# Why doesn't dark matter affect planetary motion?

If the universe is made up of ~95% dark matter, and it interacts only gravitationally then why didn't Newton and Kepler discover it before ? Why does it show itself only in the radial velocity profile of stars in galaxies and not in that of planets around the Sun ?

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better read the article in wikipedia en.wikipedia.org/wiki/Dark_matter . Today dark matter is 26% dark energy 68% and 5% normal matter . Dark matter was postulated while using Newtons equations, because galaxies would not be stable without it. Dark energy is hypothetical permeating everything en.wikipedia.org/wiki/Dark_energy – anna v Apr 10 '14 at 17:48
Newton and Kepler didn't have the observational tools that we have today which span the electromagnetic spectrum and are much more accurate. In addition they did not know about some of the velocity discrepancies which was evidence of "missing mass" in the orbital velocities of clustered galaxies. – user6972 Apr 10 '14 at 19:01
If you want to be pedantic, they did: the planets can be considered baryonic dark matter. – Mark Apr 11 '14 at 9:10

Dark matter would affect planetary motion, but the influence of dark matter on planets in our solar system is too small to detect even currently due to the low concentration of dark matter compared to ordinary matter in our solar system. See Constraints on Dark Matter in the Solar System.

The density of dark matter is very low, $<~10^{-19} grams/cm^3$, compared to the density of ordinary matter in the solar system, below the limits of detectability. On the scale of galaxies, dark matter is thought to make a large contribution and can be detected by studying the velocity of stars at various radial distances.

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The answer is because dark-matter has relatively constant density, as has been given explicitly in another answer. Then, it logically follows that the impact on the Milky Way due to this low density. To show this step, I will establish a figure of merit.

$$FOM = \frac{M_{dark}}{M_{normal}}$$

That is, the ratio of dark matter within the area of influence compared to the normal matter in that same space. For the solar system and the Milky Way, here are some ballpark figures:

$$FOM_{\text{solar system} } = \frac{ \frac{4}{3} \pi \left(50 AU \right)^3 \left( 10^{-19} \frac{g}{cm^3} \right) }{1 M_{\circ}} \approx 10^{-8}$$

$$FOM_{\text{milky way} } = \frac{ \pi \left(50,000 ly \right)^2 \left(1000 ly\right) \left( 10^{-19} \frac{g}{cm^3} \right) }{1.25 \times 10^{12} M_{\circ}} \approx 268$$

This can also be interpreted as the density of dark matter relative to the density of regular matter. Clearly, the Milky Way should be more affected because of the simple ratios at work.

But even this doesn't fully explain things. If dark-matter density was completely constant throughout the universe, and if we apply Newtonian mechanics to the problem, it won't affect the orbital period of anything because there is no net field contribution. This is where things get complicated. Most models for dark matter involve some form of "cold" distribution, meaning that they can be affected by multi-body gravitational tidal interactions... even if they don't practically interact any other way.

Thus, the way in which dark matter causes the adjustment to the galaxy rotation curve is somewhat complicated. However, the fact that there is most likely plenty of cold dark-matter out there makes this believable.

Within our solar system, the above ratio tells us that Earth's moon (7 x 10^22 kg) has a larger impact on the orbital period of Pluto than the presence of dark matter does. Our measurements aren't accurate enough to reliably measure this, but I wouldn't be surprised if some experimental tricks make a similar local dark matter discovery possible within the next century.

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Dark matter collects in larger quantities (thus a higher proportion relative to matter) in the centre of galaxies compared to in the centre of stellar systems such as the solar system. galaxies are not very dense, as stellar systems are sparsly spaced. So even though on a galactic scale the dark matter is in high ratios, on a stellar scale the ratio is smaller as stars are denser (by a very large amount) than galaxies.

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I thought dark matrer was concentrated in halos far from the center of galaxies. For example this reference: cds.cern.ch/record/320050/files/9702081.pdf?version=1 says that in the Milky Way dark matter is 5 times as dense in the halo. – DavePhD Apr 10 '14 at 19:14
Sorry i wasnt clear. I meant that galaxies are not very dense, as stellar systems are sparsly spaced. So even though on a galactic scale the dark matter is in high ratios, on a stellar scale the ratio is smaller as stars are denser (by a very large amount) than galaxies. – stanley dodds Apr 10 '14 at 19:31
@DavePhD "halo" is somewhat misleading here. The very commonly used Navarro-Frenk-White profile has its peak at the center, for example, but is still called a halo. In this case we aren't (necessarily) referring to a ring-like shape. – Robert Mastragostino Apr 11 '14 at 5:11
@RobertMastragostino That's an excellent point. I think I was misreading the reference in my comment, it is really referring to dark matter at a specific point being 5 times greater. But isn't there a "Cuspy Halo Problem" en.wikipedia.org/wiki/Cuspy_halo_problem ? Is the the NFW profile thought to be accurate in the center? – DavePhD Apr 11 '14 at 12:28

