Dark matter density is 6x10-22 kg/m3, radius of Earth's orbit 1011 m, therefore amount of dark matter within Earths radius is, (4/3) x π x 1033 x 6 x 10-22=2.53 x 1012 kg. This is much smaller than the mass of the Sun which is 2 x 1030 kg. Thus we cannot feel the gravitational effect of dark matter compared to Sun's gravitational pull.

ref: http://cdms.berkeley.edu/Education/DMpages/FAQ/question36.html

Now let us come to the rotation velocity of sun around the milky way. There are a number of methods for tracing rotation curves.

Rotation curve also depends slightly on the tracer. Using high resolution CO and HI line spectroscopy, one sees a very steep rise till R=300pc with pick velocity 250 km/sec which reduces to 200 km/sec at R=3000pc, followed by a second peak at R=6000pc and a flat part beyond the solar circle. As flatness is due to the presence of dark matter one thinks that most of the dark matter is beyond the solar circle, having R=8000pc. However the amount of dark matter which exists within the solar circle makes the rotation velocity of sun around the center more than what we would expect it to be in the absence of dark matter within solar circle.

ref: Rotation curves of spiral galaxies, Y. Sofue and V. Rubin, https://arxiv.org/pdf/astro-ph/0010594.pdf

I'm not an astronomer, but this question has been bothering me for several years. Why is there darker matter everywhere, except in the solar system?

Is it the anthropic principle working again?

Dark matter density is 6x10-22 kg/m3, radius of Earth's orbit 1011 m, therefore amount of dark matter within Earths radius is, (4/3) x π x 1033 x 6 x 10-22=2.53 x 1012 kg. This is much smaller than the mass of the Sun which is 2 x 1030 kg. Thus we cannot feel the gravitational effect of dark matter compared to Sun's gravitational pull.

ref: http://cdms.berkeley.edu/Education/DMpages/FAQ/question36.html

Now let us come to the rotation velocity of sun around the milky way. There are a number of methods for tracing rotation curves.

Rotation curve also depends slightly on the tracer. Using high resolution CO and HI line spectroscopy, one sees a very steep rise till R=300pc with pick velocity 250 km/sec which reduces to 200 km/sec at R=3000pc, followed by a second peak at R=6000pc and a flat part beyond the solar circle. As flatness is due to the presence of dark matter one thinks that most of the dark matter is beyond the solar circle, having R=8000pc. However the amount of dark matter which exists within the solar circle makes the rotation velocity of sun around the center more than what we would expect it to be in the absence of dark matter within solar circle.

ref: Rotation curves of spiral galaxies, Y. Sofue and V. Rubin, https://arxiv.org/pdf/astro-ph/0010594.pdf

Remember that the orbital speed of the Sun is determined by the total mass inside its orbit.

Most of the dark matter associated with the Milky Way is outside the Sun's orbit.

Nevertheless, the amount of dark matter inside the Sun's orbit is still substantial, and does affect the Sun's orbital speed considerably, resulting in a somewhat faster orbital speed than would otherwise be the case.

Thanks for your answers. In that case the graph by Wikipedia might not be correct. For sure all data come with some uncertainty but the same graph tries to tell us that at some regions of Milky way, within the Sun’s orbit, speeds of the stars are much less than they should be. How is this explainable? Either this graph is completely wrong or there are more puzzles to investigate in the universe.

Are these different data accessible?

To my point of view, the presence of dark matter (or required Newton's law modification) in the solar system is underestimated. Known publications assessing the presence of DM in the solar system do not take into account

a) the possible contribution of DM to Shapiro's delay in radar measurements of the orbits of planets and spacecraft.

b) The need to recalculate the masses of celestial bodies, based on the alleged presence of DM.

The orbital speed of the Sun is more or less what is expected for objects at our distance from the center of the galaxy. It is primarily in regions further from the center of the galaxy than the Sun that orbital speeds are higher than expected from the gravitational effects of visible stars alone. Whether those higher speeds are due to dark matter or something else is a matter of debate, but there is no doubt that the speeds are higher than was expected before they could be accurately measured. (Incidentally, it was very recently announced that as could have been expected, most of the 'missing mass' of ordinary matter in our galaxy has now been identified as ordinary interstellar gas scattered around the outer fringes of the galaxy that just required better ways of looking for it than had been previously available.)

Btw, though not part of the original question, the answer that wonders why there is no dark matter in the Solar System is misinformed. If dark matter exists in the form that most cosmologists would like to believe in -- namely, something that is spread throughout all the space where it lies in the form of nearly infinitely tiny, infinitesimally individually massive objects -- then there simply wouldn't be enough of it in the Solar System to make its presence of any significance. But there is a very large amount of otherwise apparently empty space between the Sun and any other star (and in most cases, between any star and any other star), and even if the amount of infinitesimally massive particles in any given part of space is very small, with such large amounts of space, the total mass can be very large. In fact, if dark matter does consist of such far spread, teensy particles, any prediction of the amount in a region as small as the Solar System would be very close to zero. So it isn't that there isn't any dark matter in our Solar System, but a heck of a lot elsewhere; it's just a question of whether a nearly infinite number of infinitesimally small particles is the correct answer. (For a brief but hopefully clear historical discussion of why cosmologists have focused on that concept, see http://cseligman.com/text/galaxies/dark.htm (Dark Matter In Galaxies).)

