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Matuchkin

What is an orbit? How do we know? What the heck?

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You can say that the Moon is orbiting the Earth every 27 days (or the ISS every 90 minutes) due to the effect of Earth's gravitational pull. But if you look at quasi satellites (or any other object in the solar system) from our frame of reference, the vast majority of them seem to be orbiting Earth as well. So how do we define an orbit? Is a quasi satellite just a satellite with an orbital period larger than 102 days (the orbital period of an object at the edge of Earth's SOI)? I mean, you can probably go into "orbit" around a small asteroid with the use of some simple orbit manipulation, and even at that point your orbit acts in the same way as an actual satellite's (i.e. you can accelerate at your periapsis [from asteroid's perspective] and elevate your apoapsis).

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Posted (edited)

A quasi satellite is an object a that has the same orbital period around the central body c as another body b that co-obits c together with b. So, seen from b, a stays behind half of the time and runs ahead the other half. That makes it look like a satellite of b, seen from b. Example: 2016 HO3. It orbits the sun together with earth. Since a and b must be in 1:1 resonance they will never get close enough to capture or to be captured.

:-)

Edit: SOIs are a game concept. Thought that got about. They don't exist in reality. Everything influences everything else in varying magnitude. Otherwise we'd have problems explaining resonance, trojans, lagrange points, planet 9, etc. pp :-)

 

Edited by Green Baron

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Posted (edited)
30 minutes ago, Matuchkin said:

You can say that the Moon is orbiting the Earth every 27 days (or the ISS every 90 minutes) due to the effect of Earth's gravitational pull. But if you look at quasi satellites (or any other object in the solar system) from our frame of reference, the vast majority of them seem to be orbiting Earth as well. So how do we define an orbit? Is a quasi satellite just a satellite with an orbital period larger than 102 days (the orbital period of an object at the edge of Earth's SOI)? I mean, you can probably go into "orbit" around a small asteroid with the use of some simple orbit manipulation, and even at that point your orbit acts in the same way as an actual satellite's (i.e. you can accelerate at your periapsis [from asteroid's perspective] and elevate your apoapsis).

It's pretty simple, really. To be in a true orbit around something, you need to be inside it's sphere of influence.

Edited by mikegarrison

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25 minutes ago, mikegarrison said:

It's pretty simple, really. To be in a true orbit around something, you need to be inside it's sphere of influence.

Except a sphere or influence is a simplifying assumption to make computations easier, they do not exist physically.

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Say, there are Sun, Earth and a useless rock between them.

One should calculate:
1. The difference between gravity accelerations caused by the Sun for the Earth and for the useless rock. Near the Earth they are more or less equal, so the difference ~0.
2. The difference between gravity accelerations caused by the Earth for the Sun and for the useless rock. The Sun is so heavy that it's acceleration is ~0, but teh useless rock is accelerated by the Earth significantly.
3. Compare them. Who makes greater relative acceleration difference, that is the better reference body for a Kepler orbit. Another one perturbates this orbit.

The hollow surface around the planet (i.e. SOI) is where the planet causes greater acceleration difference, than the Sun.

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2 hours ago, Steel said:

Except a sphere or influence is a simplifying assumption to make computations easier, they do not exist physically.

Sure they do. Math doesn't create physics, it only describes it.

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Posted (edited)
3 hours ago, Matuchkin said:

You can say that the Moon is orbiting the Earth every 27 days (or the ISS every 90 minutes) due to the effect of Earth's gravitational pull. But if you look at quasi satellites (or any other object in the solar system) from our frame of reference, the vast majority of them seem to be orbiting Earth as well. 

No they don't. This is what an Earth-centric solar system would look like:

IsHxv.jpg

From the Earth's point of view, you would see planets accelerating and slowing down and getting bigger and smaller as they follow those weird trajectories. Which, incidentally, is how the Sun-centric model appears to us.

Edited by Nibb31

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Posted (edited)
5 minutes ago, mikegarrison said:

Sure they do. Math doesn't create physics, it only describes it.

