Orbit in MOND

• A
accdd
In MOND should two small masses placed at a great distance orbit faster than in Newtonian dynamics?
Would it be theoretically possible to do this experiment in the solar system, or would the presence of the sun and earth be a problem?

accdd
Maarten Havinga
The presence of the sun is a problem in the solar system.

accdd and ohwilleke
Staff Emeritus
I'm not sure there even is an A-level answer to your thread. You obviously don't want B or I - what is it about those explanations you find unsatisfactory?

Gold Member
Would it be theoretically possible to do this experiment in the solar system, or would the presence of the sun and earth be a problem?
No.

It would not be possible, even in theory, to do this experiment in the solar system because the presence of the sun would be a problem.

In Modified Newtonian Dynamics (MOND), a phenomenological tweak to Newtonian gravity proposed in 1983 by Mordehai Milgrom to replicate the galactic rotation curves attributed with dark matter without using dark matter, there is one experimentally determined physical constant:

a0 = 1.2 x 10-10 ms-2

In MOND, this constant is the characteristic acceleration due to a gravitational field, above which ordinary Newtonian gravity applies and below which an enhanced gravitational field strength leading to flat rotation curves in spiral galaxies is present.

With only unmodified Newtonian gravity without dark matter, objects in the outer part of the Milky Way galaxy (and other galaxies), that move as fast as they are observed to move around the center of the galaxy, would be flung away from the galaxy into intergalactic space and leave its gravitational pull, instead of remaining in orbits around it.

What does this mean in reference to something understandable?

The mass of everything other than the Sun can safely be disregarded in this calculation because the Sun accounts for 99.86% of the mass of the solar system. If you needed more precision for some reason, Jupiter and Saturn together make up more than 90 percent of the mass of all of the planets in the solar system, so considering them in the calculation would get you to parts per 10,000 precision (which is spurious accuracy when the physical constant in question, a0, is only know to about ± 8 % precision). The mass of the Earth is utterly irrelevant to the calculation because it makes up such a tiny share of the total mass of the solar system and is only 1 astronomical unit (AU) from the Sun. An AU, which is 149.6 million km, is the average distance of the Earth from the Sun.

The gravitational field of the Sun alone falls to the strength of a0 at a distance of about 1,052 billion km (about 7000 AU) from the Sun.

This is about 1/9th of the light year from the Sun, which is about 175 times the average distance of Pluto from the Sun. Pluto's average distance from the Sun is about 6 billion km).

This is about 58 times more distant from the Sun that the heliosphere, which is a functional definition of where the solar system ends and deep interstellar space begins, that is about 18 billion km (120 astronomical units) from the Sun.

As of February 2018, Voyager 1, the most distant man made object from Earth, was about 21 billion km from Earth, and Voyager 2, the second most distant man made object from Earth is about 17 billion km from Earth. Both were launched 43 years ago in 1977. These probes (which will run about of power around the year 2025), will reach this distance from the Sun about 2000 years from now in around 4000 CE.

This is still much closer to the Sun than the closest star, however. Proxima Centauri, the closest star to the Sun, is just over four light-years away.

Our state of the art telescopes can't see anything dimmer than a star (unless it crosses the visual field of a star up close) at those distances.

This doesn't necessarily mean that MOND effects are actually predicted to occur at that distance from the Sun, because the theory has "external field effects" which prevent this effect from occurring if gravitational effects from other object bring the overall strength of the local gravitational field from all sources combined above the a0 acceleration constant threshold (in which case the behavior is Newtonian), or the field from external sources is below that constant but above the strength of the gravitational field from the source you are trying to observe (in which case there is only a partial MOND effect).

Also, this effect is very subtle at first and it is only discernible when Newtonian gravity, which is a function of one divided by the distance from the source squared, is significantly different from the MOND value which is a function of one divided distance from source when beyond the acceleration constant threshold.

For example, in MOND, at twice the critical distance from a mass the size of the Sun with no external field effect (i.e. at a distance of 2/9th of a light year which is about 14000 AU), the gravitational force from the Sun is twice its predicted Newtonian gravity value.

