# How do you measure the mass of a galaxy?

See hed. A Doper said it’s “really easy” (cite on request). For him, maybe.

Perhaps this reduces to “how do measure the mass” of star-type a, b, etc., and then figure out how many of them there are to make up a galaxy. But that leaves me no better off than before, with the additional question of how do they number the stars in the galaxy.

For the mass, my brilliant guess is measuring gravitational perturbations in other
systems, or the gravitational whirligigs that resulted in this current configuration, judging in the time scales of birth of all the other stars in the galaxy, identifiable by … other stuff … (color?)

How off am I, and anyway what’s the straight simple dope.

It’s derived from the orbital velocity of the stars, plus the distance of the stars from the center of the galaxy. For a given distance from the galactic center, more enclosed mass means a faster orbit.

Orbital velocity comes from the doppler shift of spectral lines in light from the stars. The distance of the stars from the galactic center are calculated from the distance of the galaxy from Earth, which derives from standard candles.

If you add up all the light from the galaxy, as you suggest, it implies a much smaller mass than the mass derived from orbital velocities. That’s the principal evidence for dark matter (there’s more to this, but that’s the basic idea).

Well, let’s step back.

How do we measure the mass of the Earth?

We can look at an object orbiting the Earth, measure the speed of the orbit and how high up it is, and then calculate how massive an object it would have to orbiting to have that exact orbit. It wouldn’t matter if the Earth was a black hole, or a neutron star, or a cloud of gas. If we know the orbits of objects orbiting the the Earth, then we can pretty precisely measure the mass of the Earth.

Same with the Sun. We know how long it takes the Earth (or Venus or Mars) to orbit the Sun, we know how far they are from the Sun, so from that we know the mass of the Sun.

And same with a galaxy. Except it’s harder to measure the orbital velocity of the Sun, and it’s distance from the center of the galaxy. But we have lots of stars out there, so we start measuring them and figuring it out.

This is much more accurate than trying to count how many stars there are and figuring out their mass. And of course when we do both, we find that it seems like the galaxy is a lot more massive than it would be if we counted all the stars and their masses and added it all up. And this is the famous “dark matter”. Mass that we know must be there because we measure the orbits of stars around the galaxy and they’re orbiting too fast if the galaxy was just made up of stars.

And we don’t think the missing mass is gas, or dust, or interstellar planets, because those things would block a lot more light from the stars than we observe. We know there is some dust and gas, because we can see it blocking some areas of space. But for it to make up dark matter there would need to be a lot more, and so we don’t think that gas or dust or rogue planets could me more than a small fraction of dark matter.

Just to expand on my last paragraph above re evidence for dark matter, where I oversimplified:

It’s not quite that we rely upon accurate knowledge of the total amount of mass that’s associated with a given total luminosity. It’s the distribution of luminosity vs mass. If we assume that all of the mass of a galaxy is distributed in the same way as the luminosity - i.e. heavily concentrated in the center - then the velocity of the orbiting stars should fall off in a certain predictable way as you get further from the center. In fact, the velocities do not follow this pattern, stars that are further out are moving faster than expected. This leads to the hypothesis of a dark matter halo, in which dark mass is distributed further out from the center.

That’s a lot more work than you actually need tomeasure the mass of the Earth (assuming you know its radius. Which, of course you do.). No orbiting necessary.

Fermi estimation.

The Cavendish experiment tells you the value of big G, which is admittedly the hardest part of the measurement. But to translate that into the mass of the Earth (or any other given object), you have to also know the acceleration it causes at some distance, and most methods of measuring that do require some sort of orbit.

Only if you consider “free fall in a vacuum” to be “some sort of orbit”. We had g measured long before we orbited anything.

“Free fall in vacuum” is pretty much the definition of an orbit.

Also, we had orbital measurements of the earth’s satellite long before we had g or G measured.

The simplest way is just a scale. No vacuum or orbit required. A 1 kg object weighs about 9.8 newtons. You can calibrate your scale by accelerating a known mass horizontally and measuring the force.

Slightly OT (though not by much), I have a recollection of reading somewhere that a person weighing 150 lbs on earth would only weigh just over twice that on the surface of Jupiter, because IIRC, although Jupiter is many times more massive than Earth, its much larger radius would negate the expected weight increase. Or something like that.

Actually, the simplest way to measure g is using a pendulum, which also doesn’t involve an orbit. But there are many other ways, and most of them do involve an orbit of some sort. Thinking back to the experiments my physics class did last semester, three of them involved measuring g in some way, and of those, one was a pendulum, one was an object dropped straight down, and one was an object launched on a parabolic trajectory.

Chronos,–if I may, on a personal note-- I always had this vague idea that you were not in academia.

Now that I think of it, however, where else do theoretical physicists go for a paycheck? (Just wondering, not asking for a personal answer…)

Nobody but physics pedants calls what a ball bearing dropped in an evacuated tube is doing an “orbit”

Irrelevant, as without G we have no way of using those measurements to do anything. Initially g was determined with Earth-based gravimeters (the aforementioned pendulums, scales and also inclined planes once the sin θ relationship was worked out), not orbital measurements.

The finance industry, for one.

(This is not a snarky response. It’s just an honest question.)

Does Jupiter even have a surface? I always thought it was a gas planet.

I think the traditional “surface” of things like jovian planets and stars is “the altitude at which they become opaque” – which is really a “zone” many kilometres thick, but compared to the radius of these objects it is a very tight bound.

One usually defines the “surface” of Jupiter to mean the height at which the clouds are opaque. In other words, what looks like the surface.

Leo Bloom, it depends on how you define “academia”. For most of the time I’ve been active on the boards, I was a grad student. Nowadays, I wear many hats, the largest of which recently has been teaching at a community college.