Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Ian Scott on 19/07/2008 10:35:53
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Ian Scott asked the Naked Scientists:
Hi
I am a big fan of The Nakedscientists and I have a question relating to the speed of gravity and its effect on orbiting bodies in space. I wonder why the finite time taken for gravity to exert influence from one body to another is not taken into account when orbital equations are presented?
If, say one galaxy is orbiting another at say 100 light-years away, then it should take 100 years for the gravitational directional force from one galaxy to influence the momentum of the other.
I guess such galaxies will have a center of mass and should behave like to balls in a circular orbit - but why is this gravitational communication assumed to be instantaneous when the equations of motion are derived? Alternatively, is there a reason why this finite time delay should be immaterial? Or could such a time delay result in instability over large distances? (like an excess phase delay can cause oscillations in a feedback loop).
I look forward to any replies to this question, thanks!
What do you think?
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Abrupt gravitiational changes are propagated at the velocity of light but planets stars and galaxies form by slow accretion processes that take millions of years and so the gravitiational changes have plenty of time to propagate remember also that the gravitational influence of a galaxy on another galaxy is not very sensitive to the distribution of that galaxy the total attraction is just the value of the mass as if it was concentrated at the centre of gravity of the mass.
It is in fact quite difficult to show that gravitiational effects are propagated at light speed about the only way is to observe relatavistic delay effects of light deflection on orbiting objects.
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You don't need 'abrupt' changes in gravitation situations to produce gravity waves; the potential due to a binary pair varies with the period of the orbit. They only behave like a point mass at infinite distance so, if you had sensitive enough equipment, you would notice the variation and its phase would be the same as the visually observed phase; both pieces of information would travel at the same speed.
The moon, being tiny but much closer causes tidal effects which are measurable in the Lab. Gravitational effects and the observed position should / could be measured to be in phase - but we are looking for 1s in 28 days, so it would be a rather demanding level of accuracy.
Afaik, it could have already been measured, tho'.
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The propagation of gravitiational effects has I believe been measured using pulsars and the planet Jupiter by measuring changes in delay due to gravitational path distortion. it was reported a few years ago but I can't find the reference at the moment.
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Thank you for your replies but they attack a different question to the one I asked. Why not just say "I don't know"?
Qualitative references to time and age are all very well but quantitatively why is non finite gravitational communication speed not taken into account? Can we stay on the subject?
Anyway I am not complaining as I have no answers myself [:)]
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If we take the general relativity view that the gravitational influence of a body is a distortion of space/time ,the well known rubber sheet analogy propagation time is irrelevant the orbiting body is moving in a straight line in curved space.
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Hi syhprum
Is a curved line longer than a straight line?
Please answer my question as posted - just deluding to complexity is not a real answer
Thanks - why not just say the "world is vast because it is green"? - also why reference "well known facts" it was "well known once" the earth was flat, it was "well known once" the sun circled the earth.Equal in all things is how we sometimes parade knowledge but in its essence knowledge comes from questions.
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Ian - I would have thought that gravitational attraction is taken as constant except for any increase in the distance between the galaxies. I can't see that there would be any sudden, or even gradual, change in the gravity of a galaxy that would be great enough to have any real impact.
If the distance between the galaxies remains at 100 light years (that's a bit close for galaxies, by the way) then the gravitational attraction will in actuality remain constant. As such, it makes sense to ignore any delay.
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Hi DoctorBeaver
Thanks for the reply. But is this armchair science? We can make simple nebulous reason for why things are as they are but is this intellectual reasoning?
A nebulous reasons(s) for why a finite time delay is immaterial (are)
1. The time delay is beyond our personal imagination
2 The impact of such time delay is beyond our personal brain space
Note I never had suggested any "sudden" change - My question is clear for those that will read it. Sudden is after all a qualitative term and the question I raise is to do with equations of motion; not arm waving.
If the finite "speed of gravity" should not be included in even the simplest 2 orbital body case then why not? I used 100 light years to illustrate a delay - could be 100 billion years - surely this should matter in orbital equations?
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Ian - I have no definite answer either way. I was, in effect, thinking aloud.
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Hi DoctorBeaver
I hope you didn't think I was too blunt - the issue has puzzled me and I tried it out in MathCad - and got oscillations but I plan to revisit this.
Nothing wrong about thinking aloud [:)]
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My expertise lies in a field other than physics. I am merely an interested amateur. I do, though, enjoy little thought experiments.
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When considering the effect of gravity 'delay' in an orbital problem, the speed of the orbiting body would be very slow wrt the speed of propagation of the gravitational wave and, in any case, the only variation in Gravitational Potential would be due only to any eccentricity in the orbit so the effect would be even less.