Hill spheres exist, but they don't define an orbit, neither are they spheres.

Edited by Gaarst

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3 hours ago, Matuchkin said:

You can say that the Moon is orbiting the Earth every 27 days (or the ISS every 90 minutes) due to the effect of Earth's gravitational pull. But if you look at quasi satellites (or any other object in the solar system) from our frame of reference, the vast majority of them seem to be orbiting Earth as well. So how do we define an orbit? Is a quasi satellite just a satellite with an orbital period larger than 102 days (the orbital period of an object at the edge of Earth's SOI)?

As other posters earlier in this thread have pointed out, real life is messier than KSP.  :wink:

Let's take Kerbin-in-KSP, versus Earth-in-real-life.

In KSP, the SoI is a real thing, with a specific, sharp boundary.  Objects inside that boundary are affected by Kerbin, and only Kerbin, and they're unambiguously orbiting Kerbin and will continue to do so forever.  Whereas objects outside that boundary aren't affected by Kerbin at all, and are unambiguously orbiting the sun, and only the sun.

Real life isn't like that.  There's no such thing as a "sphere of influence" with a sharp boundary.  Rather, there's a very blurry, gradual boundary, since every single thing in the universe exerts gravity on every other thing in the universe.

If you're really close to Earth, then it's very dominant over the Sun's gravitation, and orbits there are stable for very long periods of time, so you can speak of them as orbiting Earth.  If you're really far from Earth, then the Sun's gravity is overwhelmingly dominant, and you speak of the object as orbiting the Sun.

However, it's possible to be in a sort of fuzzy "boundary condition" where an object is orbiting the Sun with a period that either equals Earth's, or is some integer-ratio of Earth's (i.e. a "resonance"), and the object happens to be in the near vicinity of Earth.  In that case, you have an object that "can't quite make up its mind" whether it's bound to Earth or the Sun, and keeps coming back for repeated encounters.  And if its period matches the Earth's, then from our point of view it seems to trace a repeated path in the sky.

A good example of an implementation of this in KSP is in the New Horizons mod, which moves Kerbin to be a moon of a gas giant, Sonnah.  There's another moon, called Aptur, which also orbits Sonnah.  It has exactly the same period as Kerbin, but is offset somewhat, has a slightly elliptical orbit, and is somewhat inclined.  So even though it's orbiting Sonnah completely outside Kerbin's SoI, if you look at it from Kerbin, it appears to be "orbiting" Kerbin.

That's not an actual physical equivalence, of course, since the reason it stays there is the in-game modeling and not an actual gravitational resonance effect, but you can get the general idea of how such motions look.

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16 minutes ago, mikegarrison said:

Sure they do. Math doesn't create physics, it only describes it.

Except the definition of a sphere of influence when it comes to gravitational computations is a sphere in space in which the gravitation force from a body is dominant and so all other gravitational forces can be neglected. It's a bit like saying the small angle approximation exists physically. If you can give me physical example of the universe ignoring the gravitational forces of some bodies then I'll be amazed. As @Gaarst mentioned above, Hill Spheres are things that do exist, and indeed they are not spherical!

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3 minutes ago, Steel said:

Hill Spheres are things that do exist, and indeed they are not spherical!

They are neither spheres nor hills...

Quite a weird name for them really. Almost like mountain chicken.

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4 minutes ago, Steel said:

Except the definition of a sphere of influence when it comes to gravitational computations is a sphere in space in which the gravitation force from a body is dominant and so all other gravitational forces can be neglected. It's a bit like saying the small angle approximation exists physically. If you can give me physical example of the universe ignoring the gravitational forces of some bodies then I'll be amazed. As @Gaarst mentioned above, Hill Spheres are things that do exist, and indeed they are not spherical!

Please stop playing games. You call them spheres yourself, even though you (and I) know they aren't spherical.

I was answering the question, not trying to show how pedantic I can be. (Because I assure you, I can be pretty damn pedantic if I want.)

What makes the difference between something being in orbit around a body versus just co-orbiting the same larger gravity well is whether the track of the smaller body stays within the area where the gravity of the bigger object is the dominant influence. That was the original question.

