Question

1. predict: consider any relationships you see between a stars luminosity, radius, and mass.

a. as the radius of a star increases, how do you think its luminosity might change?
its luminosity will likely.
b. as the mass of a star increases, how do you think its luminosity might change?
its luminosity will likely.
c. as the radius of a star increases, how do you think its mass might change?
its mass will likely.

Explanation:

• For part A: Luminosity (\(L\)) of a star is related to its radius (\(R\)) by the Stefan - Boltzmann law \(L = 4\pi R^{2}\sigma T^{4}\) (where \(\sigma\) is the Stefan - Boltzmann constant and \(T\) is the surface temperature). If we assume the surface temperature \(T\) is constant (for a simple prediction), as \(R\) increases, \(R^{2}\) increases. So, \(L\) is directly proportional to \(R^{2}\) when \(T\) is constant.
• For part B: More massive stars have higher core temperatures and pressures. This leads to more intense nuclear fusion reactions. The mass - luminosity relation for main - sequence stars is approximately \(L\propto M^{3.5}\). So, as mass (\(M\)) increases, luminosity (\(L\)) increases.
• For part C: In general, for main - sequence stars, there is a relationship between radius and mass. More massive main - sequence stars are larger. Although the relationship is not as simple as a direct proportionality (it is more complex due to stellar structure equations), for a basic prediction, as mass increases, radius increases and vice - versa.

Answer:

A. increase
B. increase
C. increase