If the distance between us and a star is doubled, while everything else remains the same (including its luminosity), the brightness of the star will decrease to one-fourth its original value.

Here's why:

* Brightness and distance: The brightness of a star as seen from Earth is inversely proportional to the square of the distance. This means that if you double the distance, the brightness decreases by a factor of 2², or 4.

* Luminosity: Luminosity is the total amount of light energy emitted by a star per unit of time. This is an intrinsic property of the star and doesn't change with distance.

In simpler terms: Even though the star is still emitting the same amount of light (luminosity), the light is spread out over a much larger area when it reaches us at a doubled distance. This makes the star appear fainter.