Orbital Analysis of the Moon's Seasons
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**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.

I did not find data to compare here. So I will not dig into that detail further to find out about real temperature margins.

**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. During those near-sun/far-sun phases a considerable difference in temperature can be expected. If this is strong enough to impact habitability is open to speculation.