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23 minutes ago, mikegarrison said:

Please stop playing games. You call them spheres yourself, even though you (and I) know they aren't spherical.

I was answering the question, not trying to show how pedantic I can be. (Because I assure you, I can be pretty damn pedantic if I want.)

What makes the difference between something being in orbit around a body versus just co-orbiting the same larger gravity well is whether the track of the smaller body stays within the area where the gravity of the bigger object is the dominant influence. That was the original question.

Ok, maybe I was just a little being pedantic ( :P ), but your definition about being within the SOI/hill sphere/whatever else you want to call it doesn't work for all types of orbit, there are some in which the orbiting body is not in the SOI for the entirety of it's orbit.

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Posted (edited)
18 minutes ago, Steel said:

Ok, maybe I was just a little being pedantic ( :P ), but your definition about being within the SOI/hill sphere/whatever else you want to call it doesn't work for all types of orbit, there are some in which the orbiting body is not in the SOI for the entirety of it's orbit.

Well, I don't think that's an orbit. Not a stable one, anyway.

It's like that Apollo stage that sometimes drifts in and out of the Earth's little neighborhood. I don't think it's in orbit around the Earth. I think it's just co-orbiting the Sun along with us.

https://en.wikipedia.org/wiki/J002E3

Edited by mikegarrison

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Posted (edited)
3 minutes ago, mikegarrison said:

Well, I don't think that's an orbit. Not a stable one, anyway.

It's like that Apollo stage that sometimes drifts in and out of the Earth's little neighborhood. I don't think it's in orbit around the Earth. I think it's just co-orbiting the Sun along with us.

That's fair enough.

@Matuchkin

The issue really boils down to the fact that as soon as you go into the depths of n-body dynamics it becomes quite ill-defined as to what being in an orbit around something actually means, especially since we don't really know if any given orbit is stable if we look far enough forward into the future.

Edited by Steel

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Posted (edited)
54 minutes ago, Shpaget said:

They are neither spheres nor hills...

Quite a weird name for them really. Almost like mountain chicken.

https://en.wikipedia.org/wiki/Hill_sphere

i.e. Hill spheres are a thing in real life. It is an approximation of the distance at which a moon or satellite may be in orbit around another body (the moon needs to lie inside the body's Hill sphere). In practice, the limit at which a body may be in stable orbit is only about a third to a half of the radius of the Hill sphere.

Edited by Tullius

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The other thing to be careful about, in this discussion:  Are we talking about terminology (i.e. "what do we mean when we say 'orbit'?"), or are we talking about physical reality (i.e. "how do objects behave").

This matters, because it would be very easy to end up talking at cross-purposes.  :)

There's a useful discusion of quasi-satellites here:

https://en.wikipedia.org/wiki/Quasi-satellite

4 hours ago, Matuchkin said:

So how do we define an orbit?

^ From the above, it sounds like this is a question about terminology.

I think a fairly useful distinction would be, "orbit" means "path lies within Hill sphere", and would exclude bodies that follow cyclic patterns outside it, like quasi-satellites.  Certainly, that's how I've always seen it used.

Again, be really careful not to conflate "Hill sphere" with KSPish "sphere of influence".  It's not the same thing.  You can be orbiting inside the Hill sphere and have your orbit affected by things outside it.  And you can be outside the Hill sphere and still be significantly affected by the body whose Hill sphere you're outside.

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We really should have a big stickied post at the very top of this sub-forum. It would contain a link to Wikipedia and a polite request to go there first and check for an answer to your question rather than randomly spewing new threads all over the place.

No - Wikipedia is not perfect. Luckily it contains lots of links to other sources so you can verify (or not) anything you read there. Feel free to go as far down the rabbit hole of knowledge as you like. Alternatively, if you get stuck, come back here and then start a thread to ask about the bits you don't understand.

Oh - and back on topic:

Orbits

Quasi-satellites.

Here endeth the lecture.

