# Thread: Input wanted on day length & seasons on a fictional planet.

1. ## Input wanted on day length & seasons on a fictional planet.

Alternatively (as a companion to my other thread on a more generic solution) , I've got a specific situation I'd like to get a handle on. I've got a planet with a 10° axial tilt, in an orbit with a semimajor axis of 10.363 AU and an eccentricity of 0.129. It takes 22.4 years to orbit its star (a 2.2 solar mass star at 46 solar luminosities), and the planet's rotation period is 8.7 hours. As far as I can figure, surface temperatures at the 30-40° latitude range between about -35°C at aphelion and 0°C at perihelion, and the atmosphere is about 90% CO2 and 10% N2, and slightly thinner than Earth's.

It seems obvious to me that the major seasonal effects are going to be caused by the orbital eccentricity rather than the axial tilt, since its orbital distance varies between 9.026 AU and 11.7 AU - the orbit also takes it within the star's habitable zone for very close to 6 years of its 22.4 year long orbit, otherwise it is beyond it (in the zone equivalent to where Mars is in our own system).

What I'm not sure about is how the day length varies. On Earth, the day (or night) can be 24 hours long at locations north of the arctic circle (or south of the southern equivalent), located at close to 67°N and S (90° - earth's axial tilt of 23°). At this latitude, the 24-hour long day occurs at the summer solstice and the 24-hour night occurs at the winter solstice. At the poles themselves the sun sets and rises once per year.

What would happen on my fictional planet, with its much longer year, faster rotation, and smaller axial tilt? I figure that the arctic/antarctic circles would be smaller (at 80° N and S). At higher latitudes, the star can be above or below the horizon for the full 8.7 hour rotational period. The time period between solstices is much longer than on Earth however. The poles can be in total darkness for 11.2 years or in full daylight for 11.2 years - at the equator the length of the day is the same as the length of the night (8.7 hours total) for the 22.4 year orbit.

I think one thing that is confusing me is how to consider the seasons. On Earth, we have seasons largely because of the axial tilt of the planet, causing the sun to more (or less) directly illuminate parts of the surface; but they can also be defined by equinoxes and solstices, which are characteristics of the slightly eccentric orbit of the Earth.

One other thing I'm not sure about - are equinoxes generally defined by being exactly halfway between the solstices during the year (regardless of the orbital eccentricity)? Or would the equinoxes be displaced towards (or away from) one of the solstices if the orbital eccentricity was higher?

On my fictional world, the seasons would be largely determined by the variation in orbit distance over the long year, but the axial tilt would still have some influence. If there was no axial tilt, then there'd be no polar day or night because there wouldn't be an arctic or antarctic circle. But with a 10° tilt, the highest latitudes can have a polar day/night.

Figure 6i-2 (in the middle of the page) seems useful. I think I should be able to replace the y-axis with numbers going from 0 to 8.7 hours, and the x-axis with a 22.4 year long orbital period, and then slightly tweak the graph lines to get something that works for my planet.

At the 0° latitude, the day and night would both be exactly 4.35 hours long throughout the year. So between 0° and 80° we'll have some variability in the day length over the 22.4 year long orbital period, though I'm not sure how to calculate that exactly. I can surmise the following though:

At 90° latitude we'd have the 11.2 year long day and night, with the sun rising and setting at the equinoxes.

At 85° latitude (or at some point between 90° and 80°), there will be an 8 (earth) year long night, followed by a period of a couple of years when there is a day/night cycle that starts with long nights/short days and end with short nights/long days, followed by an 8 year long day, followed by a couple of years of day/night cycle starting with long days/short nights and ending with short days/long nights, and then it's back to the 8 year night.

At 80° latitude, we'd have a sinusoidal line (assuming the equinoxes are still exactly halfway between the solstices), touching the 8.7 hour line at the summer solstice and touching the 0 hour line at the winter solstice. There will be at least one 8.7 hour long day and one 8.7 hour long night during the 22.4 year long orbit at this latitude.

I guess that the lines on the graph would be flattened somewhat at the intermediate latitudes on my planet, since the 80° line there is where the 67° line would be on Earth - which would make sense since the tilt of my planet is lower, so the axial effects should be less than on Earth. So at low latitudes (within 30° N/S), the day length probably isn't going to be all that different to its duration at the equator itself - maybe it'd be about 5 hours at most, and 3 hours at the least over the year. On Earth, even at 60° - close to the polar circles the day length - the day length can still be several hours long. On my fictional planet, maybe the 70° latitude corresponds to this, so the day length here would vary between about 6.5 hours and 2 hours over the course of the year.

