Thesolar mass (M☉) is a standardunit of mass inastronomy, equal to approximately2×1030kg (2 nonillion kilograms in US short scale). It is approximately equal to the mass of theSun. It is often used to indicate the masses of otherstars, as well asstellar clusters,nebulae,galaxies andblack holes. More precisely, the mass of the Sun is
nominal solar massM☉ =1.988416×1030 kg or a best estimate ofM☉ =(1.988475±0.000092)×1030 kg.[2]
The value of the gravitational constant was first derived from measurements that were made byHenry Cavendish in 1798 with atorsion balance.[3] The value he obtained differs by only 1% from the modern value, but was not as precise.[4] Thediurnal parallax of the Sun was accurately measured during the transits of Venus in 1761 and 1769,[5] yielding a value of9″ (9 arcseconds, compared to the present value of8.794148″). From the value of the diurnal parallax, one can determine the distance to the Sun from the geometry of Earth.[6][7]
The first known estimate of the solar mass was byIsaac Newton.[8] In his workPrincipia (1687), he estimated that the ratio of the mass of Earth to the Sun was about1⁄28700. 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 to1⁄169282 in the third edition of thePrincipia. The current value for the solar parallax is smaller still, yielding an estimated mass ratio of1⁄332946.[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 theSolar System or the combined mass of twobinary 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.
The mass of the Sun cannot be measured directly, and is instead calculated from other measurable factors, using the equation for theorbital period of a small body orbiting a central mass.[10] Based on the length of the year, the distance from Earth to the Sun (anastronomical unit or AU), and thegravitational constant (G), the mass of the Sun is given by solvingKepler's third law:[11][12]
The value ofG is difficult to measure and is only known with limited accuracy (seeCavendish experiment). The value ofG times the mass of an object, called thestandard gravitational parameter, is known for the Sun and several planets to a much higher accuracy thanG alone.[13] As a result, the solar mass is used as the standard mass in theastronomical system of units.
The Sun is losing mass because offusion reactions occurring within its core, leading to the emission ofelectromagnetic energy, neutrinos and by the ejection of matter with thesolar wind. It is expelling about(2–3)×10−14M☉/year.[14] The mass loss rate will increase when the Sun enters thered giant stage, climbing to(7–9)×10−14M☉/year when it reaches thetip of the red-giant branch. This will rise to 10−6M☉/year on theasymptotic giant branch, before peaking at a rate of 10−5 to 10−4M☉/year as the Sun generates aplanetary nebula. By the time the Sun becomes a degeneratewhite dwarf, it will have lost 46% of its starting mass.[15]
The mass of the Sun has been decreasing since the time it formed. This occurs through two processes in nearly equal amounts. First, in theSun's core, hydrogen is converted into helium throughnuclear fusion, in particular thep–p chain, and this reaction converts some mass into energy in the form ofgamma ray photons. Most of this energy eventuallyradiates away from the Sun. Second, high-energy protons and electrons in the atmosphere of the Sun are ejected directly into outer space as thesolar wind andcoronal mass ejections.[16]
The original mass of the Sun at the time it reached themain sequence remains uncertain.[17] 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.[18]
^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.ISBN978-3-540-63198-9.
^Genova, Antonio; Mazarico, Erwan; Goossens, Sander; Lemoine, Frank G.; Neumann, Gregory A.; Smith, David E.; Zuber, Maria T. (18 January 2018)."Solar system expansion and strong equivalence principle as seen by the NASA MESSENGER mission".Nature Communications.9 (1): 289.Bibcode:2018NatCo...9..289G.doi:10.1038/s41467-017-02558-1.ISSN2041-1723.PMC5773540.PMID29348613.The fusion cycle that generates energy into the Sun relies on the conversion of hydrogen into helium, which is responsible for a solar mass reduction with a rate of ~ −0.67 × 10−13 per year. On the other hand, the solar wind contribution is more uncertain. The solar cycle significantly influences the solar mass loss rate due to solar wind. Estimates of the mass carried away with the solar wind showed rates between − (2–3) × 10−14M☉ per year, whereas numerical simulations of coupled corona and solar wind models provided rates between − (4.2–6.9) × 10−14M☉ per year.
