9 votes
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Why are asteroids with zero orbital inclination rare?

Short answer: The scarcity of asteroids with an inclination near zero is an expected result of normally distributed inclinations in 3-dimensions about the normal vector to the reference plane, rather ...
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9 votes
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How do tadpole, horseshoe co-orbital states arise and how are they stable?

If the body is in front of the planet (relative to the planet's orbital motion) and a little further from the sun, it will orbit the sun slightly slower than the planet. As it is slower, the planet ...
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9 votes
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At what point are orbital resonances no longer "ordered" but "chaotic?"

Consider a child on a stationary swing. The fastest way to get them going is to push once every time they swing (a 1:1 resonance). If you push 581 times for every 137 swings, the pushes will mostly ...
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8 votes
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Planetary orbital resonances

This is actually a very subtle question, much more so than the answers to the similar questions provided in the comments give it credit for. When I was in graduate school at Ohio State I routinely ...
8 votes

What exactly was the Moon's "Evection Resonance"?

The orbit of the moon is elliptical. But the direction of the major axis of this ellipse isn't fixed. Perturbation by the sun causes the axis to rotate towards the East. The time for the moon to go ...
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6 votes
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Stability of orbital resonance

I am not very familiar with orbital dynamics (so please correct me if I'm wrong). I was told that, for instance in the case of the mean motion resonances that cause the majority of the Kirkwood gaps ...
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6 votes

Why are asteroids with zero orbital inclination rare?

In spherical polar coordinates, one of the coordinates used is an angle between the direction to a point in space and a "pole". Let this "pole" be the ecliptic north pole and call ...
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5 votes
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When will Callisto be in orbital resonance with the rest of Jupiter's big moons?

we tried to answer to this question in this article: https://arxiv.org/abs/2001.01106 According to the current estimation of the tidal dissipation in the Jovian system, we expect that Callisto will be ...
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5 votes

What exactly was the Moon's "Evection Resonance"?

Does this simply mean that the angle formed by the Sun-Earth-Moon when the Moon was at perigee was the same every month? No. It means that one Earth year after the Moon was at perigee, the Moon would ...
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5 votes

Can a solar system exist where the second planet rotates fast, and the third planet is tidally locked to their star?

The tidal locking timescale depends on several factors: $$\tau_{lock} \approx \frac{0.4 \omega_0 a^5 m Q}{3 G M^2 k_2 r^3}$$ such as the initial spin rate $\omega_0$, the semimajor axis $a$, the mass $...
5 votes
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Is it still called an orbital resonance if the ratio is irrational?

From various sources such as Wikipedia, NASA, and various published papers, an orbital resonance is: when orbiting bodies exert regular, periodic gravitational influence on each other, usually ...
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4 votes

Just how "locked" are resonant-chains of exoplanets thought to be? (e.g. K2-138 and TOI-178)

Short Answer: MMR (Mean Motion Resonance) chains seem to be mostly unstable over the lifetime of a planetary system, since we suspect most planetary systems begin in some resonance lock, but we ...
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4 votes

Why are asteroids with zero orbital inclination rare?

I'll propose that it can be understood trivially. What would the inclination distribution of circles randomly distributed in three dimensions about some point? We could generate them by distributing ...
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4 votes
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What exactly are the "ν6 secular Sun-Jupiter-Saturn" and the "1:4 Sun-Jupiter" resonances?

The 1:4 (or 4:1) Jupiter resonance is a mean-motion resonance: an asteroid there takes 1/4 as long to orbit the Sun as Jupiter does. Perturbations by Jupiter at recurring ecliptic longitudes alter the ...
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4 votes
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Why does the exoplanetary system TOI-178 challenges current theories of planet formation?

The original research paper is published is found on A&A and available via arxiv, too. One of the mysteries to understand in planet formation is the distinction between terrestrial planets and ...
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3 votes

How do tadpole, horseshoe co-orbital states arise and how are they stable?

How, when approaching the planet, does the body "fall behind" instead of continuing to accelerate toward the planet? This is fundamentally the gravity assist problem. In the 2 body system, the ...
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3 votes

Could a Trappist-like planetary system exist around a sun like ours?

That is a fascinating question due to the fact that planetary orbits have both absolute and relative spacing. The absolute spacing between planetary orbits is the number of kilometers that the semi ...
3 votes

Hypothetical planet jump: Will it perturb star systems?

There is essentially no room in our habitable zone for another Earth-sized planet. The exact timescale for instability would depend on the details of where you put it, but the system couldn't survive ...
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3 votes
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How do higher numbers affect orbital resonance?

General Explanation In the history of our Solar System, the orbits of Solar System bodies have gradually evolved, passing through many "higher number" orbital resonance ratios. Only the ...
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3 votes
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How can orbital resonance sometimes have a stabilising effect, whilst other times, it has a destabilising effect?

According to my understanding, for an orbital resonance to be stable, there must be at least three circumstances present: The forces on the bodies in resonance have to cancel out over time, The ...
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Mercury's spin-orbit resonance

The first accurate determination of the rotation period and the first hints that the rotation period was different from the orbital period (as originally expected) was in 1965 from 430 MHz radar echo ...
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3 votes
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Explanation of resonance stability and instability

Mercury and Spin-orbital resonance is pretty straight forward. Planets and Moons are gravitationally lumpy and large bodies are somewhat fluid, even rocky bodies. Both aspects are prone to tidal ...
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3 votes
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Terminology: Is there a name for the points on the surfaces of tidally locked parent/satellite bodies that always face each other?

For tidally locked binary stars, the two points in question are known as the substellar points. For a tidally locked exoplanet, the point closest to the star would also be known as the substellar ...
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3 votes
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Are there other possible Laplace resonances? (e.g. 1:3:9)

The Wikipedia article you linked contains several other examples, both in our own Solar system, e.g. 18:22:33 for some of Pluto's moons, as for exoplanets. There are all kinds of ratios to be found (...
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3 votes

Where can I build my house on Mercury so that I can see double sunsets (and sunrises)? Can I do it near the poles where it's cooler?

A quick look at Stellarium (if we trust its accuracy) suggests longitudes ~90 east and west (Edit: it seems that each of these corridors get to enjoy both double sunrise and sunsets, not only one or ...
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3 votes

Relative orientation in a 1:1 resonance of a planet and a satellite

The mean motion $n$ and the time-derivative of the true anomaly ${\nu}$, are related by $$ n\,=\,\frac{(1-e^2)^{3/2}}{(1+\cos f)^{2}}~\dot{\nu}~~. $$ Therefrom it is clear that in the pericentre (i.e.,...
3 votes

At what point are orbital resonances no longer "ordered" but "chaotic?"

I don't think you are correct. If the resonance can be calculated exactly, then it's a resonance. Chaotic orbits cannot be calculated exactly, as they depend critically on initial conditions. ...
2 votes
Accepted

Is this a stable system?

Seems like it would be subject to Kozai oscillations at least-- see https://www.cfa.harvard.edu/research/ta/kozai-lidov-mechanism. That mechanism tends to swap obliquity for eccentricity, without ...
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