Solar mass

Size and mass of very large stars: Smallest example, The Pistol Star (340 R☉) is also the most massive (150 M☉). Others are Rho Cassiopeiae (450 R☉/40 M☉), Betelgeuse (1000 R☉/ 20 M☉), and VY Canis Majoris (2100 R☉/30-40 M☉). (The Sun (1 R☉/1 M☉) which is barely visible in this thumbnail is included to illustrate the scale of example stars)

The solar mass (M_⊙), 1.98892×10³⁰ kg, is a standard way to express mass in astronomy, used to describe the masses of other stars and galaxies. It is equal to the mass of the Sun, about two nonillion kilograms or about 332,950 times the mass of the Earth or 1,048 times the mass of Jupiter.

$M_{\odot }=1.98892\times 10^{30}{\hbox{ kg}}$

The solar mass can be determined from the length of the year, the distance of the Earth to the Sun (the astronomical unit) (AU), and the gravitational constant (G) as

$M_{\odot }={\frac {4\pi ^{2}\times (1{\rm {AU}})^{3}}{G\times (1{\rm {year}})^{2}}}$.

Until recently, neither the AU nor the gravitational constant was precisely measured. However, a determination of the relative mass of another planet in the Solar System or of a binary star in units of solar masses does not depend on these poorly known constants. So it was useful to express these masses in units of solar masses (see Gaussian gravitational constant).

Solar mass and related units

One Solar mass can be converted to related units:

• 27068510 Lunar mass (M_L)
• 332946 Earth mass (M_⊕)
• 1047.56 Jupiter mass (M_J)

It is also occasionally useful in general relativity to express mass in units of length.

$M_{\odot }{\frac {G}{c^{2}}}\approx 1.48~\mathrm {km}$

See also

• Chandrasekhar limit
• Gaussian gravitational constant

• Orders of magnitude (mass)
• The Sun

References and further reading

• I.-J. Sackmann, A. I. Boothroyd (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. doi:10.1086/345408.