On Earth, we experience seasons because of our planet's axial tilt.

The Earth around the sun at each solstice and equinox

It is a common misconception that the seasons are instead caused by our planet's distance from the sun changing as it orbits. The Earth's distance from the sun does change throughout the year, but the change is far too small to have any effect on the planet's temperature. In fact, in the northern hemisphere, the Earth is actually furthest from the sun during summer.

The Earth in its orbit showing the distance from the sun in summer and winter

Imagine an earthlike, inhabited planet with zero axial tilt (ignoring wobble) and a much higher orbital eccentricity than Earth (exact values aren't important at this point but feel free to calculate them for extra kudos). For this planet, "summer" is the time spent closest to the sun and "winter" is the time spent furthest from the sun.

A high-powered simulation of what such a system might look like, rendered using MS paint

Is this setup a feasible explanation for the seasons of a fictional planet?

If so, how would the planet's seasonal cycle differ from Earth's (all other things being equal)?
Would there be any notion of an equinox?

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    $\begingroup$ The solstice and equinox come from the varying length of day, your lack of axial tilt removes that. If your distance varies enough to effect seasonal changes, your seasons will not be equal in length. Summer will be shorter than winter, since the orbital velocity will be higher the closer to the star it is, and slower the farther away. Depending on how far away from the primary your planet is during the two seasons, it could be a fairly large difference. $\endgroup$
    – Seeds
    Sep 16 '16 at 21:37
  • $\begingroup$ That's right, the days would all be the same length. Hmm. Might be an interesting follow up question to see what sort of primitive astronomy might emerge on such a planet. $\endgroup$ Sep 16 '16 at 22:02
  • $\begingroup$ @ApproachingDarknessFish Well, they might find astronomy a tiny bit more boring in the beginning, but quite as useful. $\endgroup$
    – Karl
    Sep 17 '16 at 7:56
  • $\begingroup$ This is a bit outside my expertise, but I think an additional scenario is also possible: a more elliptical orbit that is not eccentric. It would have two summers and two winters per year. $\endgroup$ Sep 17 '16 at 9:03
  • $\begingroup$ @Dan Henderson I don't think that would work since the sun is always at one of the ellipse's foci (not in the center). $\endgroup$ Sep 17 '16 at 18:37

Yes, more eccentric orbits are possible and you can find or handwave reasons for it to stay that way (e.g. pumping from gas giant). In fact, this is expected to be the case for inner planets around dim red stars (much closer than Earth is to our sun to get the same total light) when a giant is also present farther out. Interestingly, the day will be synchronized with the year, and the year will only be a few Earth days, so we would call that part of the diurnal cycle and not seasons. Anyway, you can plausibly say that an Earth-like system has a more eccentric orbit, and only the most advanced readers will question the long-term dynamics and reconcile it against current formation models.

The big difference you find will be the lengths of the seasons. The planet moves slowest at the far end of the orbit (and vice versa), so you’ll have a long winter and a brief summer.

In general, you’ll have axial tilt also giving a combination effect. This will change in relative phase over thousands of years as the axis precesses. And the planet’s axis changes over tens to hundreds of millions of years, wondering every which way, so finding it where it happens to be vertical is a temporary condition and life would evolve to match because it’s such a long time scale, but would show the history of other tilts.

To stabilize the planet’s tilt, you need something like our own large moon.

To learn much more about these interrelated subjects, I suggest you check out the SETI Weekly Colloquium series. You can find them posted on Youtube.

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    $\begingroup$ Don't worry about the orbit stability. Mars orbit is not that badly excentric, and it already has a rather notable effect on the seasons. Check en.wikipedia.org/wiki/Mars#Climate $\endgroup$
    – Karl
    Sep 17 '16 at 7:50

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