Okay, so my setting for a story was a moon, and I recently heard that moons can’t have seasons... is there any possible way that my moon can have seasons, specifically summer and winter?
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Of course.
Most of the changes associated with seasons are because of a heavenly body's tilt, which is why there is so little change at the equator. As a result, a moon will always have seasons as long as it is (a) tilted, and (b) not tidally locked to the sun it is orbiting. Statistically, it is highly improbable for a moon to not fulfill these conditions; so improbable, in fact, that you can generally assume that a moon will have seasons.

In Hoc Signo
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1Okay, thanks. LoL, I was scared for a minute there... – Username reset Aug 26 '20 at 02:25
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2All moons of significant size in the solar system are tidally-locked to the planets they orbit. The determining factor of whether the moon will experience seasons is whether the plane of the moon's orbit is in the plane of the planet's orbit. – notovny Aug 26 '20 at 02:33
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"Non-tidally locked tilt is statistically the most probable state": oh really? Do you have a citation which you can bring in support of this state being the most probable for a satellite? Can you give examples of such natural satellites? – AlexP Aug 26 '20 at 05:35
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@notovny I meant in relation to the sun; it's already a given that it will be tidally locked to the planet. – In Hoc Signo Aug 26 '20 at 11:18
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@AlexP I worked it out logically with a big Punnet Square; as such, no citation. Since it's impossible for me (as only an amateur astronomer, who thus doesn't have access to the statistical data of a pro) to know for sure, I have removed the assertion. – In Hoc Signo Aug 26 '20 at 11:25
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Now that's right. The satellite is almost never tidally locked to the Sun; and if its axis of rotation is tilted with respect to the orbital plane of the planet then the satellite will indeed experience seasons. – AlexP Aug 26 '20 at 12:01
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@Confused writer Seasons on a moon will be very noticeable if the moon has a hydrosphere and atmosphere, weather and climate, and especially if it has life and growing seasons & dormant seasons, etc. If the moon is an icy rock with very little atmosphere the seasonal effects may be much less noticeable. Of course a change of a few degrees in temperature could affect how well the human explorer's pressurized vehicle can travel on the Moon's surface. – M. A. Golding Aug 26 '20 at 16:47
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How about using the habitat's environmental controls to give it seasons. – NomadMaker Aug 29 '20 at 04:12