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astronomybinarystarsmass ( ** )

Astronomy — The mass of binary stars

According to Newton’s laws of motion and gravitation, the total mass of two stars orbing each other is related to the average distance between them (a) and their orbital period (P).  If the masses are m1 and m2, then  (m1 + m2) = a³ / P² .  In this formula, we measure a in astronomical units, P in years, and mass in solar masses.  For example, if we observe a visual binary with a period of 32 years and an average separation of 16 AU, then  m1 + m2 = 16³ / P² = 4 solar masses.  Notice that this formula is related to Kepler’s third law of planetary motion.  Almost all of the mass in the solar system is in the sun.  If we apply this formula to any planet in our solar system,  the total mass is one solar mass.  Then the formula become P² = a³, which is Kepler’s third law.

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