What would the seasonal patterns be like on this world's moon?

Question

Here's the set up on this system I have: The sun is .99 solar mass, .97 luminosity. The world in question has the following orbital parameters:

• Dist: 1.253 AU Orbital Period: 1.41 (rel. to Earth)
• Radius: 7190 km
• 1.705 Earth mass
• Eccentricity: .0095
• Obliquity: 21.3 degrees

(I know, so far you're thinking, "Cold Earth"...but wait for it)

It has a moon with the following parameters:

• Dist. from planet: 1,473,950 km
• Orbital period: 152.5998 days
• Rotational Period: 22 hrs. (Due to its distance, this moon is not tidally locked. I checked using a tidal-locking spreadsheet)
• Radius: 3860 km, .1839 Earth mass
• No Eccentricity (or so slight to be negligible)
• Obliquity: 16.3
• Orbital Inclination 4.2
• Atmospheric density: .554 Earth's
• 22.3% hydrosphere
• Albedo: approx. .2289

I'm trying to get it positioned to maximize the warmth on this world's moon, much like the way Triton is orbiting Neptune so that its orbital inclination, axial tilt and the axial tilt of the primary all enhance each other. But I was curious, due to its wide orbit, would this moon experience multiple summers and winters? Would the seasons cancel each other out, or would they make them more extreme?

I know it seems like a rather tall order, but thanks in advance!

-M-

Answer 1

The planet has an orbital period of 514.65 days, the moon orbits it in 152.5998. This means the moon completes ~3.37 orbits for every orbit of the planet around it's parent star. The moon is far enough from the planet that its orbit makes a noticeable ~1% difference to the amount of insolation it receives at any given point in the planets orbit. Therefore the moon is going to experience "seasons" that don't stay in synchronicity with those of the planet.

The net insolation graph for a decade looks something like this, actual seasonal temperatures will lag slightly:

There's two-three summers and/or winters and five or six spring/autumn periods in every year. Some summers and winters are extremely mild while others are relatively extreme. The full cycle takes about 215 Earth years to repeat. I really didn't expect a 1% change in insolation to make such a marked difference so I'm not wholly certain of the magnitude of the shifts the above graph appears to indicate. I suspect that the moon's seasons will actually not be terribly noticeably different to those of the world below.

Answer 2

Orbital Analysis of the Moon's Seasons

Quick Checking Apparent Sizes

The sun is almost the same in mass and luminosity, so I assume it has a similar radius as well.

Planet's and moon's sizes vary, planet is a little larger than earth, moon almost twice as large as our moon.

Inclinations of planet and moon are very similar to our earth-moon, so I assume no differences in the amount of apparent size of the sun towards the moon.

Distance is far greater than earth-moon, almost 5x times. This is maybe compensated by the larger moon size, so I assume not much difference to the incoming sun radiation than in our sun-moon system either.

The changed sizes might have a visual impact though, when it comes to sun or moon eclipses (or sun-planet eclipses seen from the moon).

Base Data

• Planet's Orbital Year (around sun): 1.41 x 365 days = 514,65 earth-days
• Moon's Orbital Year (around planet): 152,... earth-days
• Moon's Day/Night-Period: 22 hrs

Let's assume for easier computations, that the planet experiences four seasons of equal length, thus being on a perfectly circular orbit:

• Planet's Seasons: 514,65 /4 = 128,6625 earth-days.

Seasonal Turn-around Times

Since the moon revolves within 152 earth-days around the planet, this is not much more than a planet season in length.

However, this means the begin and end of a season will not be at the same orbital position with respect to the planet. It shifts around by about 24 days per season.

Within one planet year the moon will experience (almost) four moon years. The real orbit-revolve-ratio for the moon is about 3,37 (514,65 : 152.5998 earth-days).

Thus, seen from the sun, the moon passes through (almost) 2 sun-close and 2 sun-far phases per planet-year, which will dominate the seasonal temperature changes.

Radiation Levels

Due to the larger moon orbit, it will get closer to the sun, but the planet is also on a larger orbit than our earth.

If the moon's atmosphere is not able to counter the incoming radiation levels of the sun, the impact on life on the moon would be devastating (should it be inhabited).

The moon also needs a magnetic field to counter incoming solar wind (ionized particles).

Alternatively, the planet's magnetic field could enclose the moon as well, but since that one is so far away there has to be a good explanation for an unusually strong magnetic field (or some properties of the sun, not having G-star-like solar winds/UV-levels).

Seasonal Temperatures

The moon has a day/night-cycle of 22 hours, thus it can be assumed sunlight will be evenly distributed across the surface (less towards the poles, but the total axis tilt towards the ecliptic is marginal there is not a large area of full darkness/full light at the poles).

As ascertained, the changes in distance and size can be considered compensating over the course of one planet-year or two moon-years.

However, there is a fairly huge difference between moon's sun-close-distance and sun-far-distance. (->which turns out to be in the range of 1%; see Edit below for details on temperature)

Conclusion

Habitability of the moon depends strongly on the factors of atmosphere and magnetic field. If these are insufficient, the moon will look much like our earth's moon, with same temperature margins etc.

Since the moon here receives evenly distributed day/night phases, this might account for a moderate base temperature, but also only if the atmosphere is able to hold enough warmth during night time.

As for season areas like on earth, the moon will not experience the same thing, because its axial tilt is almost negligible towards the sun.

There are orbital season phases though, which are passed through almost four times in a planet-year.

On average the planet receives 25% less sun energy because of the increased distance to 1.25 AU (moves it halfway between our Earth and Mars, for reference). However, the Moon's orbit makes almost no difference at that distance (influence about 1%).

Edit: I found one way to tackle the question of possible temperatures.

The planet is about 1.25 AU from its sun and the Moon's orbital radius is about 0.01 AU (assuming 1AU=149Gm). Thus the moon's orbit does not make a difference (1%) in the levels of incoming radiation, contradicting my previous assumption.

Using this graph of sun's energy per distance, we can conclude that at 1.25 AU the incoming energy level dropped by about a quarter or 25% (inverse square law), which turns out to be very significant.

Given your assumption that the atmosphere will be sufficient to support life on the Moon, we could assume that it is of similar composition as that of our Earth. Earth's average atmospheric temperature is about 15°C.

According to this graph of temperature ranges during the seasons the ranges for the Planet and Moon can be approximated by lowering Earth's values by 25%:

Phase	Earth	Planet/Moon
Winter	7-16	5-12
Summer	10-21	7-16
Average	15	11

Air temperatures in °C. Surface temperatures can be more extreme.