## How is galaxy mass calculated using luminosity

This seems like it would be fairly complex as any material that is not in the suns would absorb photons and convert part of that energy over to kenetic energy giving a false value for actual luminosity from the stars themselves.

Galaxies appear to be very different from one another, is it simply assumed that most galaxies have similar material properties to make the numbers easier to calculate for?

And finally what is the formula for doing calculations of luminosity vs galaxy mass?

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 Mentor You need some way to calibrate the scales. This can be done with theoretical models, or with observations of nearby galaxies (where it is possible to measure the mass via radial velocities of the stars). Depending on the required accuracy, the formula could be quite complicated.

 Quote by mfb You need some way to calibrate the scales. This can be done with theoretical models, or with observations of nearby galaxies (where it is possible to measure the mass via radial velocities of the stars). Depending on the required accuracy, the formula could be quite complicated.
Aren't the radial velocities way off from newtonian/relativistic mechanics and calculated based on a theoretical model about dark matter? I see MOND can be an excellent predictor of star velocites for very specific types of galaxies but it appears to be just a mathematical trick so it really isn't a good explanation for the higher velocities that we see.

What would be an example of a basic formula used to calculate mass without going for significant accuracy?

## How is galaxy mass calculated using luminosity

Luminous mass I believe is measured experimentally through star count, and is a fairly rough estimate. It's only real purpose is to get the order of magnitude right, which is clearly an order of magnitude less than the total mass, so it is an estimate just accurate enough to tell us that there is a lot of mass somewhere else.

Calculating the mass of the galaxy can be done using a solar systems radial velocity:

say a solar system is orbiting the center of a galaxy with radius d. The orbit is circular, but if you draw a sphere around the center of the galaxy, again with radius d so that the solar system is rotating along the edge of the sphere, then the mass contained within the volume of this sphere is :

P = orbital period
G = grav. constant

Kepler's Law: d^3/P^2 = GM/(4*pi^2)

mass in sphere: M = 4*pi^2*d^3/(GP^2) = d*v^2/G

Most of the mass, especially the "dark mass" will be located within a solar systems orbit, so this is a sufficient approximation.

 Mentor @mesa: You said "mass", radial velocity measures the total mass (inside). The number of MOND postdictions looks similar to the number of free parameters to me, so I'm not really convinced that there is anything into it. Apart from that, it has some issues with the bullet cluster and similar objects.
 @Gibby_Canes You stated: Most of the mass, especially the "dark mass" will be located within a solar systems orbit, so this is a sufficient approximation. I'm just a bystander, but I think your post was correct until that statement. If one is trying to determine the galaxy's total mass, as you point out your method only calculated the mass within the radius d. Mass outside that radius will not be included in the estimate. As I understand, to compensate Keplerian rotation curves to produce those observed, the vast majority of galacti mass (dark matter) must be located outside the periphery of the visible galaxy. Please see http://www.eso.org/public/images/eso1217b/.