you can get the necessary separation. $\endgroup$
    – legio1
    Sep 2 at 23:56
  • $\begingroup$ It was a necessary compromise because the separation needs to be large in order to get the orbital ratios that create the seasonal lengths the OP is looking for one way or another. $\endgroup$
    – Ash
    Sep 3 at 0:00
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As a two body problem, only having one star, you could have a longer winter if you stretched the year but you'd compress your other seasons, most notably the summer would be down to about an 1/8 or less of the orbital period. Now if you have a primary orbited by the planet in question and a second star in an appropriate orbital resonance you might get the effect you are looking for with winter being the season when the planet and secondary star are close to Opposition, summer being the time close to Conjunction and the spring and autumn being the in-between times. I think you want an 8:1 resonance, the planet completes 8 orbits for every 1 that the companion star makes but it may actually be a quite different ratio.

This is not quite the opposite of what Willk suggested, in this case the planet and the "winter sun" orbit the "summer sun" of his answer on different orbital tracks. Thus there is a normal day/night cycle during the winter, the day/night ratio changes through the spring and autumn and during high summer there are a few days of almost continuous daylight with the summer solstice being marked by about 48 hours (assuming an approximately 24 hour axial rotation) of daylight the world over.

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Short Answer:

You mght need to make your planet one which has been artifically terraformed to become habitable by some advanced civilization. If you want a planet with such long years and seasons to be natuarlly habitable, you will need to design your solar system very carefully.

Long Asnwer:

Part One: Planetary Year Lengths.

The problem with having a planet with seasons and years which are arbitrarily long - and which is habitable - is the habitable part.

Planet SWIFT J1756.9−2508 b has an orbital period or year around its star of about 0.0379907 Earth days or 48 minutes 56.5 seconds.

https://en.wikipedia.org/wiki/SWIFT_J1756.9%E2%88%922508

[https://en.wikipedia.org/wiki/List_of_exoplanet_extremes#Orbital_characteristics] 2

However, the primary in this case is a pulsar, a type of neutron star.

The exoplanet with the shortest known year that orbits a normal star is K2-137 b, which has an orbital period of about 0.2 Earth days. Wikipedia says 4.31 hours.

https://exoplanets.nasa.gov/exoplanet-catalog/6071/k2-137-b/

https://en.wikipedia.org/wiki/List_of_exoplanet_extremes#Orbital_characteristics

Exoplanet 2MASS J2126–8140 has a year of about 328,725,000 Earth days, or about 900,000 Earth years.

https://en.wikipedia.org/wiki/2MASS_J2126%E2%80%938140

But the year lengths of potentally habitable exoplanets, those which orbit within the circumstellar habitable zones of their planets, have much less variation.

You can see that in any list of potentially habitable exopanets, like this one:

https://en.wikipedia.org/wiki/List_of_potentially_habitable_exoplanets

Sorting the orbital period column for length, I see that as of today, September 2, 2021, there are 59 exoplanets listed with year lengths shorter than that of Earth's 365.25 days - 40 with years less than 100 days long. The shortest is 4.05 Earth days. There are three with year lenghts longer than the 365.25 days of Earth's year, at 384.8, 448.3, and 636.1 Earth days.

A season two Earth years long would be 730.5 Earth days long, a year of four such seasons would be 2,922 Earth days long.

Of course the more massive and luminous a star is, the farther away its circumstellar habitable zone will be, and thus the longer will be the years of any planets in its habitable zone. If the planet's stas is luminous enough, a planet could orbit in the habitable zone and still have a year tens or hundreds of Earth years long.

Part Two: The Limits on Types of Stars Which Can Have Naturally Habitable Planets.

But:

It is believed that it took Earth billions of years to develop an oxygen rich atmosphee and have large multicelled plants nd animals on land, and to become habitable for humans.

So if you want you fictional planet to have any of the above qualities, it should be billions of years old.

The only alternative is that sometime in the past a highly advanced society terraformed a young and uninhabitable planet and made it habitable.