The standard model of cosmology has less dark matter than you are stating,

The content of the universe is thus:

The standard model of cosmology indicates that the total mass–energy of the universe contains 4.9% ordinary matter, 26.8% dark matter and 68.3% dark energy. Thus, dark matter constitutes 84.5% of total mass, while dark energy plus dark matter constitute 95.1% of total mass–energy content

Thus dark matter is five times the luminous matter only. Dark energy is a different story and is in the mathematics of the expansion of the universe.

Estimated distribution of matter and energy in the universe

Dark mass has been postulated to fit the rotation curves of galaxies.

Rotation curve of a typical spiral galaxy: predicted (A) and observed (B). Dark matter can explain the 'flat' appearance of the velocity curve out to a large radius

A galaxy rotation curve is a plot of the orbital velocities (i.e., the speeds) of visible stars or gas in that galaxy versus their radial distance from that galaxy's center. The rotational/orbital speeds of galaxies/stars does not decline with distance, unlike other orbital systems such as stars/planets and planets/moons that also have most of their mass at the centre. In the latter cases, this reflects the mass distributions within those systems. The mass observations for galaxies based on the light that they emit are far too low to explain the velocity observations.

So the dark mass is hypothesized to exist at large distances of the center of the galaxy, so that the observed stars are embedded within a mass distribution much higher than the visible masses extrapolated from the luminocities. So it is a diffuse "gas" with mass that has no electromagnetic or strong interaction to leave an observable signal in optical telescopes.

The dark matter hypothesis supplies the missing mass, resolving the anomaly.

The planets moon, and stars are very dense in localized space and any dark matter of our galaxy will be too diffuse locally, as the other answers state, to affect measurably the orbits.

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Planck: 13.82 Gyr; 68.3% dark energy, 26.8% dark matter, 4.9% baryonic matter. http://arxiv.org/abs/1306.5534 There is no dark matter in the solar system. Dark matter inside Saturn's orbit is less than 1.7×10^(-10) M_solar. Dark matter is repeatedly reparatmeterized curve-fitting with no empirical composition. Dark matter phenomenology is wholly explained, with zero wiggle room, arXiv:1310.4009, 0906.0668, 1209.3086

Ssaying that dark matter presence is very low within the solar system as an anomaly, versus 5.47 times baryonic matter by the book, is unforgivable curve fitting. Given 100 parameters, anything can be "naturally" modeled,

MSSM is the standard model plus 120 new parameters - and it models empirically nothing.

MoND's Milgorm acceleration is sourced by correcting the defective founding postulate that births parity violations, symmetry breakings, chiral anomalies, Chern-Simons repair of Einstein-Hilbert action when masselss boson photon vacuum symmetries are assumed to be true for fermionic matter (quarks, hadrons). The bad part is that vacuum mirror symmetry violation toward matter, a trace chiral vacuum background selective toward matter (killing SUSY), is testable in existing bench top apparatus at room temperature usiing commercial materials within 90 days. Said test arises from chemistry not physics, so it is too ridiculous to perform. Th neutrino see-saw mechanism is Officially true. Go figure.

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I find this post extremely hard to read. Complete sentences would be helpful! – David Richerby Apr 10 '14 at 21:13
Milgrom's theory (AKA MoND) cannot account for anything cosmological because it is inherently non-relativistic. Therefore, it cannot state anything about large scale structure (modeled very well by DM) or the CMB (which actually constrains DM & DE). It is a poor theory that has no evidence backing it over Dark Matter theories. – Kyle Kanos Apr 11 '14 at 0:21
@KyleKanos even though I would hate to think I personnaly support MOND at this stage, there are relativistic versions of MOND e.g. arxiv.org/pdf/1403.5963v1.pdf – chris Apr 11 '14 at 16:22
@chris: Oddly, the paper you link invokes dark matter to "work." – Kyle Kanos Apr 11 '14 at 16:27
@KyleKanos well, most astronomers agree that DM works. The question is what is it? – chris Apr 11 '14 at 19:25

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