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Rho Cassiopeiae Sol VY Canis Majoris

Size and mass of very large stars, from right to left: VY Canis Majoris (17 ± 8 M), Betelgeuse (11.6 ± 5.0 M), Rho Cassiopeiae (14-30 M), and the blue Pistol Star (27.5 M). The concentric ovals indicate the size of Neptune's (blue), Jupiter's (red) and the Earth's (grey) orbits. Properly scaled, the Sun (1 M) only appears as a tiny dot in the center of the ovals (click for higher resolution to see Earth orbit and Sun).

The solar mass (M) is a standard unit of mass in astronomy, equal to approximately Template:Val. 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, about two nonillion (two quintillion in the long scale) kilograms:

Template:Math[1][2]

The above mass is about Template:Val times the mass of Earth (Template:Earth mass), or Template:Val times the mass of Jupiter (Template:Jupiter mass).

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 (Template:Math), the mass of the Sun is given by:

$ 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.

References

  1. 2014 Astronomical Constants http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf
  2. NIST CODATA http://physics.nist.gov/cgi-bin/cuu/Value?bg
  3. Cite error: Invalid <ref> tag; no text was provided for refs named harwit1998