A planet with life has to have fairly steady illumination from its star to have surface tempeatures suitable for life. And it takes billions of years of such steady illumination levels for a planet to become habitable for humans or otherwise interesting for the purposes of most science fiction stories.

And different types of stars vary vastly in how long they remain shining with a fairly steady luminosity as main sequence stars before they enter the stages of stellar evolution where their luminosity changes drastically and all life - if any -on their planets dies, and sometimes the planets themselves are destroyed.

And for decades astronomers have been able to calculate the life histories of various types of stars, including how long they can stay on the main sequence.

Stephen H. Dole, in Habitable Plenets for Man, 1964, discussed the qualities a world needed in order to be habitable. On pages 67 to 72, he discussed the properties necessary for a star to have a habitable planet, calculating lower and upper limits of mass and luminosity.

On page 68 Dole calculated the upper limit of stellar mass for for a star to possibly have a habitable planet is aobut 1.4 stellar masses, a spectral class F2V star.

https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf

There are several answers to this question:

https://astronomy.stackexchange.com/questions/40746/how-would-the-characteristics-of-a-habitable-planet-change-with-stars-of-differe/40758#40758

The answer by user177107 has a table with the chracteristics of various spectral classes of stars, including columns giving the distance at which which aplanet would receive exactly as much illuminatin and heat for th star as Earth gets from the Sun, and how long the year of a planet in such an orbtt would be.

The orbital period ranges from 3.82 Earth days around an M8V class star to 2,526.01 Earth days around a A2V class star. But the orbital period around an F2V class star - the most massive type star that Dole considered could have a habitable planet - would be only 1,018.01 Earth days.

Maybe your planet orbits near the outer edge of the star's circumstellar habitable zone and has an average temperature lower than Earth's but high enough to sustain life. How far out is the outer edge of the Sun's circumstellar habitable zone?

According to this table, scientists have often calculated the inner and outer edges of the Sun's habtable zone, and some of their calculations vary greatly.

https://en.wikipedia.org/wiki/Circumstellar_habitable_zone#Solar_System_estimates

The planet Mars orbits about 1.523 times as far from the Sun as Earth does, and a larger planet with a denser atmosphere at the distance of Mars might possibly be habitable. The year of Mars is is 686.98 Earth days, or 1.88 Earth years.

So a planet orbiting a F2V star at a distance where it receives the equivalent of Mars's radiation from its star might possibly be habitable, and it would have a year about 1.88 times as long as the year of a planet at the Earth equivalent distance, a year about 1.88 times 1,018.01 Earth days, or 1,913.8588 Earth days long.

Suppose that your planet orbits a binary F2V star, two 52V stars orbiting each other at a distance of 5 or 10million miles or so. In such a situation the planet would receive the amount of radiation it receives at distance X from one star at a distance of 1.414 times distance X. So your planet could have an orbit 1.414 times wider, and thus with 1.414 times the total circumference, as in the previous case, giving it a year 2,706.6049 Earth days long. which is about 7.410 Earth years long, and close enough to what you desire.

However that would make the mass of the pair of stars double that of one star, so that should increase the orbital speed of the planet, making its year much shorter than 7.4 Earth years long. doubling the mass should double the orbital speed require, while increasing the circumference only 1.414 times, and so should reduce the orbital period to 0.707 times the equivalent around a single star.

I calculate that an orbit around two F2V stars (with a total mass of about 2.88 times the mass of the Sun) which receives Mars-equvalent levels of radiation from those stars, should be at a distance of about 4.815 AU from the stars. According to this online calculator, http://www.calctool.org/CALC/phys/astronomy/planet_orbit a planet in that orbit would have a year of 6.22478 Earth years or 2,273.64 Earth days. That is about 0.84 times the length of a year of a Mars equivalent orbit around a single F2V star.

The Mars equivalent orbit around a pair of F2V stars would be at about 4.815 AU. That is about 3.1615233 times Mar's orbit of 1.523 AU. A pair of F2V stars would have about 10.002 times the luminosity of the Sun. 10.002 divided by 9.9952295 (the square of 3.1615233) equals 1.0006773, which is pretty close to 1.0. Thus the calculations seem to be correct.

