In 1933, Fritz Zwicky was studying several galaxies in the Coma Cluster. It's a star cluster of more than 1,000 galaxies about 330 million light-years away. Zwicky found that the galaxies in this cluster were moving so fast that they didn't have enough mass to hold the cluster together. Measuring some parameters of the universe is still tricky today, let alone in 1933, so how did Zwicky do it?
First, we have to measure the distance with some kind of standard candle. A standard candle is a star of predictable brightness, such as a Cepheid variable or a Type 1a supernova. If we know their actual brightness, we can compare it to their apparent brightness. Because light obeys the inverse square law, we can get distance from the ratio of actual brightness to apparent brightness.
Next, we're going to use the HR diagram, which can tell us almost everything about a star. If we knew the star's actual brightness and color, this map would tell us its radius, the stage of its life it's in, and ultimately it's mass. All Zwicky needed was the overall brightness of a galaxy, so he could estimate the masses of the stars within it.
Measuring velocity is a bit difficult, these objects are far away from us, so we can't actually see these things moving. To figure out velocity, we need to measure something called the Doppler redshift. When an object moves closer or farther away from us, the frequency/wavelength of the light it emits changes. But we can't see the color change with the naked eye, we have to shift the light across the spectrum and look for shifts in the spectral lines.
So Zwicky got mass, and velocity, and applied the laws of gravity to see what happens. However, there are many galaxies in the Coma Cluster, and it is quite difficult to solve the many-body problem. So, Zwicky used the viability theorem, which relates the time-averaged kinetic and potential energies in a system. From the measured galactic velocities and the effective radius of the cluster, we can calculate how much mass is needed. As a result, the measured mass is much smaller than the theoretical one.
Zwicky reasoned that there must be invisible dark matter out there. However, the dark matter it refers to is not the same as the dark matter now though. The dark matter Zwicky was referring to is a matter that doesn't emit or reflect enough light to be invisible from Earth. Under this definition, many ordinary things are also dark matter, such as huge clouds of cold diffuse gas. Zwicky argues that stars account for only a small fraction of the mass of the universe, with most of the rest being gas clouds.
In 1951, Harold Ewen and Edward Purcell discovered the 21 cm hydrogen line, which allows us to find all the cold hydrogen between stars and galaxies. Even though the hydrogen is cold and in a diffuse gas cloud, it still emits this 21-centimeter light. That means we can measure their mass, but that still isn't enough to explain Zwicky's mass problems.
Then in 1962, we used space probes to discover the first source of X-rays outside our solar system. Earth's atmosphere absorbs a lot of X-rays from space, so our X-ray detectors have to be in space to see it. X-ray astronomy opened up a whole new way of looking at the universe when we saw something new: hot hydrogen. But sadly, it's still not enough to explain the quality issues.
The dark matter problem didn't make headway until the early 1970s when Vera Rubin was using a spectrometer built by Kent Ford to study galaxy rotation. She mapped the distribution of hydrogen in several galaxies, but when she studied the rotation rates of these hydrogens, she noticed something strange. Based on her maps of the hydrogen distribution, she predicts a drop in the orbital velocity of stars near the outer edges of galaxies. But the observational data show something different, the outer edge velocity does not decrease but tends to be flat.
So she asked herself a question: What if galaxies had more mass than we can see? Yes, that sounds familiar, and she's talking about dark matter, which is the same argument Fritz Zwicky made in the 1930s, but Vera Rubin made it with the right amount of data, making the dark matter a science for the first time.
So let's take a look at the latest composition of matter. Active stars account for about 1.5% of the matter in the universe, planets, moons, asteroids, and comets about 0.005%, diffuse gas and dust clouds about 14.5%, and 84% unaccounted for. This is what we call dark matter.