Final answer:
Without additional information about the relative distances from the center of mass or velocities, it is impossible to determine the mass of Star B in a binary system. If such data were available, the mass of Star B could be calculated using the formula relating mass to the semi-major axis of the orbit and the orbital period.
Step-by-step explanation:
To determine the mass of Star B when Star A has a mass of 1 M (where M represents the mass of the Sun) and the center of mass is at position Y, we need to have more information about the system, specifically the distances of each star from the center of mass. In binary star systems like the Sirius binary system mentioned, the center of mass is a point where the masses of the system are balanced out.
Without the relative distances or the velocity of the stars around the center of mass, we can't calculate the exact mass of Star B. However, if we had these distances or velocities, we could use the equation M1 + M2 = (a³)/(P²), where a is the semi-major axis of the orbit and P is the orbital period, to solve for the remaining mass.
For example, if we knew that the center of mass was located at the position of Star A (implying that Star B's mass is much less), then Star B would have a mass significantly less than the Sun's mass (1 M). Conversely, if the center of mass was equidistant between Star A and Star B, both stars would have equal masses of 1 M.
The context given in the question, such as other scenarios involving binary star systems and the center of mass, implies understanding how gravitational forces and orbital mechanics dictate the motion of celestial bodies.