So a planet in a Mars equivalent orbit around a pair of idential stars would have amuch longer orbit around them than it would have in a Mars equivalent orbit around only one of those stars. But it would orbit much faster and so wouldhave a shorter oribitlaperiod than if it had the shorter orbit around only one of the stars.

So it seems to me that a habitable planet with a year 7 or 8 Earth years long would be close to the extreme limit of scientific plausibiity and would be a very rare situation.

Part Three: An Aritifically Habitable Planet With a Long Year.

An alternative would be if the planet had not become habitable by natural processes over billions of years. Instead the planet orbited a spectral clas A or B star, and an advanced society had terraformed the planet to make it habitable, not caring that the habitability wouldn't last for more than a few hundred thousands or millions of years.

Or possibly the super advanced society found an already habitable planet which orbited a star which was aobut to leave the main sequence and become a red giant, and moved that planet into orbit around a hot young massive star where the planet now has a year 8 earth years long, not caring that they would have to move it again in a few million years.

Part Four: A Naturally Habitable Planet With a Year 8 Earth years long.

Assume there is one F2V star. One F2V star would have 1.44 times the mass and 5.001 times the luminosity of The Sun. A planet at a distance where it would receive the same amount of radiation from the star as Earth, at a distance of 1 AU, gets from the Sun, would orbit at a distance which was the square root of 5.001, or 2.236, AU. The table I referred to above says 2.236 Au, and that the planet would have a year of 1,018.1 Earth days.

Assume that there is a smaller star orbiting the larger star, and the planet orbits the smaller star. Maybe the planet is a K2V type star with a mass of 0.78 solar mass and a luminosity of 0.337 solar luminosity. According to the table I mentioned above, a planet getting the same amount of light and heat as Earth gets from the Sun would orbit at a distance of 0.58 AU and have a year 182.93 earth days long. Or maybe the planet would orbit at the Mars equivalent distance which would be 1.523 tiems as far, or 0.883 aU, andit would have a year 1.88 times 182.93 Earth, or about 343.9 Earth days.

But the planet of the smaller star would also receive some radiation, light and heat, from the larger star. The closer it got to the larger star, the more heat it would get from it. And if the smaller star and its planet has an elliptical orbit relative to the larger star, the amount of light and heat the planet gets from the larger star would change with its changing distance.

Exoplanets have been discovered in binary star sysems. Some of them orbit both the stars in a circumbinary or P-type orbit, and others orbit one of the stars in an S-type orbit, with the other star farther away from the planet. This situation would be an S-type orbit.

According to the list of exoplanet extremes, the closest binary stars with a planet in orbit around one of them in an S-type orbit is the system OGLE-2013-BLG-0341LB with a separation between 12 and 17 AU. The planet OGLE-2013-BLG-0341L b has an orbit with a semi-major axis o f0.7 AU, so the separation betwenthe stars is 17.14 to 24.28 time the orbit of the planet around one of the stars.

https://en.wikipedia.org/wiki/List_of_exoplanet_extremes

And perhaps the stars could get much closer than that without perturbing the orbit of the planet too much.

In non-circumbinary planets, if a planet's distance to its primary exceeds about one fifth of the closest approach of the other star, orbital stability is not guaranteed.5

https://en.wikipedia.org/wiki/Habitability_of_binary_star_systems

http://www.solstation.com/habitable.htm#sthash.WLPv5bxd.dpbs

Possibly the smaller star could have an elliptical orbit around the larger star star which takss it to between 5 and 10 times the radius of the planet's orbit.

The F2V star would have about 5.001 times the luminosity of the Sun, and the K2V star would have about 0.337 times the luminosity of the Sun, so if the two stars were at the same distance from the planet it would get about 14.839 times as much heat from the larger star as from the smaller star.