I'm brainstorming a bit here and I don't know if that makes much sense... but if anyone spots any obvious errors or has any thoughts about the implications of this then please let me know! The very long polar days and nights intrigue me - the planet doesn't usually get very warm and I doubt that and 11.2 year long day at the poles would really melt the polar ice or anything... but I'm wondering what the effect of an 11.2 year long night at the poles would be - could it get cold enough there to freeze CO2 out of the atmosphere?

2. Is your world terrestrial or a gas giant?

Either way, it's going to be windy with that 8 hour rotation. Really windy.

3. The only one I feel I really answer is the equinox one.

For the sake of simplicity, let's say that the northern solstice happens at perihelion. The southern solstice would happen 180 degrees from that, and the (whatever the heck plural of equinox is) would happen at 90 degrees from either, since they are based on the axial tilt.

The tricky bit is that with that eccentricity, the time between them all might be much different, since the planet will cover from 0 to 90 degrees in a much different time than from 90-180.

That's the way It looks to me, at least.

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Originally Posted by Tog
whatever the heck plural of equinox is
Just equinoxes. Or equinoctes if you want it fancier
Both are correct.

5. Originally Posted by Githyanki
Is your world terrestrial or a gas giant?

Either way, it's going to be windy with that 8 hour rotation. Really windy.
Terrestrial.
I was wondering about the rotation though... The coriolis effect is going to be stronger (the coriolis parameter is 2*(angular velocity)*sin(lat) ), but would it really have rougher weather too? I have global duststorms that pick up in the summer years, but no hurricanes (the only body of water on the planet won't get warm enough for that).

6. Originally Posted by Tog
The tricky bit is that with that eccentricity, the time between them all might be much different, since the planet will cover from 0 to 90 degrees in a much different time than from 90-180.
That's what I'm not sure about. Are the equinoxes still halfway between the solstices in an eccentric orbit, or not?

7. Originally Posted by EDG
That's what I'm not sure about. Are the equinoxes still halfway between the solstices in an eccentric orbit, or not?
Take the star away and look at the axis of your planet. No matter where your planet is in that orbit the orientation of the axis never changes.

Now measure the distance from the actual spot on the planet where the north pole would sit if it were the barber pole from the cartoons, to the surface of the star. Call that distance x-10. Measure the distance tot e south pole and you find that it's x+10. That is the northern solstice.

The equinox happens with those two distances are exactly equal. Where on the orbit would happen? The picture in my head says that it has to be 90 degrees around the orbit, no matter the shape. At one end, it's x-10, at the other it's X+10. Half way there should be X.

I think they would be off as far as the amount of time goes however. The arc of each leg would be 90 degrees as seen from the top and centered on the ellipse. From the POV of the star the arc from a to b would be small, but the arc from b to c would be huge. so would think you'd end up with solstices in June and December, and equinoxes is late January and Early November.

Remember though, I had two tries at algebra 1, and I'm doing all this in my head and moving a coke can around my head for a reference.

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At 10 degrees axial tilt, the seasonal effects should be pretty small, especially with such a large eccentricity.

As for where the equinox are, they are 90 degrees along the orbit as measured from the star. This means that if the summer solstice was at the same time as the perihelion, then the equinox are at the semi-latus rectum of the orbital ellipse.

9. Ignore everything I said. My limited educations pays off yet again.

Sorry for the confusion.

Looking at that link and moving my coke can around I see where I went wrong.

10. Originally Posted by korjik
At 10 degrees axial tilt, the seasonal effects should be pretty small, especially with such a large eccentricity.
I figured that much, but the fact remains that there will still be some seasonal effects. I don't want to dismiss them out of hand. For example, the polar days and nights being over a decade long might make a difference to the overall climate.

As for where the equinox are, they are 90 degrees along the orbit as measured from the star. This means that if the summer solstice was at the same time as the perihelion, then the equinox are at the semi-latus rectum of the orbital ellipse.
But as Tog points out, while that may be true, does that mean that they occur exactly halfway in time between the two solstices as well? The planet moves more quickly in orbit nearer perihelion and more slowly nearer aphelion after all. If the Winter Solstice was in the equivalent of December and the Summer one was in June, then would the equinoxes necessarily be in March and September? Or would they be pushed toward the Summer Solstice, and occur in (say) April and August instead?

11. I had the position wrong. I had it at 90 degrees based on the center of the ellipse, not the foci that holds the star. It's going to be moving fastest though that part of the orbit, so you may hit equinox, solstice, equinox in a very short time, then have to wait for a very long time to reach the other solstice, where the orbital speed is the slowest.

