# Solar mass

The solar mass (M) is a standard unit of mass in astronomy, equal to approximately 2×1030 kg. It is used to indicate the masses of other stars, as well as clusters, nebulae, and galaxies. It is equal to the mass of the Sun (denoted by the solar symbol ⊙︎). This equates to about two nonillion (short scale) or two quintillion (long scale) kilograms:

M = (1.98847±0.00007)×1030 kg[1][2]

The above mass is about 332946 times the mass of Earth (M), or 1047 times the mass of Jupiter (MJ).

Because Earth follows an elliptical orbit around the Sun, the solar mass can be computed from the equation for the orbital period of a small body orbiting a central mass.[3] Based upon 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:

${\displaystyle M_{\odot }={\frac {4\pi ^{2}\times (1\,\mathrm {AU} )^{3}}{G\times (1\,\mathrm {yr} )^{2}}}}$

The value of G is difficult to measure and is only known with limited accuracy in SI units (see Cavendish experiment). The value of G times the mass of an object, called the standard gravitational parameter, is known for the Sun and several planets to much higher accuracy than G alone. As a result, the solar mass is used as the standard mass in the astronomical system of units.

## History

The value of the gravitational constant was first derived from measurements that were made by Henry Cavendish in 1798 with a torsion balance.[4] The value he obtained differs by only 1% from the modern value.[5] The diurnal parallax of the Sun was accurately measured during the transits of Venus in 1761 and 1769,[6] yielding a value of 9″ (9 arcseconds, compared to the present 1976 value of 8.794148). From the value of the diurnal parallax, one can determine the distance to the Sun from the geometry of Earth.[7]

The first person to estimate the mass of the Sun was Isaac Newton.[8] In his work Principia (1687), he estimated that the ratio of the mass of Earth to the Sun was about 1/28 700. 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 (1 AU). He corrected his estimated ratio to 1/169 282 in the third edition of the Principia. The current value for the solar parallax is smaller still, yielding an estimated mass ratio of 1/332 946.[9]

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, provided that orbital radius is measured in astronomical units and orbital period is measured in years.

The mass of the Sun has been decreasing since the time it formed. This occurs through two processes in nearly equal amounts. First, in the Sun's core, hydrogen is converted into helium through nuclear fusion, in particular the p–p chain, and this reaction converts some mass into energy in the form of gamma ray photons. Most of this energy eventually radiates away from the Sun. Second, high-energy protons and electrons in the atmosphere of the Sun are ejected directly into outer space as the solar wind and coronal mass ejections.

The original mass of the Sun at the time it reached the main sequence remains uncertain. The early Sun had much higher mass-loss rates than at present, and it may have lost anywhere from 1–7% of its natal mass over the course of its main-sequence lifetime.[10] The Sun gains a very small amount of mass through the impact of asteroids and comets. However, as the Sun already contains 99.86% of the Solar System's total mass, these impacts cannot offset the mass lost by radiation and ejection.

One solar mass, M, can be converted to related units:

It is also frequently useful in general relativity to express mass in units of length or time.

The solar mass parameter (G·M), as listed by the IAU Division I Working Group, has the following estimates:[11]

• 1.32712442099×1020 m3s−2 (TCG-compatible)
• 1.32712440041×1020 m3s−2 (TDB-compatible)

## References

1. "Astronomical Constants" (PDF). The Astronomical Almanac. 2014. p. 2. Retrieved 10 April 2019.
2. "Newtonian constant of gravitation". Physical Measurement Laboratory. Retrieved 10 April 2019.
3. Harwit, Martin (1998), Astrophysical concepts, Astronomy and Astrophysics Library (3rd ed.), Springer, pp. 72, 75, ISBN 978-0-387-94943-7
4. Clarion, Geoffrey R. "Universal Gravitational Constant" (PDF). University of Tennessee Physics. PASCO. p. 13. Retrieved 11 April 2019.
5. Holton, Gerald James; Brush, Stephen G. (2001). Physics, the human adventure: from Copernicus to Einstein and beyond (3rd ed.). Rutgers University Press. p. 137. ISBN 978-0-8135-2908-0.
6. Pecker, Jean Claude; Kaufman, Susan (2001). Understanding the heavens: thirty centuries of astronomical ideas from ancient thinking to modern cosmology. Springer. p. 291. Bibcode:2001uhtc.book.....P. ISBN 978-3-540-63198-9.
7. Barbieri, Cesare (2007). Fundamentals of astronomy. CRC Press. pp. 132–140. ISBN 978-0-7503-0886-1.
8. Cohen, I. Bernard (May 1998). "Newton's Determination of the Masses and Densities of the Sun, Jupiter, Saturn, and the Earth". Archive for History of Exact Sciences. 53 (1): 83–95. doi:10.1007/s004070050022. JSTOR 41134054.
9. Leverington, David (2003). Babylon to Voyager and beyond: a history of planetary astronomy. Cambridge University Press. p. 126. ISBN 978-0-521-80840-8.
10. Sackmann, I.-Juliana; Boothroyd, Arnold I. (February 2003), "Our Sun. V. A Bright Young Sun Consistent with Helioseismology and Warm Temperatures on Ancient Earth and Mars", The Astrophysical Journal, 583 (2): 1024–1039, arXiv:astro-ph/0210128, Bibcode:2003ApJ...583.1024S, doi:10.1086/345408
11. "Astronomical Constants : Current Best Estimates (CBEs)". Numerical Standards for Fundamental Astronomy. IAU Division I Working Group. 2012. Retrieved 2018-06-28.