Since acceleration due to gravity at this distances is very small, and the observable is distance and not acceleration, which is the second derivative of distance (i.e. the rate at which velocity changes which is in turn the rate at which distance changes), even a fairly substantial change in gravitational acceleration is not easy to observe in objects that are, by definition, very far away from any realistic terrestrial observer.

The external field effect in MOND violates the strong equivalence principle of general relativity that "The outcome of any local experiment (gravitational or not) in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime," but not the weak equivalence principle that "All test particles at the alike spacetime point, in a given gravitational field, will undergo the same acceleration, independent of their properties, including their rest mass."

To be clear, toy model MOND is not an accurate description of reality. It is a non-relativistic theory, it underestimates the magnitude of dark matter phenomena at the scale of galactic clusters, and it doesn't predict the dynamics of stars outside the galactic plane in a spiral galaxy as well as inferred dark matter halos fitted to a spiral galaxies rotation curve speed.

But MOND does accurately describe rotation curves of objects up to the scale of the largest galaxies in a way that can make concrete predictions (which dark matter particle theories don't do very well at all), and can inform your intuition of how dark matter phenomena behave and in which circumstances they arise, with just one simple physical constant and one simple equation.

There are efforts to do conceptually similar tests of MOND, however.

Wide binary systems (i.e. stars in gravitationally bound binary star systems with a large separation) should behave in a non-Newtonian fashion in some (but not all) modified gravity theories that reproduce MOND-like behavior on a galactic scale. But, in LambdaCDM and other dark matter particle halo theories, the dark matter halos should be too large to materially change the dynamics of wide binary systems.

So, it is a good data set to distinguish the two approaches to phenomena normally attributed to dark matter, and there are at least 9,000 such binary systems that have been detected by GAIA. But the data aren't yet sufficiently precise because it can't rule out that what appear to be binary systems are really three or four star systems in which not all of the stars have been seen. Fortunately, progress is being made in distinguishing false positive binary systems in order to allow the dynamics of wide binaries to be rigorously studied with a large data set.

Several recent studies have shown that velocity differences of very wide binary stars, measured to high precision with GAIA, can potentially provide an interesting test for modified-gravity theories which attempt to emulate dark matter; in essence, MOND-like theories (with external field effect included) predict that wide binaries (wider than ∼7 kAU) should orbit ∼15% faster than Newtonian for similar orbit parameters; such a shift is readily detectable in principle in the sample of 9,000 candidate systems selected from GAIA EDR3 by Pittordis and Sutherland (2022). However, the main obstacle at present is the observed fat tail" of candidate wide-binary systems with velocity differences at ∼1.5−6× circular velocity; this tail population cannot be bound pure binary systems, but is likely to be dominated by triple or quadruple systems with unresolved or undetected additional star(s).

While this tail can be modelled and subtracted, obtaining an accurate model for the triple population is crucial to obtain a robust test for modified gravity. Here we explore prospects for observationally constraining the triple population: we simulate a population of hierarchical triples observed" as in PS22 at random epochs and viewing angles; then evaluate various possible methods for detecting the third star, including GAIA astrometry, RV drift, and several imaging methods from direct Rubin images, speckle imaging and coronagraphic imaging. Results are encouraging, typically 90 percent of the triple systems in the key regions of parameter space are detectable; there is a moderate dead zone" of cool brown-dwarf companions at ∼25−100 AU separation which are not detectable with any of our baseline methods. A large but feasible observing campaign can clarify the triple/quadruple population and make the gravity test decisive.
Dhruv Manchanda, Will Sutherland, Charalambos Pittordis, "Wide Binaries as a Modified Gravity test: prospects for detecting triple-system contamination" arXiv:2210.07781 (October 14, 2022) (Submitting to Open Journal of Astrophysics).