When the larger star was 5 times as far way the planet would get 14.839 divided by 25, the square of 5, or 0.593 times as much heat from the larger star as from the smaller star, while when the larger star was 10 times as far way the planet would get 14.839 divided by 100, the square of 10, or 0.14839 times as much heat as from the smaller star.

A planet orbiting a K2V type star might be tidally locked to its star, so one side wuld always face the star and be heated by it, and the other side would never get any heat or light frum the star. scientific opininis divided whether such a plent could be habitiable. In this star system, as the planet orbited the smaller star, the inner and outer sides of the planet would take turns facing toward the larger star and getting heat and light from the larger star, which might improve the odds that the planet would be habitable.

If such a situation is acceptable, you can make the star even smaller and more likely to tidally lock the planet.

If the planet orbited a K5V with 0.165 times the luminosity of the Sun, it would receive Earth's amount of radiation from the smaller star at a distance of 0.406 AU and with a year of 144.84 Earth days. A F2V type larger star would be 30.3 times as luminous as a K5V star, so at 5 times the distance it would give the planet 1.2 times the radiation from the smaller star, at 10 times the distance it would give the planet 0.301 times the radiation, at 20 times the distance it would give the planet 0.075 times the radiation, and so on.

If the planet orbited a K8V star with 0.079 times the luminosity of the Sun, it would receive Earth's amount of radiation from the smaller star at a distance of 0.281 AU and with a year of 70.95 Earth days. A F2V type larger star would be 63.303 times as luminous as a K8V star, so at 5 times the distance it would give the planet 2.53 times the radiation from the smaller star, at 10 times the distance it would give the planet 0.633 times the radiation, at 20 times the distance it would give the planet 0.158 times the radiation, and so on.

There are many other possible combinations of star types, including making one or both of the stars binary stars, which can differ in mass and luminosity themselves.

Thus it should be possible to construct a star system where a habitable planet orbits a smaller star which orbits a larger star, and where the changing distances between the two stars cause changes in planetary temperature and drive the seasons o the planet, and hwere the orbital period of the stars equal 8 Earth years.

Part Five: Using the Orbit of the Planet Around the Smaller Star.

I thought that you could possibly have the two stars have more circular orbits, but as close together as possible, so the planet's orbit around its own star makes a significant difference in the amount of radiation it receives from the farther star.

If the two stars are separated by 5 times the planet's orbit, the distance between the planet and the farther star would vary between 4 and 6 times the distance of the planet's orbit arund the nearer star. So if the farther star was 2 times as luminous as the near star, for example, the radiation it gave to the planet would vary between 0.125 and 0.0555 that of the nearer star.

But in that case the orbit of the planet around the smaller star would determine the seasons, and so it wuld have to be 8 Earth years long, and I have already pointed out the problems with a habitable planet havinga year 8 earth years long.

Conclusion:

It does not seem totally impossible for a planet to have a year 7 or 8 years long, and still receive about as much radiation from its star as Mars gets from the Sun. A larger planet that Mars, with more water and more greenhouse gases in its denser atmosphere, might be much warmer than Mars despite receiving no more radiaitn than Mars gets.

And there is also the possibiity of making your planet orbit close to a smaller star which in turn orbits a larger star close enough to get significent heat formthe more sdistant larger star andhave the smaller star orbit the larger star with a period of about 8 Earth years.

If the orbit is eccentric and the distance between the star and the planet determines the seasons, the seasons will not be equally long. On Earth the seaons measured by astronomers are equally long, but the weather seasons in the local regions and climate zones are of various lengths differing from the astronomical seasons.

And on your planet even the astronomical seasons would be of varying length, since the planet would move faster closer to the star and slower farther from the star. Thus winter could be as long as the other three seasons combined, for example.

Added 09-04-2021.

Your question specifies that the orbital period of the planet (it's year according to the normal definition of a year) should be eual to ours, but a cycle of the seasons lasts for 8 years.

That is almost impossible. Seasons should be fractions of years.

But if the world inquestion s orbits around an astronomical object which orbits around another astronomical object, then it might work.

