How could a planet have a 40 hour day cycle with its nights only lasting 3 hours?

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Yes, but not in the way you imagined.

Vincent mentioned a Worldbuilding question which directly addresses the possibility of a figure-8 orbit. No offense intended, I don't think any of the answers there properly addressed the question - although Vincent may have decided against addressing it because a Physics question had already covered it, which he mentioned in his answer, and it had a fairly comprehensive answer.

Quoting Thriveth in his/her answer there,

In order to orbit in a figure eight, you have to imagine that the ball has to roll across the ridge between the two indentations in the 3D part of the figure. It is clear that this is possible, but also intuitively clear that this would only be possible for a narrow range of orbital energies (a little less and it would go into one of the holes, a little more and it would simply just orbit them both), and that it would not be a stable orbit. The ball would have to roll in an orbit where it exactly passes the central saddle point at the ridge (L1) in order to stay stable, the tiniest little imperfection will get it perturbed even further away from its ideal trajectory.

So such an orbit is possible, but very unlikely, and pretty unstable.

That doesn't mean that a planet couldn't follow a circumbinary orbit around both stars. Indeed, many planets have been found with such orbits. And it means that your 40-hour day and 3-hour night is possible.

Look at the Moon on the right side of this animation (I couldn't separate the two):

^{Image courtesy of Wikipedia user Stigmatella aurantiaca under the Creative Commons Attribution-Share Alike 3.0 Unported license.}

This Moon (incorrectly; our Moon is like the one on the left) doesn't rotate from the perspective of a fixed observer above the Earth. Still, the face pointed towards the Earth is constantly changing.

Now change the Earth to a pair of close binary stars, and the Moon to our planet. In fact, make the orbit really eccentric, so it swings out to the far reaches of the system. Because of Kepler's second law, it travels faster near the stars. This means that for one half of the planet, the night will last for 3 hours and the day will last for 40 hours; for the other half of the planet, the night will last for 40 hours and the day will last for 3 hours. To my knowledge, there is no configuration that will let you have the same length of night for both sides and still have the 40/3 scenario.

posted almost 10 years ago