The introduction to the paper explains:
A number of recent studies have shown that velocity differences of wide stellar binaries offer an interesting test for modified-gravity theories similar to MoND, which attempt to eliminate the need for dark matter (see e.g. Hernandez et al. (2012a), Hernandez et al. (2012b) Hernandez et al. (2014), Matvienko & Orlov (2015), Scarpa et al. (2017) and Hernandez (2019)). Such theories require a substantial modification of standard GR below a characteristic acceleration threshold a0 ∼ 1.2×10−10 m s−2 (see review by Famaey & McGaugh (2012)). A key advantage of wide binaries is that at separations > 7 kAU, the relative accelerations are below this threshold, so MoND-like theories predict significant deviations from GR; while wide binaries should contain negligible dark matter, so DM theories predict no change from GR/Newtonian gravity. Thus in principle the predictions of DM vs modified gravity in wide binaries are unambiguously different, unlike the case for galaxy-scale systems where the DM distribution is uncertain.
Wide binaries in general have been studied since the 1980s ((Weinberg et al. 1987; Close et al. 1990)), but until recently the precision of ground-based proper motion measurements was a serious limiting factor: wide binaries could be reliably selected based on similarity of proper motions, see e,g, Yoo et al. (2004), L´epine & Bongiorno (2007), Kouwenhoven et al. (2010), Jiang & Tremaine (2010), Dhital et al. (2013), Coronado et al. (2018). However, the typical proper motion precision ∼ 1 mas yr−1 from ground-based or Hipparcos measurements was usually not good enough to actually measure the internal velocity differences, except for a limited number of nearby systems.
The launch of the GAIA spacecraft (Gaia Collaboration 2016) in 2014 offers a spectacular improvement in precision; the proper motion precision of order 30 µas yr−1 corresponds to transverse velocity precision 0.0284 km s−1 at distance 200 parsecs, around one order of magnitude below wide-binary orbital velocities, so velocity differences can be measured to good precision over a substantial volume; and this will steadily improve with future GAIA data extending eventually to a 10-year baseline. Recent studies of WBs from GAIA include e.g. El-Badry et al. (2021) and Hernandez et al. (2022).
In earlier papers in this series, Pittordis & Sutherland (2018) (hereafter PS18) compared simulated WB orbits in MoND versus GR, to investigate prospects for the test in advance of GAIA DR2. This was applied to a sample of candidate WBs selected from GAIA DR2 data by Pittordis & Sutherland (2019) (hereafter PS19), and an expanded sample from GAIA EDR3 by Pittordis & Sutherland (2022) (hereafter PS22). To summarise results, simulations show that (with MoND external field effect included), wide binaries at & 10 kAU show orbital velocities typically 15 to 20 percent faster in MOND than GR, at equal separations and masses. This leads to a substantially larger fraction of “faster” binaries with observed velocity differences between 1.0 to 1.5 times the Newtonian circular-orbit value. In Newtonian gravity, changing the eccentricity distribution changes the shape of the distribution mainly at lower velocities, but has little effect on the distribution at the high end from 1.0 to 1.5 times circular velocity. Therefore, the predicted shift from MOND is distinctly different from changing the eccentricity distribution within Newtonian gravity; so given a large and pure sample of several thousand WBs with precise 2D velocity difference measurements, we could decisively distinguish between GR and MOND predictions.
The main limitation at present is that PS19 and PS22 showed the presence of a “fat tail” of candidate binaries with velocity differences ∼ 1.5 to 6× the circular-orbit velocity; these systems are too fast to be pure bound binaries in either GR or MOND, and a likely explanation (Clarke 2020) is higher-order multiples e.g. triples where either one star in the observed “binary” is itself an unresolved closer binary, or the third star is at resolvable separation but is too faint to be detected by GAIA; the third star on a closer orbit thus substantially boosts the velocity difference of the two observed stars in the wide “binary”.
In PS22 we made a simplified model of this triple population, then fitted the full distribution of velocity differences for WB candidates using a mix of binary, triple and flyby populations. These fits found that GR is significantly preferred over MOND if the rather crude PS22 triple model is correct, but we do not know this at present. Allowing much more freedom in the triple modelling is computationally expensive due to many degrees of freedom, and is likely to lead to significant degeneracy between gravity modifications and varying the triple population. Therefore, observationally constraining the triple population, or eliminating most of it by additional observations, is the next key step to make the WB gravity test more secure.
In this paper we explore prospects for observationally constraining the triple population: we generate simulated triple systems “observed” at random epochs, inclinations and viewing angles, and then test whether the presence of the third star is detectable by any of various methods including direct, speckle or coronagraphic imaging; radial velocity drift; or astrometric non-linear motion in the future GAIA data; we see below that prospects are good, in that 80 to 95% of triple systems in the PS22 sample should be potentially detectable as such by at least one of the methods.
Basically, we need to be able to measure deviations from the predicted orbital velocity of confirmed true wide binary systems in a large statistical sample with an average uncertainty of about ± 2-3% to conclusively compare the expected behavior of wide binary systems to their actual behavior in a way that could falsify or prove that MOND was an accurate description of these systems (since conclusive results require results distinguishing hypotheses that is about five time greater than the uncertainty in the measurement).

