So it's essentially two radii.

Bigger objects have bigger Schwarzschild radii.

Smaller objects have smaller Schwarzschild radii.

Some galaxies have both. A different radii.

larger radii or larger luminosities have shallower profiles.

So the shape of the surface brightness profile changes at smaller radii.

Typical mean separation cluster radii between galaxies are of the order of a few megaparsecs.

You can see as you go to ever larger radii, the Axis seemed to rotate.

They're giant ellipticals, but unlike other giant ellipticals, they have an extra fuzzy envelope at large radii.

As you can see, at smaller radii, visible material dominates, something we already learned from kinematical studies.

But thus you go to larger radii, stellar density decreases, the relative importance of the dark matter rises.

With galaxies we're talking about Einstein ring radii of the order of an arc second. Observations with the

Dark matter halos are fluffier and dominate more at large radii. This is certainly true in elliptical galaxies as well.

This is the silk that's used to make the frame and radii of an orb web, and also the safety trailing dragline.

And a different parallel, synthetically at large radii, and there is some transition radius between them where one bends into the other.

Most of the astrophysical objects in galaxies or clusters are vastly larger than their Schwarzschild radii, so the effect isn't quite as strong.

We think that's because the dragline silk, which is used to make the frame and radii for a web, needs to be very strong.

And so, people who study this have come up with a broken power law or nuker profile, that has one parallels synthetically smaller radii.

If you turn the contrast up in some of the elliptical galaxies, you'll see these shell like structures of the radii and now we think we know where they come from.

The frame and radii of this web is made up of one type of silk, while the capture spiral is a composite of two different silks the filament and the sticky droplet.

And carrying on with what happens at larger radii, you see that more luminous ellipticals tend to be those that have flat cores and small ellipticals tends to be those with cusps.

And the answer is that the inner visible parts of the elliptical galaxies, visible material dominates the gravitational potential, but as you go to ever larger radii, the contribution of the dark matter does increase.

A more interesting correlation is between mass of the black hole and the velocity dispersion of its host galaxy measured at large radii, where the influence, dynamic of influence of black hole is completely negligible.

So the diameter is made of these two radiuses (or radii as I should call it I think that's the plural for radius) and so the length of a diameter is going to be twice the length of a radius.

The van der Waals radius of an atom is the radius of an imaginary hard sphere which can be used to model the atom for many purposes. Van der Waals radii are determined from measurements of atomic spacing between pairs of unbonded atoms in crystals.

If you go all the way around a circle, you have gone 2 pi radians which is really just you say you've gone 2 pi radii, whatever the radius of the circle is and that's where actually the definition of the radian comes from

But before Descartes is generally viewed. that geometry was euclidean geometry. and that's essentially the geometry that you studied in geometry class in 8th or 9th or 10th grade. in a traditional high school curriculum. and that's the geometry of studying the relationships between triangles, and their angles. and the relationships between circles. and you have radii and then you have triangles inscribed in circles and all the rest and we'll go into some depth in that in the geometry playlist.