# How is Dark Matter Needed?

• I
The bulge of the milky way is 40 parsecs in radius.
There is 288.218 stars per cubic light-year in the milky way bulge.
At the density, spacetime for the entire 40 parsec radius should be severely distorted.
The total stellar mass of the bulge is about 25 billion Solar masses.
The Milky Way has an approximate radius of 50 000 light years

F = (6.67 x 10^-11)(25 x 10^9)(1,989E30) (1,989E30) / [ (50,000)(9.4605284 × 10^15) ]^2
F = (6.5968 X 10^60) / (2.2375 x 10^41)
F = 2.94829 x 10^19 Newtons

Let's calculate the gravitational attraction between Ceres (dwarf planet) and Sun

F = 6.67 x 10^-11)(1,989E30)(8,958 x 10^20) / (414 x 10^9)^2
F = (1.884 x 10^41) / 1.7139 x 10^23)
F = 1.099 x 10 ^ 18 Newtons

We can see that the gravitational force exerted by the distorted space the bulge of the milky way provides sufficient force hold onto solar mass objects at the edge of the milky way disk.

I ask again, why is Dark Matter needed?
The closer you are to the Sun, the greater the depression in spacetime.
But if you have a 40 parsec radius spacetime depression relative to disk and arms...
A depression in spacetime is a depression in spacetime period.
There is no need for dark matter.
Imagine two people pulling a blanket, and a third person putting a small bowling ball in the middle.
How can you say, the bulge or bowling ball does not curve the spacetime around it? It does.
The blanket is the milky way, and the bowling ball is the bulge.

Nugatory
Mentor
We can see that the gravitational force exerted by the distorted space the bulge of the milky way provides sufficient force hold onto solar mass objects at the edge of the milky way disk.
But is that force sufficient to explain the observed rotation rate? For all the galaxies that we can observe? It's not enough to calculate the force (I haven't checked your calculations, but we can assume for the moment that they're correct) between the core of a galaxy and the rim and say that it is looks to be enough to hold an object in orbit around the core. You also have to show that the force Implies an orbital velocity consistent with what we observe; and when we do that we find that there's not enough visible matter to produce the necessary force.

There are many other observed phenomena that cannot be explained by the gravitational attraction of all the matter that we can see; you'll find a partial list in the Wikipedia article on dark matter.

Chronos
Gold Member
The people who assembled WMAP data and this paper https://arxiv.org/abs/1703.09233,Mapping dark matter on the celestial sphere with weak gravitational lensing, would be very surprised and disappointed to discover that DM is not needed. It really strains credibility to even suggest these prominent scientists have managed to overlook these and similarly naive objections to DM.

Staff Emeritus
2021 Award
There is 288.218 stars per cubic light-year in the milky way bulge.

You know this number to six decimal places? Really?

If I were going to kick off a thread arguing that everybody else is wrong, I wouldn't start it this way.

"So the team used this data to determine the mass of our galaxy. What they found was that within a radius of 60,000 light years the mass is about 210 billion solar masses. It should be emphasized that this is only the mass of our galaxy within a 120,000 light year diameter, which is about the diameter of the visible galaxy. Beyond this region our galaxy is dominated by dark matter, which makes up most of the total mass of our galaxy. So we can say that the Milky Way has roughly 200 billion stars."

I did the math and the velocity works to be 221542 m/s which is consistent with observed data. In other words, if we define the milky way to be 120, 000 light years in diameter and the mass of the galaxy is 210 billion solar masses, then the milky way does not violate Newton's law of gravitation. In other words, there sufficient stellar matter not only to hold onto Stars in the galaxy, but also to explain the mean velocity of stars at the edge of the disk. The way it has ever been described to me at any corner of the web is, "there is insufficient stellar matter to explain galactic star retention and orbital speed of stars in the disk". This statement appears incredibly incorrect in lieu of Newton's gravity laws and Einstein's general relativity (spacetime).

However, I what about the orbital velocities of clusters which the milky way holds onto outside of the disk, right? I am having difficulty finding a good dataset for this. Please provide so that I can continue my analysis.

PeterDonis
Mentor
I did the math and the velocity works to be 221542 m/s which is consistent with observed data.

The velocity of what? Consistent with what observed data?

Note that if you're calculating the velocity of the solar system around the galactic center, the solar system is within the radius that your quote explicitly says is not dominated by dark matter, so you would not expect the solar system's velocity calculated on the basis of visible matter to be different from observation. You would have to find an object significantly further out from the center than 60,000 light years, which the solar system is not (it's only about 30,000 light years from the center).

what about the orbital velocities of clusters which the milky way holds onto outside of the disk, right? I am having difficulty finding a good dataset for this. Please provide so that I can continue my analysis.

In other words, you don't even have the data you need to back up the extreme claims you are making. And rather than go get it yourself, you want us to provide it? Sorry, it doesn't work that way.