Large Body Orbiting a Small One?

[Incognito310]

When I was in school (over 20 years ago in a backwoods town), I leaned all kinds of wrong things about science. I think this might be one of those things.

Back then we were taught that—hypothetically—if the Sun were to instantly, inexplicably, be reduced to the size of a basketball (while maintaining its mass), all of the planets and everything else in the solar system would continue along their orbits as though nothing ever happened.

Is this still considered accurate (if it ever was)? I currently suspect that other bodies in the solar system would either also reduce in size in proportion to the Sun's or be torn apart in the immediate aftermath of the Sun's change.

So what would happen in the above hypothetical based on the current understanding? If the answer is the same as what I was taught way back when, is that theoretical, or has it been observed?

Obviously stars don't just shrink for no reason, so when I ask if it's been observed what I'm asking is if a larger, lower mass body has been observed orbiting a smaller, denser one? Maybe around a neutron star? In a weightless environment, would a balloon orbit a baseball?

 

[Bandersnatch]

Yes, it's correct. Gravity is the force that governs orbital motion, and its strength doesn't depend on spatial extent of the massive body. A gravitational field far away from the central body looks the same whether it's a regular star, neutron star, a black hole, or an imaginary point source of equivalent mass. (mathematically, the Shell Theorem explains why it is so)

There's just no doubt about it, considering that it's a rather basic implication of theory of gravity(whether Newtonian, or General Relativity), and we know that works. Don't we?

The orbits of exoplanets during the transition from a star to a neutron star/black hole(which doesn't strictly conserve the progenitor star's mass anyway) have never been observed. However, the first exoplanet ever was discovered around a pulsar(http://en.wikipedia.org/wiki/PSR_B1257+12), which corroborates the prediction of stability.

As for other bodies, there is a plethora of pulsar binaries observed. These are systems featuring a pulsar(i.e., neutron star) and either another neutron star, or a white dwarf orbiting each other. The pulsars are much massive, yet more compact than white dwarfs, so the barycentre(the point in space the two bodies orbit - it's never exactly in the centre of anyone body) lies close or within the pulsar.

There's also stars orbiting black holes:
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/blkbin.html#c4

 

[Simon Bridge]

When I was in school (over 20 years ago in a backwoods town), I leaned all kinds of wrong things about science. I think this might be one of those things.

Back then we were taught that—hypothetically—if the Sun were to instantly, inexplicably, be reduced to the size of a basketball (while maintaining its mass), all of the planets and everything else in the solar system would continue along their orbits as though nothing ever happened.

Is this still considered accurate (if it ever was)?

Yes.

I currently suspect that other bodies in the solar system would either also reduce in size in proportion to the Sun's or be torn apart in the immediate aftermath of the Sun's change.

Nope.

The gravity from the sun depends on the total mass of the sun and the distance from the center of mass. As long as these two things do not change, nothing changes.

So what would happen in the above hypothetical based on the current understanding? If the answer is the same as what I was taught way back when, is that theoretical, or has it been observed?

It is a dircet consequence of the law of gravitation. You can work it out for yourself.

Obviously stars don't just shrink for no reason, so when I ask if it's been observed what I'm asking is if a larger, lower mass body has been observed orbiting a smaller, denser one? Maybe around a neutron star? In a weightless environment, would a balloon orbit a baseball?

I understand that large stars have been found to orbit black holes.

I think there is a fundamental misunderstanding here though ... planets do not orbit the Sun.
What happens is that the Sun and the planets orbit their common center of mass.
It is only because that center of mass is inside the Sun that people talk like they do.

Consider how it would work if both bodies were the same size and mass.

 

[Incognito310]

Thank you for the replays. I really appreciate the distinction about bodies orbiting a common center of mass. It makes sense that the orbits of the masses would remain the same regardless of the bodies' volumes.

 

[Simon Bridge]

I looked for an example of a star orbiting a black hole:
Found a bad astronomy mention of a red dwarf star orbiting a BH.
http://www.slate.com/blogs/bad_astr...star_orbits_black_hole_in_only_2_4_hours.html

Looking closer:
The BH has 3-20 solar masses, probably around 10. The red dwarf is about 0.2 solar masses.
you can work out the relative sizes - i figure the dwarf is around 1000x bigger than the BH (using the Schwarzschild radius for the BH)

Ballpark figures:
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/blkhol.html
... gives about 30km for the BH Sr.

http://www.enchantedlearning.com/subjects/astronomy/stars/startypes.shtml
... gives a typical red dwarf at 0.4 solar radii (278200km)
(smallest ever is 0.08 solar radii (55640km))

i.e. here is an example of a big object orbiting a small one.
where the big one is 1000 to 10000x the radius of the small one.

 

[Bill_K]

I think there is a fundamental misunderstanding here though ... planets do not orbit the Sun.
What happens is that the Sun and the planets orbit their common center of mass.
It is only because that center of mass is inside the Sun that people talk like they do.

