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Not much else to the question. I want a solar system which has a habitable planet with a pretty exaggerated elliptical orbit, one that's definitely going to need to be in a solar system with an oval goldilocks zone to remain habitable but I don't know if that's at all possible.
Is an oval goldilocks zone possible?
Yes, with more than one star. A single star produces spherically symmetric radiation so the habitable zone also has spherical symmetry. With more than one star, however, the contributions of all stars add and this does not generally produce a symmetric habitable zone (nor a static one).
Here is a habitable zone calculator for multiple stars with literature references for the methodology, referenced in the linked article above.
Habitable Zones in Multiple Star Systems
Image from Müller & Haghighipour (2014).
The example above is quite extreme to demonstrate the point, and this example would be obviously unlikely to allow a habitable world in a stable orbit.
Whether or not stable planetary orbits would exist for any given binary (or higher order) star system that would also fall within the (dynamic!) habitable zone would require either a lot of calculation or some degree of hand waving. We do know for certain that there are binary star systems which host planets in stable orbits.
Binary and trinary systems are also extremely common in the universe, as far as we can tell, and new research even suggests that all stars may be born in pairs. As for how many of them have habitable planets in stable orbits, this is currently a topic of active research.
One interesting idea that might fit a story would be a habitable planet which was itself an L4/L5 trojan of an orbiting binary star. There would certainly be some configurations like this which could be stable for a very long time and would allow the planet to receive reasonably constant radiation from both stars. Being a Lagrange trojan, however, does put certain limits on how eccentric the orbit can be.
I think Goldilocks Zone is inherently tire-shaped, circular, but as @L.Dutch says before me, a somewhat elliptic orbit can be found within it; since the "tire" part (not including the hub) is pretty wide.
However, what makes it "habitable" are reasonable temperatures. It is possible that an elliptical orbit that spends most of its time in the habitable zone, but makes excursions outside it, could still support life and civilization. They just have to be prepared to survive some wicked cold winters.
But that is possible, if the planet itself has a hot molten core and provides some warmth. Pressure and core temperature can provide warmth, we suspect that is the case on some moons of Jupiter (Titan, Ganymede, Io) that we suspect have liquid water oceans under the ice. There the temperature is provided by periodic gravitational flexing of the moon in its orbit around Jupiter.
But technology can also provide the heat to survive. Suppose our own star captures a rogue planet, in its own elliptical orbit, and it pulls Earth out of its nearly circular orbit into an elliptical orbit that will eventually bring us out of the Goldilock's zone for half our orbit. But this is happening very gradually, we have ten thousand years before we are pulled completely out of the Goldilocks Zone.
What do we do? Get busy building habitats and moving to solar and nuclear power that don't depend on a warm environment.
Where do we build them? Under the Ocean. In the part of our orbit outside the Goldilocks Zone, the oceans are going to freeze solid on the surface, perhaps a few hundred yards thick. A lot of surface fish will die. All the plants and animals on land will die. (That also mean no oxygen production by surface plants.) It will probably reach -60C,
But ocean ice is a good insulator, there are miles of liquid water under it, and it will be reasonable warm; at the boundary between ice and liquid about 28F. That is where we live and work; nuclear powered underwater habitats, for farms, ranches for our animals; artificial sunlight, luxury apartments, whole cities, with nuclear powered transportation between them. Technologically we need to produce our own oxygen and dispose of our CO2.
Note this won't work for an Earth ejected into the cold of space; it depends on periodic warming by the sun when we are IN the Goldilocks Zone.
Without any Sun, we need a similar self-sustaining closed habitat on the surface and a lot more nuclear power. We are just riding a rock through space.
But for the original scenario, part-time excursions, we've got 10,000 years, we can do it. Or some civilization could do it, and pretty much at our own level of technology. If not now, with a few hundred years, if we were so motivated.
If you look at our solar system, the habitable zone is a rather large belt, whose extension varies according to the criteria used for its estimate, below showing just 2 possible outcomes
As you can see, due to its extension, you could have a planet swinging in distance between Mars and Venus orbits and still be in the habitable zone. That would be more eccentric than the orbit earth has, though not as extreme as the one of, for example, Halley's comet.
The habitable zone is defined for orbits with rather small eccentricities.
Highly eccentric orbits (provided they are stable enough) can be habitable by plunging in and out of the zone, because the planet is thermally inert.
Be aware that high-eccentricity orbits spend more time near their apoapsis and less near their periapsis.
It is impossible to have an oval habitable zone around a single star.
If there are two stars, they could have two separate habitable zones separated by space. In that case any habitable planet would have to orbit around only one of the stars in only one of the habitable zones. That is called an S-type orbit.
Or the two stars could be close enough that their two habitable zones overlapped a little or a lot.
If the habitable zones of the two stars overlapped a lot, a planet orbiting around both of the stars in a P-type or circumbinary orbit could be within the combined habitable zone of both.
For a planet in a P-type or circumbinary orbit to have a stable orbit it's distance from the center of gravity of the two stars should be at least 2 to 4 times the separation between the two stars.
The minimum stable star-to-circumbinary-planet separation is about 2–4 times the binary star separation, or orbital period about 3–8 times the binary period. The innermost planets in all the Kepler circumbinary systems have been found orbiting close to this radius. The planets have semi-major axes that lie between 1.09 and 1.46 times this critical radius. The reason could be that migration might become inefficient near the critical radius, leaving planets just outside this radius.[9]
https://en.wikipedia.org/wiki/Habitability_of_binary_star_systems
So the farther away a habitable planet is from the two stars, compared to the separation between them, the wider the circumstellar habitable zones of the two stars will be, compared to the separation between them.
