Are Rask and Rusk planets

[K^2]

5 hours ago, JoeSchmuckatelli said:

Neanderthal question time: if the barycenter of Jupiter and Sun is outside the sun (hope I'm reading that equation correctly), the sun is making tiny circles in time with Jupiter in its orbit of SagA... correct?

So - what's happening to the orbit of the other planets when Jupiter is at right angles from the planet's eliptical length?

That movement has to have some effect over time, doesn't it?

You're selling yourself short. All good questions.

First, all planets influence all other planets, both directly via gravity and indirectly by shuffling the Sun around. The latter is most relevant with the gas giants, of course, but even the Earth's gravity requires the Sun to act as a counterweight a little bit. All in all, the dance of barycenter relative to the Sun ends up rather intricate.

Spoiler

Solar System barycenter relative to Sun's position. Via Wikipedia.

Likewise, the trajectory of planets around Solar System's barycenter do not make perfect ellipses. They are pretty close, because over multiple revolutions, all of these deviations mostly average out, but the discrepancy is certainly there for every planet. If you keep very careful track of the position of Uranus over many years, for example, and then compare it to where you expect it to be under influence of the Sun, Jupiter, and Saturn, you might find that you are still off by a measurable amount, which may lead you to discover Neptune. In fact, that's exactly what astronomers of the 19th century did, making Neptune the first (and so far the only) planet to be discovered based on motion of other planets rather than direct observation. Although, there is strong evidence that it has been observed, but mistaken for a star prior to that.

Similarly, the Sun isn't merely orbiting Sag A*. The combined gravitational pull of the Alpha Centauri system alone is about 20% of the Sag A*'s gravity as experienced by the Sun. And then there are all the other stars with their contributions. So the Solar System's barycenter is already taking a more complex trajectory than a simple ellipse around Sag A*, and the Sun does its little dance around that trajectory, making the overall track of our star anything but straight forward.

Of course, all of these effects are fairly small compared to the scale of the entire galaxy. So if you replace all of the other stars in the Milky Way with a single attractor in the center with a carefully chosen mass, the Sun's trajectory wouldn't change a whole lot. Unless, of course, we're currently heading for a near-miss with another stellar-mass object, which could fling us far off course, but lets stay optimistic.

[MADV]

On 1/31/2022 at 12:24 AM, K^2 said:

Note that the mass of the candidate moon doesn't factor in at all, and the planet is simply whichever one's more massive of the two.

Well, the mass of the candidate planet does factor. So you could do the computation for both, and call the pair planet and moon if only the most massive passes, planets pair if both pass, and proto-planet or planetoid pair or whatever if neither passes (proto Earth and Theia probably were like that once, both orbiting the Sun but not so close to each other).

[MADV]

The big grip I have with the IAU's definition of a planet is that it is a dynamical one. By contrast, a black Hole is a black hole as long s it's smaller than its Schwarzchild's radius A star is a star grosso modo as long as it can sustain fusion.

Now one might argue there is something in the etymology or connotation of "planet" which, like satellite or moon, suggest a planet depends on a Star, and even propose an other term for a celestial body that is rounded, but not a star. Term such as Planemo, or the very common but very weird "planetary-mass object" ; "-So you're saying there is a range of mass which define planets? -Yes, but also... no.". And still, the IAU has inconsistency like "rogue Planets", which are planemo not orbiting any star.

 

Now for the definition of orbit, instead of trying to impose a vision and then search for convoluted arguments and twisted definitions to fit it, I think everybody should take a step back and have a look at the most simplistic, indisputable example :

A universe with only 2 point-like objects, A and B. A is massive, B is mass less. Then it can be shown that B follows a conical trajectory in the (inertial) frame where A is immobile. In particular, if (and only if) B have not enough energy to escape, its trajectory will be bounded, periodic, and will follow an ellipse. We can all agree to say that B orbits A.

In my opinion, a practical approach to enlarge the definition of an orbit is to quantify how much reality differs from the ideal model. In particular, are A and B close enough to be considered isolated? And Is B light enough to be considered mass-less?

That's why I don't like K^2's tug-of-war dynamical definition of a planet/orbit. First, it takes no account of the proximity or discrepancy of size (though it could as per my previous post). Second, and most importantly, the absolute value of the Sun attraction plays no role in influencing a system in a way that would invalidate the isolation approximation.

 

To answer "are A and B close enough to be considered isolated from a third body C?", it seems more relevant to compare the magnitude of the forces between A and B to the variation of forces C exerts on the whole system. C might exert twenty Gajilions gs on A and B, if the acceleration of C is the same within the whole A-B system, the frame accelerated by C is as good as inertial, in other word, C makes no difference in the motion of A relative to B.

For the example of is Earth-Moon relevant as a system? and how much is it influence by the Sun, it makes a lot more sense to consider the gradient of Sun's attraction, rather than the absolute force. So we should compare:

G M_EM/R_EM² ,
the force of A and B exert on each other, where M_EM=M_E+M_M the mass of the system Earth-Moon and R_EM is the highest possible distance between Earth and Moon to be conservative, so the Moon's Apogee, center to center.

with :
G (2M_S/R_SE³).D_EM
where M_C is the mass of the Sun, R_SE is the Sun Earth distance (in the worse case, so at perihelion) so that (2M_S/R_SE³) is the typical amplitude of the gradient of the Sun's attraction, to be multiplied by the diameter of the Earth-Moon system D_EM.

