This occurs through two processes in nearly equal amounts. The mass of the Sun has been decreasing since the time it formed. By the time the Sun becomes a degenerate white dwarf, it will have lost 46% of its starting mass. This will rise to 10 −6 M ☉/year on the asymptotic giant branch, before peaking at a rate of 10 −5 to 10 −4 M ☉/year as the Sun generates a planetary nebula. The mass loss rate will increase when the Sun enters the red giant stage, climbing to (7–9) ×10 −14 M ☉/year when it reaches the tip of the red-giant branch. It is expelling about (2–3) ×10 −14 M ☉/year. The Sun is losing mass because of fusion reactions occurring within its core, leading to the emission of electromagnetic energy, neutrinos and by the ejection of matter with the solar wind. As a result, the solar mass is used as the standard mass in the astronomical system of units. The value of G times the mass of an object, called the standard gravitational parameter, is known for the Sun and several planets to a much higher accuracy than G alone. The value of G is difficult to measure and is only known with limited accuracy ( see Cavendish experiment). ![]() Based on 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 solving Kepler's third law: M ⊙ = 4 π 2 × ( 1 A U ) 3 G × ( 1 y r ) 2 The mass of the Sun cannot be measured directly, and is instead calculated from other measurable factors, using the equation for the orbital period of a small body orbiting a central mass. 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. Īs a unit of measurement, the solar mass came into use before the AU and the gravitational constant were precisely measured. The current value for the solar parallax is smaller still, yielding an estimated mass ratio of 1⁄ 332 946. He corrected his estimated ratio to 1⁄ 169 282 in the third edition of the Principia. 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. In his work Principia (1687), he estimated that the ratio of the mass of Earth to the Sun was about 1⁄ 28 700. The first known estimate of the solar mass was by Isaac Newton. From the value of the diurnal parallax, one can determine the distance to the Sun from the geometry of Earth. The diurnal parallax of the Sun was accurately measured during the transits of Venus in 17, yielding a value of 9″ (9 arcseconds, compared to the present value of 8.794 148″). ![]() The value he obtained differs by only 1% from the modern value, but wasn't as precise. ![]() The value of the gravitational constant was first derived from measurements that were made by Henry Cavendish in 1798 with a torsion balance.
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