9

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 will slowly catch it up. (It takes many "years" for the planet to get close to the body.) As the planet catches up with the body, the gravitational effect of ...


8

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 from perigee to perigee is slightly longer than the time it takes for the moon to orbit the Earth. The direction of the major axis of the moon slowly rotates ...


8

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 asked this question to visiting dynamicists and invariably got different answers. The very basic answer is that if you have two sufficiently strong resonances ...


7

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 than selection bias or an orbit "clearing" around zero degree inclination. Long answer: Orbital inclination is typically defined as the angle between ...


6

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 in the asteroid belt, not only the ratio of the periods, but also the timing is important. Let's take Pluto as an example, which is in 2:3 resonance with ...


6

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 the angle the inclination $i$ (i.e. the inclination is the angle between the direction that the orbital axis points and ecliptic north pole). If lots of ...


5

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 once again be at perigee. This could happen for two reasons: The Moon's apsidal line is fixed, or The Moon's apsidal line rotates at one revolution per year. ...


5

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 $m$, the solar mass $M$, the radius $r$ and various dissipation parameters $Q$ and $k_2$. Two planets that merely differ in $a$ will have the inner one lock ...


4

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 the normals to their orbital planes uniformly on a unit sphere, and call the midplane or the plane defined by $\theta=\pi/2$ the ecliptic. Orbits with an ...


4

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 asteroid's orbital period, so asteroids do not remain long in this state. The Kirkwood gaps in the asteroid belt include this and other mean-motion resonances ...


4

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 captured into resonance in about 1.5 billions of years, forming 1:2:4:8 resonant chain with the other Galilean moons.


3

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 stabilizing effects of the most stable "lower number" resonance ratios have been enough to overcome the forces causing orbital migration. When we look at ...


3

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 momentary forces shouldn't be that high that the orbits are changed significantly, after a perturbation, the bodies should pull each other back into resonance. For ...


3

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 gasous planets - there is no continuous distribution curve. That means that different processes must be involved. Understanding how the involved processes interact,...


3

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 measurements from the now-collapsed Arecibo Observatory (RIP) in Puerto Rico. These were reported in a very short paper (1/2 page) in Nature by Pettengill and ...


3

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 major axis of the orbit of the outer planet exceeds the semi major axis of the orbit of the inner planet by. The relative spacing is the ratio between the semi-...


3

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 long term. Most investigations of the long-standing question of solar system stability (without any additional planets) find that the system is stable in the ...


3

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 (among two, three or even more bodies); instability is often caused (as far as I know) by a massive mass difference, not because of some 'unlucky' ratio. There's ...


3

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 forces and that can lead to spin-orbital resonance if the tidal forces are strong enough. Mercury's somewhat high eccentric orbit balances out with a 3:2 spin-...


3

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 smaller object falls towards the Earth, accelerates, misses, then flies away from the earth giving back the velocity in flying away that it added flying towards. ...


3

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 point. If the star was also tidally locked to the planet, then there would be a subplanetary point. For a moon locked to a planet, the point on the moon would ...


3

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 another!). Yes, you can experience that effect near the poles, but take into account the local topography, as this is a timid effect we're talking about, and the ...


2

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 changing the energies of the orbits, so it is fueled by torque rather than work. It is easier to get a slow torque from two inclined orbits than it is to get work ...


2

You may take a look at the lates parametrization file by JPL-NAIF for the precession, nutation and pole orientation of the largest known bodies. Although, for the large time scales you are asking, I expect you will need to propagate the data and make your own wild guess, or dig into appropiate literature about solar system physics.


2

There are two main contexts for orbital resonance, and these can be thought of as "Jupiter scattering asteroids" and "Jupiter's moons in a 1:2:4 resonance" In the case of scattering, orbital perturbations from Earth, Mars, Saturn, Jupiter can cause asteroids to change their orbital characteristics over time. Each planet is constantly ...


1

I don't know if there are rules of thumb for initializing resonant orbital simulations. I might suggest: Setting initial state vectors' Z-Components to zero. Keeping the whole simulation in the X-Y plane can help with debugging and visualization. Choosing initial state vectors that are equivalent to orbits with non-zero eccentricity. Orbital resonances ...


1

I think you may have given each star too many planets. Alpha Centauri AB is a fairly close system, with a semimajor axis of 23 AU and an eccentricity of 0.52, which means the stars approach to within 11 AU of each other. Planets aren't stable unless the binary star surrounding them is more than 3-4 times more distant, so I think your outer planets may be ...


1

While it's true that planets closer to their star, being under the influence of a much stronger gravitational field than outer planets, are more likely to become tidally locked, that's not a hard and fast law. There's no a priori reason that a more distant planet couldn't have been formed, e.g., as the collision of two solid but highly dissimilar (in ...


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