Question

the hubble space telescope has an aperture of 2.4 m and focuses visible light (400-700 nm ). the arecibo radio telescope in puerto rico is 305 m (1000 ft ) in diameter (it is built in a mountain valley) and focuses radio waves of wavelength 75 cm . part a under optimal viewing conditions, what is the smallest crater that each of these telescopes could resolve on our moon? express your answers in meters separated by a comma.

Answer 1

The smallest crater that the Hubble Space Telescope can resolve on the moon is approximately 96.3 meters, while the Arecibo Radio Telescope can resolve craters as small as 11.9 kilometers.

Step-by-step explanation:

To determine the smallest crater that the Hubble Space Telescope and the Arecibo Radio Telescope can resolve, we need to use the formula for angular resolution. Angular resolution is given by the formula θ = 1.22 * λ / D, where λ is the wavelength of light and D is the diameter of the telescope's aperture.

For the Hubble Telescope, λ = 400-700 nm = 4-7 * 10^-7 m and D = 2.4 m.

Plugging these values into the formula, we find

θ = 2.51 * 10^-7 rad.

To determine the size of the smallest crater, we can use the formula s = θ * d, where s is the size of the crater and d is the distance to the moon.

Taking d = 3.84 * 10^8 m, we find

s = 9.63 * 10^1 m.

For the Arecibo Telescope, λ = 75 cm = 7.5 * 10^-1 m and D = 305 m.

Plugging these values into the formula, we find

θ = 3.11 * 10^-2 rad.

Using the same formula as before with

d = 3.84 * 10^8 m, we find

s = 1.19 * 10^7 m.