We aren't there yet, but we might be there in a decade or two.

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Drakkith and accdd
accdd
I'm not sure there even is an A-level answer to your thread. You obviously don't want B or I - what is it about those explanations you find unsatisfactory?
All answers from all levels are welcome

Maarten Havinga
Staff Emeritus
But you're still not explaining what you don't like about the simple answers. Why not tell us what you've found out and what you found unsatisfactory about those?

Motore
Maarten Havinga
But you're still not explaining what you don't like about the simple answers. Why not tell us what you've found out and what you found unsatisfactory about those?
I don't get it. On my phone, it shows nowhere that accdd found anything unsatisfactory about whatever. This looks like it is off-topic, can you explain?

Motore
Staff Emeritus
First, it's the A at the top. When the OP posted the thread, he selected a level, Basic/Intermediate/Advanced that was the level at which he wanted an answer. By saying he wanted a graduate-level answer, he is telling us he doesn't want a pre-college or undergraduate answer. Which is fine, but of course if he doesn'tt tell us what he doesnt like about the lower level answers. Which makes it hard to provide a better answer.

Maarten Havinga
Ah now I get it. Thanks :)

Well, an "Any"-level (partial) answer to the first part of the OP's question, i.e.,

@accdd said:
In MOND should two small masses placed at a great distance orbit faster than in Newtonian dynamics?
...is that the crucial feature of MOND is an acceleration scale, not a length scale.

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kodama
Well, an "Any"-level (partial) answer to the first part of the OP's question, i.e.,

...is that the crucial feature of MOND is an acceleration scale, not a length scale.
does e&m also have a special acceleration scale, not a length scale.

does e&m also have a special acceleration scale, not a length scale.
Not that I know of, but in (classical) accelerating electrodynamics one finds a time scale ##\tau_0 \approx 10^{-23} s## associated with the Lorentz-Abraham-Dirac version of electromagnetism, where the generalized equation of motion is of the form: $$m_0 \,\ddot {\mathbf r} ~=~ {\mathbf f}_{\text ext} ~+~ m_0 \tau_0 \, \dddot {\mathbf r} ~,~~~~ \text{where}~~ \tau_0 = \frac{q^2}{6\pi\epsilon_0 m_0 c^3} ~.$$ Associated with this is the so-called "Schott energy", or "acceleration energy", which I'm still trying to understand in better detail. At this stage I have no idea whether it has any relationship to, or gravity-analog with, MOND.

dextercioby and kodama
kodama
Not that I know of, but in (classical) accelerating electrodynamics one finds a time scale ##\tau_0 \approx 10^{-23} s## associated with the Lorentz-Abraham-Dirac version of electromagnetism, where the generalized equation of motion is of the form: $$m_0 \,\ddot {\mathbf r} ~=~ {\mathbf f}_{\text ext} ~+~ m_0 \tau_0 \, \dddot {\mathbf r} ~,~~~~ \text{where}~~ \tau_0 = \frac{q^2}{6\pi\epsilon_0 m_0 c^3} ~.$$ Associated with this is the so-called "Schott energy", or "acceleration energy", which I'm still trying to understand in better detail. At this stage I have no idea whether it has any relationship to, or gravity-analog with, MOND.
since Deur compare GR with QCD does QCD also have a special acceleration scale, not a length scale.

mitchell porter
since Deur compare GR with QCD does QCD also have a special acceleration scale, not a length scale.
I am not a QCD expert. Perhaps someone else can answer that.

kodama
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Does even questions about MOND and other (non quantum) gravitiy theories besides Einsteins GR belong in this subforum?

