Solar mass

Comparison of several stars with the Sun (gray point to the left). The orbit of Jupiter (red) and Neptune (blue) can be observed.

The solar mass (M_☉), is a unit of measurement used in astronomy and astrophysics to comparatively measure the mass of stars and other very massive astronomical objects such as galaxies, is equivalent to an approximate value of 2 x 10³⁰ kg. It is equivalent to 332,946 times the mass of the Earth (M_🜨) and 1,048 times the mass of Jupiter (M_J). Specifically M_☉ = (1.98847 ± 0.00007) × 10³⁰ kg.

Because the Earth has an elliptical orbit around the Sun, the solar mass can be calculated from the equation for the orbital period of a central mass body. The orbital period T{displaystyle T} That's it.

T=2π π a3μ μ {displaystyle T=2pi {sqrt {frac {a^{3}}{mu }}}}}},

where:

• a{displaystyle a} It's the major semieje of the orbit.
• μ μ =GM{displaystyle mu =GM}is the standard gravitational parameter, G{displaystyle G} is the gravitational constant and M{displaystyle M} is the mass of the most massive object.

Considering the length of the year, the distance from the Earth to the Sun and the gravitational constant (G), the mass of the Sun is given by

MΔ Δ =4π π 2× × (1UA)3G× × (1a)2{displaystyle M_{odot }={frac {4pi ^{2}times (1,mathrm {UA})^{3}{Gtimes (1mathrm {a})^{2}}}}}}.

The value of G times the mass of an object, called the standard gravitational parameter, is known on the Sun and various planets with much greater precision than just the value of G alone. Therefore, the solar mass is used as the standard mass in the astronomical system of units.

History

The value of the gravitational constant was derived from measurements made by Henry Cavendish in 1798 with a torsion spring. The value he obtained differs by 1% from the present value. The diurnal parallax of the Sun was accurately measured during the transits of Venus in 1761 and 1769, gave a value of 9 arcseconds, compared to the current 1976 value of 8,794148. The scientist Isaac Newton was the first to estimate the mass of the Sun. In his Philosophiæ Naturalis Principia Mathematica he made an estimate that he corrected to a more accurate value in the third edition of his work.

The original mass of the Sun at the time it reached the main sequence remains unknown. The early Sun had much higher rates of mass loss than today, it is estimated that it lost between 1 and 7% of its natal mass in its lifetime.

Until recently, neither the AU nor the gravitational constant were known with precision. However, the 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 determined constants. So it was useful to express these masses in units of solar masses (see the Gaussian gravitational constant). Today, AU has been measured extremely precisely using interplanetary radar techniques and G is well measured, but solar mass remains one of the esoteric historical conventions of astronomy.^{[citation needed ]}