Biswajoy Brahmachari and Courtney Seligman . Thank you for your answer.

Dear all

The question is about contrasting/confusing data. As our interpretation and analysis of dark matter are solely based on these types of data then one need to know which one is correct. The fact that at least two sets of dissimilar data exists for Milky way does not raise confidence. For example, the one shown in Wikipedia suggests there might not be any dark matter in the region of the galaxy near our solar system. In that case, looking for it within solar system is pointless and a costly mistake.

In these papers dated 2013, an estimate of the upper limit of the DM density in the solar system and references to early works are given: Article Relativistic effects and dark matter in the Solar system fro...

Article Constraints on Dark Matter in the Solar System

However, mostly thinking of the possible gravity law modification, I believe the constraints are underestmated.

Here are some more works regarding DM estimates in Milky Way.

Dynamical constraints on the dark matter distribution in the Milky Way

https://arxiv.org/abs/1504.06324

Joint constraints on the Galactic dark matter halo and Galactic Centre from hypervelocity stars

https://arxiv.org/abs/1608.02000

Constraints on dark matter in the Milky Way and the Local Group. Matthias Steinmetz (Postdam)

http://online.kitp.ucsb.edu/online/cdm-c18/steinmetz/

Ziaedin

Dark matter within our solar system cannot affect the Sun's orbital speed.

If you are looking for dark matter within our solar system, then you probably need to look for WIMPS.

The other type of dark matter (MACHOS) are unlikely to be found within our solar system.

And as mentioned above by biswajoy, the amount of DM within our solar system, will in any case be tiny.

Thanks Robert,

I meant all the underground facilities in which scientists are looking for DM.

Dear Thierry.

Sorry to bother you. Or you are making some mistake, or you are presenting something so revolutionary, that no one has glimpsed before.

If you are right, why everyone has done wrong calculations in the last 50 years? Now I am not capable of it, but I remembered when I studied physics I have done simple calculations regarding the effect of the objects' shape to their gravity field. And I was just a student of Chemical Engineering! Taking this, any Physics graduate should be able to derive: i) the same as you got or ii) the mainstream idea that dark matter is needed.

So, what's happening?

I am not capable of it, But I have a general idea. Let's define the Galaxy with with a function rho(xyz), in which rho means "normal mass" per volume. knowning this, put several known stars (the most the computer can handle) in the most variate positions and their real velocities. All these data are already known, so no guess is required. Then simulate the system for several million years and see if the Galaxy remains as a whole or it is completely shredded. YOU can do it! Or it was this that you have done? Nevertheless, I am still asking. Which is the change you've made for getting a different result?

Now I am disagreeing with you. Do you think using computers is a thing for the ignorant? Let me tell you: Nothing useful from the last century has been made analytically. The systems have become too complex for it. That is your error.

Dear Thierry

Please do not get angry and disrespectful. RG is a platform to learn from each other.

To start with, we first need to know the problem. The problem is that data for speed of stars in various galaxies and speed of galaxies in cluster of galaxies do not agree with our predictions.

we know that no solution is yet found. There are a lot of theories but they do not answer all the challenges DM has created.

Apparently accurate data is needed and experimental physicists are eagerly waiting for the completion of the Large Synoptic Survey Telescope.

My question is also about the data as I was amazed when saw the graph in Wikipedia. It not only shows higher speed in some regions but also shows lower speed in other regions. Do you know if this data is correct or where it is coming from? Unfortunately, I do not have access to all the sources mentioned in the Wiki article for the graph.

The graph at Wikipedia contains three certain references. However, DM is a very broad topic. For ex., one may find some recent talks, names of researchers and references here: http://homer2.kitp.ucsb.edu/cgi-bin/rcarini/search.py?title_words=dark+matter&speaker=&field=%25&min_scope=0&since_year=2005&inst=

ZS: Are these different data accessible?

That depends on the source, if it's an illustration from a book, it will probably be subject to copyright but textbook plots are usually based on or taken from real studies. Put "milky way rotation curve" then select "images" and see what you get. Look only at the ones with error bars, those will be real rather than illustrative. Compare a few and you'll see they vary widely, often depending on the technology used. Hydrogen alpha measures free gas while optical methods measure stars so there are real differences. Similarly the estimated curves without DM depend on the assumptions the author makes.

What is common to both your graphs is that the curve without DM must fall whereas real measurements have much higher velocities at large radii.

Dear Thierry

In your short article R0 is not defined.

It is claimed that "n and k are linear function which go through zero ..." , and then it is claimed Vr2=constant. The latter claim is only true if n/k is constant and n=k if both claims are true which is confirmed in your example as you further claim k=n for the milky way. Why do you think they can be the same?

The data being referred to involve different types of matter. Near the center of the Galaxy is a large central massive object as evidenced lby the rotation of stars around Sgr. A*.measuring in the thousands of km/s (4000-6000). The rotation of several chemicals show the rotation curve declining to near zero (

Dear Thierry

One cannot decide on the amount of observed mass in the bulge and different sections of the disk by pure analytical approach. You need to find out n and k with data from every galaxy. Then show your predictions are correct.

Dear Thierry

In your article it is claimed that the mass of spherical galaxy has been condensed into a disk one. Do you have any reason/evidence for this claim?