In this unit, you learned about the Hertzsprung-Russell diagram which is used to classify stars based on their temperature and luminosity. How would you classify stars based on their radii on that diagram (you can draw a picture if that is easier for you to articulate). Please explain your reasoning

Identify the location in the H-R diagram of the phases of stellar evolution. (For each statement select the proper symbol in the picture.) 1) red giant, helium flash2) white dwarf3) red giant with helium burning shell4) hydrogen fusion in shell around core5) helium fusion in core6) envelope ejected, planetary nebula7) main-sequence star8) helium used up, core collapses9) hydrogen used up, core collapses

The stars in a CCD image include stars in a cluster and stars in front of the cluster (i.e. starts that don't belong to it). One group has parallaxes clustered around of 3 milli-seconds of arc (or "3 mas"). The parallaxes of the other group range from 10 mas to 15 mas. Which group contains the stars in the cluster? Explain your answer.

The figure above shows a track on the H-R diagram corresponding to the evolution of a star like the one you’ve just considered. Six stages are numbered. Six stages of stellar evolution are listed below – for each stage, write the number corresponding to its position on the diagram (four of these stages are the same stages you considered in the first part of this tutorial). Horizontal branch: Asymptotic giant branch: White dwarf: Main sequence: Planetary nebula: Red giant branch: What is the approximate mass of this star, in solar masses? Explain how you can tell.

(Answer don't copy with hand written please)As a star runs out of hydrogen to fuel nuclear fusion in its core, changes within the star usually cause it to leave the main sequence, expanding and cooling as it does so. Would a star with a radius 12 times that of the Sun, but a surface temperature 0.5 times that of the Sun, be more, or less luminous than the Sun? Show and explain your reasoning. You may assume the surface area of a sphere is A = 4πr2.

I am uncertain of how to calculate luminosity. My biggest problem is determining by how much.  This question that I attached is asking about the luminosities, could you show me how I would work this out. Also, explain how to determine if star A is more luminous how to find out by how much more luminous than star B it would be.