The center of mass of the solar system is sometimes inside the sun, sometimes outside, depending mainly on whether Jupiter and Saturn are currently on the same or opposite sides.

 

[Incognito310]

I looked for an example of a star orbiting a black hole:
Found a bad astronomy mention of a red dwarf star orbiting a BH.
http://www.slate.com/blogs/bad_astr...star_orbits_black_hole_in_only_2_4_hours.html

Looking closer:
The BH has 3-20 solar masses, probably around 10. The red dwarf is about 0.2 solar masses.
you can work out the relative sizes - i figure the dwarf is around 1000x bigger than the BH (using the Schwarzschild radius for the BH)

Ballpark figures:
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/blkhol.html
... gives about 30km for the BH Sr.

http://www.enchantedlearning.com/subjects/astronomy/stars/startypes.shtml
... gives a typical red dwarf at 0.4 solar radii (278200km)
(smallest ever is 0.08 solar radii (55640km))

i.e. here is an example of a big object orbiting a small one.
where the big one is 1000 to 10000x the radius of the small one.

Thank you for this! It's almost exactly what I was looking for. I was hoping for a system with huge gas giant and a tiny neutron star, but this will give me something to chew on for a while. Thank you!

 

[Simon Bridge]

The deatails of the solar system com wrt the center fo the Sun are available in wikipedia and elsewhere:
Wikipedia - barycenter
... though I think still a tad confusing, ferinstance: I always thought the primary of a two body system would be the most massive, not the "biggest".
Anyway: the keyword here is "barycenter".

Discussion about "barycenter" for the layman:
Crockett Astronomy: barycenter

Note: the com/barycenter of Jupiter-Sun system is simple to work out.
At max, it does indeed appear outside the mean solar radius by about 78000km.
If we took the com as coincident with the center of the Sun, that would introduce a systematic error to the orbit radius of: 0.095%. This would be too big for some calculations but for the kind of thing one does at secondary-school level...

The Barycenter for the whole solar system can indeed get quite a ways from the Sun.

@Incognito: no worries - once you've got that idea, a whole lot of other things start to make sense.
Black holes can be a bit tricky conceptually - i.e. how does one define the "size" of one... if you used the singularity then it's radius is zero, the ultimate small object(!) - but they do give the kind of extreme example you want.

Initially I figured a Neutron star is unlikely to have a big companion because f the way they form, but it seems that it is not unlikely. A Red Giant star closely orbiting a neutron star can give the neutron an accretion disk so it will be a bright-ish object. I'm having a nasty time finding a specific example though since a certain Red Giant with a neutron start core is dominating searches. But now you know what to look for - enjoy.

 

[dean barry]

Two body orbital mechanics

Here attached is the basic two body calcs, given both masses and center to center distance you can find the barycentre position plus velocities etc.
Handy hint : in stable orbit, both bodies will have equal momentum.

 

[Incognito310]

Thanks again for all the help. I think the question I was trying to ask was less about orbits (although that is very useful & helpful so I'm glad for all of the info), and more about how the density of planets is achieved. I have to reiterate that I have no background in Astronomy or Physics, so sometimes I don't even know how to explain what I'm trying to understand.

I imagine each planet reaches an equilibrium between gravitational forces pushing in and electromagnetic forces pushing out (I just made that up, so sorry if it's completely dumb), but what I was wondering when I first posted—I think—is if the density of other bodies within the solar system (most notably the Sun), have an effect on how densely the other planets settle into themselves.

More to the point, and this is a bit embarrassing, I've had a sort of a corpuscular view of gravitation stuck in my head for about two years now. It's like an annoying song that won't go away. I know it's wrong, but I don't know why. I have such a limited understanding of math and science that whenever I try to read about why my way of thinking about gravity is incorrect, it goes over my head. I've tried talking to physicists in order to hopefully get a common-sense explanation of where I'm going wrong, but I'm such a dunce I can't even articulate the models that I have in my head. They seem like exceedingly simple models, but I don't have the language to describe them. So it's been kind of a project of mine to find something that my idiot brain can both understand and can disprove a corpuscular theory of gravity.

If gravity were corpuscular in the way that I'm thinking, gravitational screening wouldn't allow for a large non-dense body to orbit a smaller, dense one. The flow of the corpuscles (as it works in my head anyway) would cause the larger body to constrict (or be torn apart). So I was hoping to find an instance of a gas giant and star with a smaller diameter in orbit with each other. That would serve as proof of my wrongness that even I can understand.

I'm at a bit of a loss. So if anyone can forward an argument against corpuscular gravity that a bone-head can comprehend, I'd love—LOVE—to hear it.

…And now that I've gotten on to the topic (in the original post and earlier in this one), I am really am interested in how the planets' densities are achieved. I'm sure like most things there are more factors to it than I can possibly understand, but I would love to get the broad-stokes, if possible.

Thanks again. This forum has been great so far.

 

[Simon Bridge]

Density of matter:
How the size of an object depends on it's mass depends on a lot of things - hot objects, for example, will generally be less dense for the same mass than cold objects. Also the makeup of the object is important - nickle-iron asteroids will be more dense than, say, water-rich asteroids. At different scales, different forces come to dominate.