 

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One way of looking at it is if one body has an orbital velocity relative to another it is in orbit with that body.  How long it will continue to be "in orbit" is another question.

A harder question is "is this orbit stable?", or "how long is a string?".  Since real world physics doesn't include SOI, orbits merely continue until acted on by an additional (third or more body) force.

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16 minutes ago, wumpus said:

One way of looking at it is if one body has an orbital velocity relative to another it is in orbit with that body.

I'm probably missing something but isn't that a bit of a circular definition? How are you defining an orbital velocity here?

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An orbit is a trajectory - the relative path that an object trace through. There's no limitation of what they could be, whether they have to be of a certain shape, certain distance, or having to be periodical.

However, under newton's law of gravitation and laws of motion, the path traced around a gravitating body by an external object follows a conic section, follows the same-area-sweep rule, and having the semi-major axis related to the period by some powers (keppler laws. Any trajectory that fails to meet these definition means that they are "not newtonian" in nature; either they are a completely different object under a different rule or obeys the same law but in respect to another object. It doesn't mean that you can't call them orbit, but for the sake of space travel and navigation, "orbit" is meant to be newtonian gravity trajectories that, to the stricter sense, periodic.

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21 hours ago, Nibb31 said:

No they don't. This is what an Earth-centric solar system would look like:

IsHxv.jpg

From the Earth's point of view, you would see planets accelerating and slowing down and getting bigger and smaller as they follow those weird trajectories. Which, incidentally, is how the Sun-centric model appears to us.

Damn, I forgot.

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On 7.3.2017 at 6:50 PM, Nibb31 said:

*ptolemaios snipped*

The outer planets actually go backwards from time to time. Opposition loop. Jupiter is just about, Saturn is next (i think). The astrophotographers here will love it because then they will have him high in sky all spring at part of the summer.

That simply happens while the earth overtakes on the inner track, in front of the background of distant stars the outer planet then seems to go backwards.

To put it in funny words:

Ptolemaios then painted these spirals as a weak excuse because with the earth in center he couldn't explain what was already clear to many others centuries before. Of course he was scoffed at at the end of the antique, but got a revival in the Renaissance when the church needed "science" against that new fangled sun-is-in-the-center stuff :-)

Hope that wasn't too impertinent.

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4 hours ago, Green Baron said:

Hope that wasn't too impertinent.

As an aside, I always found it interesting that one of Ptolemy's blunders continued to influence politics 1400 years later:

It is a myth that the establishment during the time of Columbus thought the world was flat. Some uneducated people certainly did think the world was flat, but scientists had known that the world was spherical since ancient Greek times. Eratosthenes even calculated the Earth's size to within a few percent of the actual value. Unfortunately, Ptolemy screwed it up when he redid Eratosthenes' calculation and estimated the Earth's size at about 60% of the true size. The church liked Ptolemy's science, though, so his value for the size of the Earth became the accepted value for the next 1400 years or so.

It was only after Magellan's crew completed the first circumnavigation that people realized that their estimates for the Earth's size were vastly wrong; the navigators of Magellan's fleet were surprised and even scared by the size of the Pacific ocean when they crossed it from Patagonia to the Philippines. The Spice Islands should have been just around the other side of the Americas by their reckoning but it didn't turn out that way. The whole point of the expedition was to prove that the very valuable Spice Islands were in the Spanish half of the world, as defined by the Treaty of Tordesillas. They would have been in the Spanish half if the world was 26000 km around as Ptolemy predicted, but sadly for the Spanish (at least in this regard), he was wrong.

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On 3/8/2017 at 7:38 AM, KSK said:

I'm probably missing something but isn't that a bit of a circular definition? How are you defining an orbital velocity here?

The idea was to deal with bodies that might appear in a much more loosely bound orbit (such as a rather distant orbit) that might be under at least as much pull by other bodies.  By the time someone shows up here, I tend to expect the basics of orbit to be understood.  I'm rather surprised that Newton's "cannon on a mountain" hasn't shown up, but that is shown in the wiki that had already been referenced when made my statement.

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