Which gives G M_EM/R_EM² = 6.674*10^-11 * (5.9724 + 0.07346)*10^24 / (4.067*10^8)^2 = 2.4 * 10^-3 m.s^-2 as already computed by K2 here (they find 3 likely because they take  the average Moon Earth Distance)

and G (2M_S/R_SE³).D_EM = 4 * 6.674*10^-11 * 1,989*10^30 / (1.471*10^11)^3 * 3.84*10^8 = 6.4 * 10^-5  m.s^-2

In other words, the attraction of the Earth over the Moon* is at any time at least 37.5 times bigger than the biggest variation in of the Sun's attraction over a revolution of the Moon around the Earth (or 75 times higher than the tidal Forces of the Sun at any given time).

Such a high ratio tends to show that "Earth and Moon orbit their barycenter of mass, which in turns orbits the Sun" is a valid and more accurate description than "Earth and Moon both Orbit the Sun".

Btw, this criteria does not depend on the size of the bodies, just their mass.

We can use similar reasoning to say that the Earth does not orbit Jupiter. This time, take them at their closest. Look at their mutual attraction force. Compare with the variation of the Sun force (eg Sun force exerted over Earth minus forces exerted over Jupiter).

As computed by K2, the Sun exerts an acceleration of  a =6 . 10^-3 m.s^-2 over the Earth.

Jupiter is about 5 times further away from the Sun, so the Sun exert on It an acceleration of a/25.

At their closest, Jupiter and Earth are 4 AU apart. Jupiter is about 1000 times less massive than the Sun. So the attraction of Jupiter over Earth is a/16000

So we are comparing a relative acceleration of 24/25 a caused by the Sun to a Jovian acceleration of a/16000. We can safely say that the Earth does not orbit Jupiter.

 

Now as to whether we can say that the Moon orbit the Earth, I think the second question, "is B light enough to be considered mass-less?" is the most relevant to the matter.

1. For example, if B's Hill sphere is smaller than B itself, B will have negligible gravitational effect. For example, an astronaut cannot orbit the space station as the Astronaut's Hill's sphere would be 120cm. In particular, such objects are necessarily held together by a force other than gravity.
2. When B is heavier than 4% of A's mass, L4 and L5 are no longer stable. So that could be a sensible limit between considering one body clearly orbit the other and a pair of bodies orbiting each other, as the simplified 3 body mechanics resulting by adding a third mass-less point (eg. a spacecraft) start to really differ. For reference the Moon is 1.23% the Mass of the Earth.

 

By the way, I don't know whether KSP2 will stick to patched conics, I doubt they would if they are introducing a bunch of pairs of bodies, but these kind of questions can directly translate into practical choices of modeling. If A and B are isolated enough, one can assume 2 body mechanics and put A and B on rails around their barycenter. If B is smaller than its hill's sphere, one can consider it mas-sless, for the purpose of interaction with player's craft. If B is small enough, B can be on rails around A and A can be the barycenter instead of orbiting around it. If B is big enough, some 3 body mechanics might be needed in some regions; some of these 3 body mechanics might be split into 2 cases depending on the value of the mass ratio compared to 25.

Edited February 23, 2022 by MADV
typoes

[Bej Kerman]

On 2/23/2022 at 4:27 PM, MADV said:

We can all agree to say that B orbits A.

Where do you go from B orbiting A to  B and A orbiting each other?

[MADV]

1 hour ago, Bej Kerman said:

Where do you go from B orbiting A to  B and A orbiting each other?

Near the end :

On 2/23/2022 at 5:27 PM, MADV said:

Now as to whether we can say that the Moon orbit the Earth, I think the second question, "is B light enough to be considered mass-less?" is the most relevant to the matter.

1. For example, if B's Hill sphere is smaller than B itself, B will have negligible gravitational effect. For example, an astronaut cannot orbit the space station as the Astronaut's Hill's sphere would be 120cm. In particular, such objects are necessarily held together by a force other than gravity.
2. When B is heavier than 4% of A's mass, L4 and L5 are no longer stable. So that could be a sensible limit between considering one body clearly orbit the other and a pair of bodies orbiting each other, as the simplified 3 body mechanics resulting by adding a third mass-less point (eg. a spacecraft) start to really differ. For reference the Moon is 1.23% the Mass of the Earth.

 

In a sense, A and B are always orbiting each other, but looking at the frame of reference centered at their mass barycenter, it makes sense and is more descriptive to say B orbits A when B is massless, and say that A and B orbit each other when they are the same mass. Where should we go from one to the other is up to debate, but some value, such as 1/25, make sense.

Edited February 26, 2022 by MADV

[Bej Kerman]

5 minutes ago, MADV said:

In a sense, A and B are always orbiting each other, but looking at the frame of reference centered at their mass barycenter, it makes sense and is more descriptive to say B orbits A when B is massless, and say that A and B orbit each other when they are the same mass. Where should we go from one to the other is up to debate, but some value, such as 1/25, make sense.

1/25 is a pretty random value, don't you think? Point is many things can't be solidly defined, no matter how confident you are in your own definition. Even the line between brown dwarf and red dwarf gets hazy. The devil is in the details.

[MADV]

20 hours ago, Bej Kerman said:

1/25 is a pretty random value, don't you think?

No, I don't think so.

I agree things are hazy, but I think definitions can be handy, even hard ones to come up with.

The "mass being within the heaviest body or not" (used by IAU) is a very fine line to draw. So is "A twice as massive as B". I'm fine with both really.

1/25 is not random, it corresponds to the point beyond which Lagrange points 4 and 5 become unstable.

Since the matter is the trajectory of bodies, my slight preference would go to any criteria which has a bearing with gravitiy. 1/25 has, 1/2 and center of mass within heavy body haven't (the gravity field of nearly spherical objects only depends on their mass, not their size/density), hence 1/25 has my slight preference. If you can come with an other number related with gravity fields and behavior, it would have my preference as well.

I'd rather have a line drawn than none, but I could tolerate hearing that the Earth and the ISS orbit each other, or that the Sun and the Tesla car orbit each other.

Edited February 27, 2022 by MADV