Artist's view of the Milky Way. ESA.
If you want to be sure of your quality, it's easy. Just step on the scale and see the number it gives you. This number tells you about the Earth's gravitational pull on you, so if you feel that this number is too high, rest assured that the Earth is just finding you more attractive than others. The same scale can also be used to measure the mass of the Earth. If you put a kilogram of mass on the scale, the weight it gives is also the weight of the Earth in the kilogram gravitational field. With a little mass, you have the mass of the earth.
It's not that simple. The Earth is not a perfectly spherical, completely homogeneous mass, so its gravitational pull is slightly different across the globe. But this method gives a reasonable approximation that we can use to estimate the mass of other objects in the solar system. But how do we determine the mass of a larger object, such as the Milky Way? One way is to estimate the number of stars in the Milky Way and their mass, then estimate the mass of all interstellar gas and dust, and then roughly calculate the amount of dark matter. It all gets very complicated.
A better approach would be to observe how the orbital velocity of the star changes with distance from the center of the Milky Way. This is called the rotation curve and gives the upper limit of the mass of the Milky Way, which appears to be about 600 billion to one trillion solar masses. The great uncertainty gives you an idea of how difficult it is to measure the mass of our Milky Way. However, a new study posted to the ARXIV preprint server introduces a new method that can help astronomers identify the problem.
The method looks at the escape velocities of stars in our galaxy. If a star moves fast enough, it can overcome the gravitational pull of the Milky Way and escape into interstellar space. The minimum velocity required to escape depends on the mass of our galaxy, so measuring one will give you the other. Unfortunately, only a few stars are known to be escaping, which is not enough to handle the galactic mass well. Therefore, the team studied the statistical distribution of stellar velocities measured by the Gaia spacecraft.
Estimated escape velocities for different galaxies' radii. Roche et al.
The method is similar to weighing the moon with a handful of dust. If you stand on the moon and throw dust upwards, the slower-moving dust particles will reach lower altitudes than the faster ones. If you measured the velocity and position of the dust particles, the statistical relationship between velocity and altitude will tell you how much the Moon is pulling on the dust and thus the mass of the Moon. It would be easier to take our kilograms and scales to measure the mass of the moon, but the dust method works.
In the Milky Way, stars are like dust specimens that hover in the gravitational field of the Milky Way. The team used the velocity and position of a billion stars to estimate the escape velocity at different distances from the center of the Milky Way. From this, they can determine the overall mass of the Milky Way. They calculated the mass of 640 billion suns.
This is the low end of early estimates, and if accurate, it means that the Milky Way has a little less dark matter than we thought.
More information: Cian Roche et al., Escape velocity profile of the Gaia DR3 Milky Way, Arxiv (2024). doi： 10.48550/arxiv.2402.00108