Question

A double star system consists of two stars A and B which have time periods TA and TB, radius RA and RB and the mass MA and MB respectively. Then

A If TA>T′B then RA>RB
B If TA>T′B then MA>MB
C (TA/TB)²=(RA/RB)³
D TA=TB

Answer 1

The student's question relates to a binary star system and the relationships between the stars' periods, radii, and masses. Using Kepler's third law, we can infer that the square of the ratio of the periods is equal to the cube of the ratio of the radii of the orbits. The question does not provide enough information to conclusively determine the other comparisons between the stars' properties. however option c is correct.

Step-by-step explanation:

The question pertains to binary star systems and the relationships between the orbital periods, radii, and masses of the two stars in such a system. According to Kepler's third law, reformulated by Newton for objects in mutual revolution, there is a specific mathematical relationship between the square of the period (P) of orbit and the cube of the semi-major axis (D), which is proportional to the sum of the masses (M1 + M2) of the binary stars.

If we assume circular orbits for simplicity, we can derive the following conclusions:

• If TA > TB, then it does not necessarily mean RA > RB or MA > MB without additional information on the relationship between their orbits.
• The correct option that can be inferred based purely on Kepler's law is that (TA/TB)² = (RA/RB)³, assuming that the orbital radii are similar to the semi-major axis lengths of their orbits.

It's also important to note that in a binary system where both stars orbit their common center of mass, the star with a higher mass will be closer to the center of mass, while the star with the lower mass will be farther from it.