# How was the speed of the Sun (around the Milky Way Galaxy) calculated?

The Sun travels around the Milky Way Galaxy with a speed of 220 km/s. The question is: where did this value come from? Is there any article about the calculation?

Reformulated question: What are the different approaches that can be used to estimate the speed of Sun (around the Milky Way Galaxy)?

• Did you tried Googling? en.m.wikipedia.org/wiki/Galactic_year Nov 17, 2021 at 3:30
• References (in Wikipedia, and others) does not take to calculations, only the value 220~230 km/s: starchild.gsfc.nasa.gov/docs/StarChild/questions/… scientificamerican.com/article/how-fast-is-the-earth-mov Nov 17, 2021 at 3:38
• So, "how is the galactic year calculated?" seems to be the more relevant question. Nov 17, 2021 at 17:22
• The article in Scientific American gives details of how was calculated the speed of Earth (and Solar System: 390 km/s), using Cosmic Microwave Background Radiation (CBR). For instance, I could find some ways to calculate the speed of Earth (rotation, and orbit around the Sun). But the speed of the Solar System (220 km/s) around the Milky Way is somewhat different. Was it calculated a hundred years ago, or is it a computer simulation solution? Nov 17, 2021 at 23:08
• The most accurate method uses observations to Sgr A*, the (radio source associated with the) supermassive black hole in the Galactic centre. From its proper motion and distance follows the Solar angular speed (which is 250km/s btw). The distance is obtained in various ways, for example by modelling the motion/orbits of the so-called S-stars orbiting Sgr A*. Nov 18, 2021 at 1:05

The rotation of our Milky Way in general is derived from observations of the kinematics of gas and stars throughout our galaxy. See for instance a recent compilation of Milky Way rotation curve data from which this figure is taken

The rotation curve of the Milky Way as derived from gas kinematics (blue), star kinematics (orange) and masers (black).

• What is the difference between the filled and unfilled points? The error bars are huge here, and most of the data points are not even visible by eye. How can one deduce the speed of the Sun from this plot, which is the actual question posed by the OP? Dec 4, 2021 at 9:54
• @DaddyKropotkin Yes, many of the error bars are very big, especially for the outer regions, and generally more so for data relating to stellar kinematics. As for the different symbols, see the explanations in the top image here ars.els-cdn.com/content/image/… Dec 4, 2021 at 11:34
• It would be best if you could explain the figure in your answer. How can one deduce the speed of the Sun from this plot, which is the actual question posed by the OP? As is, your answer does not explain the figure nor does it answer the OP's question. Dec 4, 2021 at 12:34
• @DaddyKropotkin The OP apparently assumed that the speed of the Sun can be calculated from a simple formula similar to Kepler's laws. This is not possible as the mass distribution within the galaxy is poorly known. In fact, if you accept the dark matter hypothesis, it is practically completely unknown. So on the contrary, measurements of the velocities in the galaxy are needed to derive the mass distribution. The figure shown gives results of such measurements. The link provided gives more details how these have been obtained. SE would not be the place to discuss this in detail. Dec 4, 2021 at 14:50
• The original paper listed does not provide evidence to estimate the speed of the Sun, rather it makes a "reasonable choice" of those parameters from the literature and uses those values in their models of galactic rotation (pg 56), though from what I can tell the value they use (230 km/s) isn't actually mentioned in the papers they cite. Those papers give 240, 246, 200-279, and 218 km/s Feb 23, 2023 at 22:26

It seems the 220~250 km/s value was calculated from "Oort Constants", originally published in 1927 (IAU 1964: $$R_0 = 10\ kpc, θ_0=250\ km\ s^{−1}, A = 15\ km\ s^{−1} kpc^{−1}, B = −10\ km\ s^{−1} kpc^{−1}⁠$$).

• And where did the Oort constants come from?! Dec 7, 2021 at 8:00
• I still don't know how Oort Constants are calculated, but I am learning: en.wikipedia.org/wiki/Oort_constants Dec 7, 2021 at 16:56
• The Oort constants are measured (or derived from measurements) and that offers one route to answering this question. Dec 7, 2021 at 17:40