12. Ah! Now I get it. So my last post was correct then - on an eccentric orbit the equinoxes will be closer to the summer solstice.

13. That's how I see it based on korjik's link. Now.

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Originally Posted by EDG
Ah! Now I get it. So my last post was correct then - on an eccentric orbit the equinoxes will be closer to the summer solstice.
Only if the summer solstice occurs close to perihelion. Then the planet would sweep from spring to autumn equinox (through summer) faster than it would move from autumn to spring equinox (through winter).
On Earth, this is true if you live in the southern hemisphere.

Grant Hutchison

15. Originally Posted by EDG
Ah! Now I get it. So my last post was correct then - on an eccentric orbit the equinoxes will be closer to the summer solstice.
If the solstices are at or near the line of apsides, the equinoxes will be closer to whichever solstice is at perihelion. Here on Planet Earth that is the December solstice, which is summer south of the equator.

If the orbit of a hypothetical planet is eccentric enough and the obliquity is low, the eccentricity just might dominate the insolation cycle and make it summer all over the planet around perihelion.

16. Right. I'm going to assume that the summer solstice is around perihelion just to make things simpler.

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On Earth the closest approach to the sun occurs about January 4, so summers are theoretically warmer South of the Equator than North of the Equator, certainly not near the South Pole. Typically the Southern hemisphere is not warmer, apparently due to the shape of the land and ocean currents which are the third, and forth factors determining temperature. The January 4th date drifts very slowly over many centuries, with respect to the equinox and solstice. Likely this will occur also on your planet. The bottom line is the tilt and the eccentricity will reinforce in some locations and cancel in other locations. If your planet has oceans, a giant ice cap will occur at the cooler pole, then try to switch at 22 year intervals. The result will likely be most of the water will be trapped at the poles and the oceans will be small. The faster rotation will likely make the spheroid effect = flattening of the poles more pronounced than, Earth thus the sun will never be more than about 9 degrees above the horizon at the poles. Close to the poles night time will exceed day time by several percent on the average = the flattened polar regions and the 10 degree tilt tend to make the poles colder. Large ice caps may make the equator colder. Please correct if my thinking is in error. Neil

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Try to switch in an 11 year cycle. 11 years between summer in the north and summer in the south.

For the planetary weather, there should be four large scale effects:
Heating/cooling due to distance from sun
seasonal variation due to axial tilt
Numerous hadley cells due to rapid rotation
water cycle

The last of these is actually the first thing to look at. If there are no oceans on an area where the temp goes above freezing, then the planet is just a windy iceball (or dirtball if there isnt much water). There would not be enough atmosphereic water to make any real weather patterns. All you would get is wind.

Now if you have at the perihelion that the poles are still below freezing and the tropics are still above, then the liquid water will get pumped into the polar regions over time. Evaporation in the tropics will follow the hadley cells to an are that is below freezing and the snow out. Over time, all the water should end up in regions where the water is stuck as ice. End result should be a breezy iceball again.

Now that I think about it, I think that this setup would always result in a situation with the water locked in the polar ice caps. The caps may extend half way to the equator, but since the temp would not get above freezing, the water would not go anywhere.

19. Hm. I can't really change the orbit at this stage, and I've got it as a mars-like planet, with a single small oval-shaped sea at the equator. Most of the ice elsewhere is locked up in the ground, like on Mars, it just thaws around the equator during the summer and refreezes again as it gets colder (i.e. for the rest of the orbit). The sea also has hydrothermal vents at its base. The planet's only a billion years old, so maybe there's not been enough time for all of the ocean to be transported to the polar latitudes. I might have to bend reality and make the water cycle not work as quickly as it should a bit to make this work, but I can live with that! So I guess in the summer when the sea surface is liquid, there'd be snowfall at the mid-latitudes?

The hadley cells are interesting. I'll see what effect they might have.

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Originally Posted by EDG
Hm. I can't really change the orbit at this stage, and I've got it as a mars-like planet, with a single small oval-shaped sea at the equator. Most of the ice elsewhere is locked up in the ground, like on Mars, it just thaws around the equator during the summer and refreezes again as it gets colder (i.e. for the rest of the orbit). The sea also has hydrothermal vents at its base. The planet's only a billion years old, so maybe there's not been enough time for all of the ocean to be transported to the polar latitudes. I might have to bend reality and make the water cycle not work as quickly as it should a bit to make this work, but I can live with that! So I guess in the summer when the sea surface is liquid, there'd be snowfall at the mid-latitudes?

The hadley cells are interesting. I'll see what effect they might have.
You can fudge things a bit to make the story go. It isnt like anyone has any proof that you are off