Please note that this forum deals with topic related to theories beyond the Standard Model of elementary particle physics. It includes String, Superstring, Supersymmetry, Quantum Gravity, etc. Topics that deal with complexities in quantum field theory, relativity, etc. should be posted in those specific forum, not in here.

Does even questions about MOND and other (non quantum) gravitiy theories besides Einsteins GR belong in this subforum?

Please note that this forum deals with topic related to theories beyond the Standard Model of elementary particle physics. It includes String, Superstring, Supersymmetry, Quantum Gravity, etc. Topics that deal with complexities in quantum field theory, relativity, etc. should be posted in those specific forum, not in here.
MOND/MoG stretches across several disciplines, including (extensions of) classical mechanics, relativity, astrophysics, cosmology. I think it's better to have MOND/MoG threads in one forum than spread over many. If not the BTSM forum, then... where?

Homework Helper
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If not the BTSM forum, then... where?
I was thinking that this subforum needs a re-naming and a change in description. Or, just put it in the "other physics" sub-forum.

It is just not particle physics (theories beyond the Standard Model of elementary particle physics) that is being discussed here.

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I was thinking that this subforum needs a re-naming and a change in description.
I agree. Maybe "Beyond the Standard Models" (plural), together with enlargement of the forum description?

Or, just put it in the "other physics" sub-forum.
Actually, this thread was moved from "Other Physics" to BTSM at my suggestion.
I also suggested that Mentors and Advisors should perhaps try to reach a consensus about which forum MOND threads should find a default home. But that's a discussion for the Advisor's forum.

Gold Member
I also suggested that Mentors and Advisors should perhaps try to reach a consensus about which forum MOND threads should find a default home. But that's a discussion for the Advisor's forum.
I think it will be hard to do that.

Strictly speaking, a very large share of cosmology is BSM. For example, cosmological inflation, baryogenesis, and leptogenesis are all BSM.

Even fundamentals of black hole theory like Hawking Radiation, really are crude approximations of quantum gravity, which is BSM.

Moreover, really all explanations of dark matter phenomena are BSM (unless it is just due to a GR effect that has been underestimated or emergent gravity from SM quantum effects), not just MOND, but also all dark matter particle theories.

Dark matter particle theories and gravitational explanations of dark matter phenomena belong in the same category since they are both BSM explanations of the same things. Indeed, many DM particle theories also introduce a fifth force that amounts to a gravity modification, either in the form of DM particle self-interactions, or DM particle interactions with ordinary matter.

Dark energy that takes the form of a cosmological constant is part of GR, however.

malawi_glenn
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Moreover, really all explanations of dark matter phenomena are BSM (unless it is just due to a GR effect that has been underestimated or emergent gravity from SM quantum effects), not just MOND, but also all dark matter particle theories.
Problem is that MOND is not a particle theory, it is modified (non quantum) gravity.
Therefore, MOND is not an extension of the SM of particle physics.

I agree. Maybe "Beyond the Standard Models" (plural), together with enlargement of the forum description?
I would be fine with that. Beyond the standard models of particle physics and gravity.

Gold Member
Problem is that MOND is not a particle theory, it is modified (non quantum) gravity.
Therefore, MOND is not an extension of the SM of particle physics.

I would be fine with that. Beyond the standard models of particle physics and gravity.
MOND is basically an extension of GR, and while the forum is called BSM, it has always appeared to me to really be beyond "core theory" which is SM + GR.