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. Based upon 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:
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.
The value of the gravitational constant was first derived from measurements that were made by Henry Cavendish in 1798 with a torsion balance. The value he obtained differs by only 1% from the modern value. The diurnal parallax of the Sun was accurately measured during the transits of Venus in 1761 and 1769, yielding a value of (9 9″arcseconds, compared to the present 1976 value of 148″). From the value of the diurnal parallax, one can determine the distance to the Sun from the geometry of Earth. 8.794
The first person to estimate the mass of the Sun was Isaac Newton. In his work Principia (1687), he estimated that the ratio of the mass of Earth to the Sun was about 1/28 700. 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 (1 AU). He corrected his estimated ratio to 1/169 282 in the third edition of the Principia. The current value for the solar parallax is smaller still, yielding an estimated mass ratio of 1/332 946.