Final answer:
When an extrasolar planet blocks 1% of its host star's light, it suggests that its radius is 10% of the star's radius, because the transit depth measures the ratio of areas, which is proportional to the square of the ratio of the radii.
Step-by-step explanation:
When a transiting extrasolar planet is observed to block 1% of its host star's light, we are discussing a comparison of the areas of two circles, one of the planet and one of the star. Since the area of a circle is proportional to the square of its radius, if the planet blocks 1% of the star's light, the ratio of their areas is 1%. This means that the ratio of their radii squared is equal to 1% (0.01), which can be expressed as:
(Radius of planet / Radius of star)² = 0.01
To find the ratio of the radii, we take the square root of both sides, giving us:
Radius of planet / Radius of star = √0.01 = 0.1
Therefore, the radius of the planet is 10% of the radius of the star, so the correct answer is:
D) The planet's radius is 10% of the host star's radius.