And why would any time delay be "beyond any personal imagination"? It is perfectly easy to comprehend the 1s delay in radio signals from the Moon and to realise that the light reaching us from distant stars has taken millions of years to reach us. So where is the problem in considering a delay in the effect on us of a large change in Gravitational Potential taking place a long way off.
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Ian Scott.
What was the system that you were modeling in Mathcad? I fancy that the Model not the Maths was in error.
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Hi Sophiecentaur
All things "are in error" otherwise we would be perfect or in another viewpoint why not doubt conventional wisdom? We learn as we ask.
I read your question and you presume one body to be more massive than the other - I stated two orbiting galaxies - anyway it is of no importance.
Maths is fun of course so why eliminate variables like finite time delay without objective reason?
To state a claim that time delay is insignificant requires in itself a justification (not anger) just as we understand through questioning accepted positions we advance.
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Ian Scott you are talking rubbish and not trying to understand anything. I have clearly explained the answer to your question and there is nothing more to say.
If you continue in this vein any longer I will add you to the list of trolls.
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Soul Surfer
I apologize I just ask questions.
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Hi Sophiecentaur
All things "are in error" otherwise we would be perfect or in another viewpoint why not doubt conventional wisdom? We learn as we ask.
I read your question and you presume one body to be more massive than the other - I stated two orbiting galaxies - anyway it is of no importance.
Maths is fun of course so why eliminate variables like finite time delay without objective reason?
To state a claim that time delay is insignificant requires in itself a justification (not anger) just as we understand through questioning accepted positions we advance.
And which bit was the "Angry" bit? You are too sensitive where you, yourself, are concerned but not so sensitive in your words to others.
I was not assuming any particular size of orbiting object - make them both the same if you like - they will both orbit their common cm, as usual. Still the relative change of GP will be very slow compared with the time for the (time differential of the) gravity waves to communicate between the two objects. Orbit times of years could correspond to orbital diameters of 'light minutes' for orbiting planets is what I meant. Orbit times for Galaxies would be much bigger, of course and our lifetimes are not enough to measure phases accurately, in any case.
And you still haven't offered your model for scrutiny. If it has flaws then the Maths will show you but don't blame the Maths.
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Sophie
Lets just agree to think differently and not be contending on this
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Without your actual Model, I can't agree or disagree with you.
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The proposed model is to add time delay based on distance. The contention of this is why the delay, that we know exists, is immaterial.
To prove this immateriality requires some maths but I only positioned the question for general interest.
There has been some general conjecture offered on angular movements but nothing solid as yet. I guess there is no answer to wait for.
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OK let me have another go. Think about the following things. there are the result of the way our universe works and properties of the inverse square law.
In our universe massive objects do not suddenly appear out of nowhere or suddenly vanish although small quantities of individual atomic particle's mass can be converted into energy and vice versa.
Most massive objects moving under gravity in this universe are travelling very much slower than the velocity of light.
The materials these objects have been made of have been around since the big bang. So the individual gravitational effect of every atom has had time to permeate the entire universe.
If you have an evenly distributed material (gas or dust particles) if indefinite extent (ie you can't get to the edges) (I avoid the word infinite because that is mathematical and can be subject to all sorts of silly conclusions we are talking physics here) there is no net gravitational vector in any direction because the mutual attractions of all the particles cancel each other out. However the moment you distrub this even distribution by making one bit a little bit denser than another there is a gravitational attraction towards the centre of the denser bit.
This shows that it is only the general differences form even distribution produce a gravitational effect
If I have a uniform spherical shell of material. Outside the shell there is a gravitational field as if all the mass was concentrated at the centre of the sphere
inside of the spherical shell the gravitational field is zero because all the gravitational effects of the various bits of the shell cancel out exactly.
This shows that on the whole if you are inside a sphere of moderately evenly distributed material you only need to consider the local gross departures form uniformity.
The net result of all this is that for two galaxies interacting at a distance only large changes will have an effect on what is a simple reaction in fact galaxies can pass through each other and come out distorted but substantially whole look up galaxy zoo and see some wonderful pictures of actual interacting galaxies.
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A philosophical argument but not one to rest easy'
Your comments deserve thought though
I am thinking
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The proposed model is to add time delay based on distance. The contention of this is why the delay, that we know exists, is immaterial.
To prove this immateriality requires some maths but I only positioned the question for general interest.
There has been some general conjecture offered on angular movements but nothing solid as yet. I guess there is no answer to wait for.
Come on, that's not a model; it's one principle which you can apply to a model. I mean what system were you modeling and what calculations did you do? Was it calculating a simple mutual orbit? Was is to show the remote effect on a distant object? Did you actually do it?
You were so assertive about the result that you must surely have some evidence. Mathlab only does what you tell it to do.
Did you do a simple orbit calculation but with the attraction vector pointing 'a bit behind ', where the other object was some time ago, to make up for the time delay? Just say.