Answer: C. Binary star systems
Let’s see your options:
a) The <em>color of the star</em>: the color is not used in calculating the mass of a star, because it has no relation to it. Think about a red supergiant and a red dwarf: they have the same color, but they are completely different stars, with respectively a big and a small mass.
b) <em>Kepler’s laws</em>: these laws can be applied in what is called the “approximation of 1 body”, which means that is assumed that one body has a much bigger mass than the other and can be considered at rest. This is the case of a star-planet system and the mass that can be calculated is that of the planet.
c)<em> Binary star systems</em>: these are the only cases in which is possible the direct measure of the mass of the stars. Binary systems are classified as follows:
- Visual binaries: each star can be resolved and the motion around the center of mass can be measured.
- Astrometric binaries: only one star is visible, but the presence of the companion can be inferred by the movement of the first star around the system’s center of mass.
- Eclipse binaries: the two stars are not resolved (separated), but the luminosity varies periodically when one star eclipses the other.
- Spectroscopic binaries: the two stars are not resolved, but their spectrum reveals that they are a binary system.
In all these cases we have a “two-body problem” that can be solved by changing system of reference: the motion of bodies 1 and 2 is equivalent to the motion of a body of mass equal to the system’s reduced mass
moving in the potential generated by the total mass (M1 + M2) considered at rest. Hence, we can determine the masses of the two stars.
Let’s see your options:
a) The <em>color of the star</em>: the color is not used in calculating the mass of a star, because it has no relation to it. Think about a red supergiant and a red dwarf: they have the same color, but they are completely different stars, with respectively a big and a small mass.
b) <em>Kepler’s laws</em>: these laws can be applied in what is called the “approximation of 1 body”, which means that is assumed that one body has a much bigger mass than the other and can be considered at rest. This is the case of a star-planet system and the mass that can be calculated is that of the planet.
c)<em> Binary star systems</em>: these are the only cases in which is possible the direct measure of the mass of the stars. Binary systems are classified as follows:
- Visual binaries: each star can be resolved and the motion around the center of mass can be measured.
- Astrometric binaries: only one star is visible, but the presence of the companion can be inferred by the movement of the first star around the system’s center of mass.
- Eclipse binaries: the two stars are not resolved (separated), but the luminosity varies periodically when one star eclipses the other.
- Spectroscopic binaries: the two stars are not resolved, but their spectrum reveals that they are a binary system.
In all these cases we have a “two-body problem” that can be solved by changing system of reference: the motion of bodies 1 and 2 is equivalent to the motion of a body of mass equal to the system’s reduced mass