7

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

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 ...


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 ...


4

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

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

The only way to answer the question about stability is to do the integration, because this problem does not have an analytic solution. There are approximate solutions for the stability of two-planet systems (although these are based on a somewhat weaker constraint that allows the outermost object to escape to infinity) but they do not necessarily generalise ...


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 ...


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

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 ...


2

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-...


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 ...


1

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. ...


1

I have not heard "antipodal points" used in this way before, but it is probably fine. For a tidally locked moon, this point is called the inner pole. It should in some sense also apply to the parent body, as that point is also facing the barycentre. The direction "down" is generally called Nadir. For planetary coordinate systems, the constantly parent-body ...


1

If the question is "if I throw two planets to orbit a star at random direction, would they form an orbital resonance?" -- then in general, no. A resonance is an integral ratio (1/1, 2/1, 3/5, etc.) between the periods of motion of objects -- i.e., the ratio of their periods forms a rational number. Formally speaking the odds of getting a integral ratio (let ...


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