Solar mass

The solar mass (M☉) is a standard unit of mass in astronomy, equal to approximately 2×1030 kg. It is approximately equal to the mass of the Sun. It is often used to indicate the masses of other stars, as well as stellar clusters, nebulae, galaxies and black holes. This equates to about two nonillion (short scale), two quintillion (long scale) kilograms, 2000 quettagrams, or 2 quettakilograms:
M☉ = (1.98847±0.00007)×1030 kg
The solar mass is about 333000 times the mass of Earth (MEarth), or 1047 times the mass of Jupiter (MJ).
== History of measurement ==
The value of the gravitational constant was first derived from measurements that were made by Henry Cavendish in 1798 with a torsion balance. The value he obtained differs by only 1% from the modern value, but was not as precise. The diurnal parallax of the Sun was accurately measured during the transits of Venus in 1761 and 1769, yielding a value of 9″ (9 arcseconds, compared to the present value of 8.794148″). From the value of the diurnal parallax, one can determine the distance to the Sun from the geometry of Earth.
The first known estimate of the solar mass was by Isaac Newton. In his work Principia (1687), he estimated that the ratio of the mass of Earth to the Sun was about 1⁄28700. Later he determined that his value was based upon a faulty value for the solar parallax, which he had used to estimate the distance to the Sun. He corrected his estimated ratio to 1⁄169282 in the third edition of the Principia. The current value for the solar parallax is smaller still, yielding an estimated mass ratio of 1⁄332946.
As a unit of measurement, the solar mass came into use before the AU and the gravitational constant were precisely measured. This is because the relative mass of another planet in the Solar System or the combined mass of two binary stars can be calculated in units of Solar mass directly from the orbital radius and orbital period of the planet or stars using Kepler's third law.
== Calculation ==
The mass of the Sun cannot be measured directly, and is instead calculated from other measurable factors, using the equation for the orbital period of a small body orbiting a central mass. Based on the length of the year, the distance from Earth to the Sun (an astronomical unit or AU), and the gravitational constant (G), the mass of the Sun is given by solving Kepler's third law:
{\displaystyle M_{\odot }={\frac {4\pi ^{2}\times (1\,\mathrm {AU} )^{3}}{G\times (1\,\mathrm {yr} )^{2}}}}