Final answer:
The observed brightness of a star will dim by the square of the planet's diameter relative to the star's diameter during a transit. For a planet with 3% the diameter, the dimming effect results in a brightness decrease of 0.09%, so the closest option is (a) 3%.
Step-by-step explanation:
If a transiting planet has 3% the diameter of its parent star, the observed brightness of the star will dim by the square of the planet's diameter compared to the star's diameter during the transit. Since the area of a circle is given by πr² (where r is the radius), we calculate the area of the planet's disk in relation to the star's disk to determine the dimming effect.
The diameter is directly related to radius by a factor of 2 (D = 2r), so a planet with a diameter 3% that of its star means its radius is also 3% of the star's radius. The area ratio (and thus the dimming percentage) is the square of the radius ratio, meaning (0.03)² = 0.0009 or 0.09%. Therefore, the correct choice is (a) 3%, based on the mathematical relation of areas, not the actual percentage, which would be 0.09%.