Suppose that there was a Earth sized giant moon orbiting a giant planet or a brown dwarf with a period of about 1 Earth year, and that giant planet or brown dwarf in turn orbited a star with a period of about 8 Earth years.

The Planet Jupiter has over 60 moons which orbit so far away from Jupiter that they have orbital periods more than one Earth year long - 16 have orbital periods over 2 Earth years long.

Of course all those outer moons are irregular moons. But maybe the giant moon could have been an Earth like planet in an independent orbit that was captured by the giant planet or brown dwarf.

If the orbit of the giant planet or brown dwarf was eccentric, the amount of heat and light received by an Earth sized moon would vary over the "superyear" of 8 Earth years instead of the ordinary year of 1 Earth year.

But if the brown dward or giant planet orbits the star at a distance where it has a year 8 Earth years or 2,922 Earth days long, it will receive a bit less than the heat Mars receives from the Sun, and probably be too cold.

And many people might consider the "superyear" around the star to be the real year of the giant planet and eEarth sized moon and the orbital period of the Earth sized moon around the planet to be a month and not a year.

So we can change it to make the Earth like planet orbit around a Sun like star in a period of about one Earth year, which in turn orbits around the center of gravity with another star in a somewhat elliptical orbit in a period of about 8 Earth years.

So the planet would be orbiting its star at a distance of about 1 AU. If the the stwo stars aproached to 5 AU at their closest, the planet would be somewhere between 4 AU and 6 AU during that closest pass.

If the other star was exactly the same as the primary star of the planet, very similar to the Sun, it would give the planet 0.625 Times as much heat at a distance of 4 AU, 0.04 times as much heat at a distance of 5 AU, 0.02777 times as much heat at a distance of 6 AU, 0.01 times as much heat at a distance of 10 AU, 0.0025 times as much heat at a distancee of 20 Au, and so on.

If the other star was an F2V type star, it would have 5 times the luminosity of the primary star of the planet. So it would give the planet 0.3125 of the heat from the prmary at a distance of 4 AU, 0.2 times the heat from the primary at a distance of 5 AU, 0.138 times the heat of the primary at a distance of 6 AU, 0.05 times the heat from the primary at a distance of 10 AU, 0.0125 times the heat from the primary at a distance of 20 AU, and so on.

So most of the time the heat contribution from the other star would be very minor, and the planet woulde xperience normal seasons. But if the planet had a very minor axial tilt, the normals seasons would not make muchof a difference in the temperatures of varius climate zones. The temeratures in the hottest summers and the coldest winters weould be almost the same.

But when the primary star and the planet passed closest to the other star there would be a signifcent increase in heat and there would be a very hot summer all over the planet.

I also note that as seen from the planet, the two stars would sometimes be lined up and sometimes be on opposite sides of the sky, and sometimes be at every angle between. The greater the angle between the two stars when they were closer together thelonger would be theperiods when at least one stars was in the sky,and the shorter the periods of night.

So the farther apart the directions, as seen from the planet, to the two stars get during the period when the stars pass closest together, the hotter the planet will get.

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KerrAvon2055 raised an interesting point, you could vary the distance between the planet and it's host star year on year. The existing answer proposes that magic would be needed and that may be correct but:

I shudder to think how massive and possibly how close it would have to be in order to have a large enough effect, KerrAvon2055 suggests 0.02 AU quick is not at all a small variation but it's probably not big enough for Earthlike seasons. Anyway if you have a super Jovian world in the same system you can shift the barycentre of the star system outside the primary. It may actually require a close binary with a yellow primary and a brown dwarf that supplies negligible light/heat. The star will then be orbiting the same point as the planet rather than the planet actually orbiting the star itself. The distance between the two will then fluctuate in a predictable pattern of oppositions and conjunctions, it may not be consistent year on year but it will create long period "seasonal" variations.

Actually given the difference in insolation that is needed (~50%) the super Jovian world/brown dwarf also fulfills another function, it shares an elliptic with the planet in question and blocks a large amount of the light of the primary during the winter, otherwise the variation in sunlight intensity simply isn't great enough.

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