So the combined habitable zone of the two stars can not be very oval, or the planet as it orbits would sometimes be outside of it.
Note that the quote says that if the minimum stable orbit of a circumbinary planet is 2 to 4 times the separation between the two stars, the minimum orbital period of the circumbinary planet will be 3 to 8 times as long as the orbital period of the stars around their center of gravity.
So since the planet will take longer to orbit the 2 stars than the two stars will take to orbit each other, the relative orientations of the two stars and the planet will change.
Sometimes the planet will be on the line between star A and star B, beyond star B. As star B orbits faster than the planet, it will move ahead of the planet. Eventually the line between star A and star B will be at a right angle to the line between their center of gravity and the planet.
As star A orbits faster than the planet, it will catch up to the planet, and eventually star B, star A, and the planet will be in a straight line, with the planet beyond star A.
So if the habitable zone is very oval, it will move faster than the planet, and sometimes move so far ahead that the planet will be outside of it.
The habitable planet can never have a orbit where it moves at the same speed as the outer point of the combined habitable zone of the two stars. And it would greatly reduce the habitability of the planet if it was sometimes outside the habitable zone.
So there is a considerable limit to how oval the combined habitable zone can be, even if the planet has a perfectly circular orbit. And if the planet has a more eccentric elliptical the habitable zone, moving relative to the planet, will have to be less oval so that the planet will never be outside of the habitable zone.
So while the combined habitable zone of two stars could be slightly or very oval in shape, depending on their separation, no planet in an P-type or circumbinary orbit, whether circular or elliptical, could stay within the moving combined habitable zone all the time if the zone was very oval.
So you might as well go with a single star with a perfectly circular habitable zone, and make the planet have an eccentric elliptical orbit that stays within the habitable zone, and so is reasonably but not highly eccentric.
And of course you could have a planet with an orbit that takes either closer to the star, or farther from the star, or maybe both, than the habitable zone, giving it short periods of intense heat or intense cold, or both. That could work if the planet spends most of its orbit and time within the habitable so its temperatures are mostly endurable for most of the orbit.
My comment at: https://moviechat.org/tt0058824/Lost-in-Space/58c7261d5ec57f0478eea649/The-orbit-of-Plrplanus is an attempt to explain how a planet with a highly eccentric orbit might possibly, repeat possibly, have comfortable temperatures most of the time.
The habitable zone is directly dependent on the amount of energy delivered to the planet from the sun. Energy famously radiates equally in all directions, so for a single star the habitable zone must be circular.
Because the energy is controlled by the inverse square law the habitable zone becomes wider the further you get from the star. So if you want a planet with an eccentric orbit to remain within the habitable zone you need a really hot star (i.e. emits a lot of radiation) and the planet to orbit far from it. I don't know if that does what you want.
How about an elliptical orbit with a reasonably long period, plus a negative feedback mechanism for greenhouse gases? Unlike our own planet, you'd need to up the greenhouse effect when things get cold: maybe a methane emitter that thrives at colder temperatures?
Your planet orbits a star with a rapid rotation. The star, being an ellipsoid, is substantially brighter when seen from above one of its poles, because it is larger in the sky when seen from that perspective. (There really are such stars) So the planet is hot at its closest approach, and also hot (maybe hotter) before and afterward as it passes over the star's poles. But in addition, we're going to tilt the planet so that one pole faces the star at closest approach, and the other faces it at a greater distance. As a result, the habitable side of the planet has two hot summers separated by a short dark winter and a long bright winter. But if its orbit were circular, the long bright winter would become a third hot summer uniting the other two in a searing siege, and the short dark winter would become a long dark winter like we have on Antarctica. Thus the habitable zone must be oval from the perspective of that half of the planet.
This Article references a paper that is now 404, but that considered habitable planets around a pulsar. If you expand "habitable zone" to include "habitable by life not as we know it", then you may end up with a habitable zone that is greatly extended along the sweep path of the pulsar's beam. I'm assuming that a planet that was receiving usable energy from the pulsar at all would obtain usable energy from the pulsar beam. And since this beam doesn't seem to require any particular alignment with the rotation (based solely on online animations), you probably get a really weirdly shaped energy density map around the star, along with a weirdly shaped subset of that that would be "habitable". So it would just depend on making your characters non-human, or living in artificial habitats capable of sustaining their environments off of the pulsar's energy.
If we instead keep the spherical habitable zone (so only one star), then we need to find a way to keep the planet habitable when its outside the zone. It that case make the planet a moon of a gas giant (where the gas giant is in the eccentric orbit around the star). The gas giant can then heat up the planet through tidal forces, keeping it warm during what will be the cold, dark winters.
Direct answer: No, not stable.
But planet's climates represent the average of their orbit. You could have eliptical orbit whose apistar inner edge was inside the GZ and whose peristar was beyond the outer edge.
Note: Review Kepler's equal area law. (The line connecting a planet to it's star sweeps out an equal area in equal time.) The planet will do the part of the orbit between ascending node and descending node (nearest the star) in much less time than the other end.
Your net result is short very hot summers, and very long cold winters.
You will need an orbital simulator to play around with to put numbers on it. My guess is that you could be 10-15% inside the inner edge and 20% outside the outer edge.
This could mean:
Many animals will estivate during the summer, or hibernate in winter or both.
You may have creatures that live out their life cycle in a season, and only eggs/larva/seeds last until the next season.
You may have creatures that alternate generations. E.g the haploid form is very different in strucuture from the diploid form. Or they metamorphose into a very different form depending on the season.
See Hal Clement's novel "Ice & Fire"