Corpuscular gravity:
I am not going to discuss this theory of gravity as that opens a whole new can of worms and it is not relevant.
I am certain that it is possible to tweak some corpuscle theory to fit the facts, but that is besides the point - there are any number of theories that can account for gravity - finding new theories is not the difficult part of science - what we need, what is hard, is choosing between them.
What we use is a combination of empiricism and occams razor.

The bonehead-level answer is that the corpuscle theory, in order to account for everything we know, is just too complicated. Nobody wants to do maths that hard and we don't need to. We have a perfectly good theory of gravity which is nowhere near as complicated so we use that.

Quest for understanding:
Off your statements, if you are serious about persuing an improved understanding of physics, you absolutely have to get comfortable with the maths. There is no other way.

 

[Incognito310]

Thank you Simon. I'm working on the maths (started doing the courses at khanacademy.org about a year ago). And I do hope to get serious about physics at some point. I won't be able to go back to school for it in the immediate future, but I'll do as much studying as I can in the meantime.

I can say it'll be nice to let go of trying to disprove the corpuscle theory, which is what has been driving me thus far. Maybe I can cut myself some slack for subscribing to it too. If I'm understanding you correctly, it's a philosophically plausible (potentially anyway) but wildly inefficient physical model.

 

[Simon Bridge]

So I got the right corpuscle theory? What I described is basically the historical Le Sage model.
You'll probably get further by exploring under that title.

I don't think I made myself clear: "does not work" is a more accurate description than "philosophically plausible but wildly inefficient".

Feynman devotes part of a lecture in The Character of Physical Law, you may want to see that. If nothing else the series should help you understand the subject better.

 

[mfb]

So I was hoping to find an instance of a gas giant and star with a smaller diameter in orbit with each other. That would serve as proof of my wrongness that even I can understand.

See the planets around pulsars, or dwarf stars orbiting neutron stars or black holes. In both cases the smaller, more massive object does not move much, while the larger, less massive object moves a lot.

While it is not possible to get true orbits on the surface of Earth (because everything falls down), the gravitational forces between objects of different mass, size and composition have been measured with high precision in experiments similar to the Cavendish experiment and the Eötvös experiment. No density-dependence has been found.

 

[Incognito310]

So I got the right corpuscle theory? What I described is basically the historical Le Sage model.
You'll probably get further by exploring under that title.

I don't think I made myself clear: "does not work" is a more accurate description than "philosophically plausible but wildly inefficient".

Feynman devotes part of a lecture in The Character of Physical Law, you may want to see that. If nothing else the series should help you understand the subject better.

"Does not work." Got it. I don't disagree—I really don't. But I still don't know why so I'm back to square one.

I've read a bit (not enough) about the Le Sage theory and it seems pretty close to what I'm trying to debunk for myself. I can't follow what most of the objections to it are. I don't doubt them—they're just simply beyond my understanding. I have to reiterate I don't think the model in my head is correct. I actually think it's dumb and I would never defend it. I'm just having a really hard time understanding why its incorrect.

I watched the Feynman series too. If I remember correctlye addressed drag argument against corpuscles. But in my idiot-brain the corpuscles act rather more like light than a traditional medium. I don't know, but in my ignorance I can't say for sure say whether or not drag would be a factor if the speed/force force of impact of the gravitational corpuscles was constant for all observers. As an object moves through space, the corpuscles more or less cancel each other out except where fewer are getting through due to the gravitational screening.

I didn't have the greatest education (I was an undiagnosed dyslexic in a rural community) and I knew nothing at all about relativity or space-time when I got into this mess (I still know next-to-nothing). It makes sense on the surface, but I just can't shake the vision of the gravitational field being ever-shifting corpuscles that actually exist in a literal sense rather than mathematical concept.

I think in the end the only cure for my lack of general understanding about anything scientific is a serious education. I've been picking at the scab of my own ignorance for over a year now, and it hasn't gotten me anywhere. I'm not in a position in life to drop everything and pursue that in a serious way right now. I'll just have to put it on my to-do list for a future date. But I have to say that it's not easy to know that you have a core belief that is fundamentally wrong. That said, I appreciate your patience with me and the advice you've offered. I'm sorry that I'm a bit of a lost cause currently.

 

[Simon Bridge]

I can't follow what most of the objections to it are.

If you do not understand the arguments, then you need to gain the background knowledge to understand them.

But in my idiot-brain the corpuscles act rather more like light than a traditional medium.

...even a flux of light will produce a drag force. As an object moves through a stream of light, it has to push through.

I think in the end the only cure for my lack of general understanding about anything scientific is a serious education.

Yes. You are correct ... at least a systematic study.
You can self-teach - but that means that when you don't follow something, you need to work out what knowledge you need to understand it and then go in search of it. Each time you get stuck, try and work out how you are stuck.

Just saying you don't follow the reasoning is no good - you need to be able to work out where you get stuck.