Mass of sun derivation
Answers
Answer:
The solar mass (M☉) is a standard unit of mass in astronomy, equal to approximately 2×1030 kg. 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 (denoted by the solar symbol ⊙︎). This equates to about two nonillion (short scale) or two quintillion (long scale) kilograms:
M☉ = (1.98847±0.00007)×1030 kg[1][2]
The above mass is about 332946 times the mass of Earth (M⊕), or 1047 times the mass of Jupiter (MJ).
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 (G), the mass of the Sun is given by:
{\displaystyle M_{\odot }={\frac {4\pi ^{2}\times (1\,\mathrm {AU} )^{3}}{G\times (1\,\mathrm {yr} )^{2}}}}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.
Explanation:
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To actually compute the mass of the Sun, we need to know how far the Earth is from the Sun and how fast it is moving around the Sun. The value for G, the universal constant of gravitation, is 6.67 x 10-11 N m2 kg -2 (where N is Newtons).