The correct answer to the question is option 4: size, temperature, and distance from the earth.

The brightness of a star is determined by several factors. The first factor is the size of the star. Stars that are larger tend to be brighter than smaller stars. This is because larger stars have a greater surface area, which allows them to radiate more energy.

The second factor is the temperature of the star. Hotter stars emit more energy and appear brighter, while cooler stars emit less energy and appear dimmer.

The third factor is the distance from the earth. As the distance between a star and the earth increases, the amount of light reaching the earth decreases. Therefore, stars that are closer to the earth appear brighter than those that are farther away.

So, to accurately determine the brightness of a star, we need to consider its size, temperature, and distance from the earth.