Final answer:
The Keck telescope gathers 16 times more light than the Mount Wilson telescope, determined by squaring their diameters, with the Keck's 10-meter diameter versus Mount Wilson's 2.5-meter diameter.
Step-by-step explanation:
The amount of light gathered by a telescope is proportional to the area of its aperture (the opening through which light passes). Since the area of a circle (which represents the aperture of a circular telescope mirror) is calculated using the formula πd²/4, where d is the diameter, we can compare the light-gathering power of the Keck telescope and the Mount Wilson telescope by squaring their respective diameters.
The Keck telescope has a diameter of 10 meters, while the diameter Mount Wilson telescope is 2.5 meters. To find the factor by which the light-gathering ability of the Keck is greater, we square both diameters and compare: (10^2) / (2.5^2) = 100 / 6.25 = 16. Therefore, the Keck telescope gathers 16 times more light than the Mount Wilson telescope.