Double Star System: Analyzing Masses and Orbital Periods
How can we determine the mass of stars in a double star system?
By analyzing the periods of revolution and relative orbital speeds of the two stars in the system.
What does it imply if one star has a longer period of revolution compared to another star in a double star system?
It implies that the star with the longer period has a greater mass.
Answer:
In a double star system, the mass of a star can be determined by analyzing the periods of revolution and relative orbital speeds of the two stars. If one star has a longer period of revolution compared to the other star, the former star has a greater mass.
Explanation:
In a double star system where two stars of masses m1 and m2 are rotating about a common center of mass in radii r1 and r2, with periods t1 and t2, we can determine their relative orbits and masses using Kepler's third law and the law of gravitation.
The period of revolution of the stars around the center of mass is related to their masses and the semimajor axes of their orbits. If one star has a longer period of revolution (Ta) compared to the other star (Tb), it implies that the star with period Ta has a greater mass (Ma) than the star with period Tb (Mb).
The relationship between the period of revolution and the distance from the center of mass can be derived from Kepler's third law equation, D³ = (M₁ + M₂)P². Therefore, by analyzing the periods and orbital characteristics, we can determine the masses of the stars in a double star system.