An astronomer sees two stars in the sky. both stars are equally far from earth, but the first star is dimmer than the second star. which of the following is a valid conclusion about the first star?

it is larger than the second star.
it is smaller than the second star.
it is older than the second star.
it is younger than the second star.

It is smaller than the second star

Explanation: The brightness of a star depends on two factors: The distance from the Earth and size of the star. More the distance from the Earth, the star appears dimmer. And bigger the star, brighter it is.

Where L is the luminosity,d is the distance

Luminosity depends on the surface area of star

Here, it is given that the two stars are at the same distance from the Earth. The first star is dimmer.  We can conclude from this that first star star must be smaller than the second star.

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.