Question

(a) What is the angular size of the Moon as viewed from Earth's surface? See the inside back cover for necessary information. (b) The objective and eyepiece of a refracting telescope have focal lengths \(80 \mathrm{cm}\) and \(2.0 \mathrm{cm}\) respectively. What is the angular size of the Moon as viewed through this telescope?

Short answer

Answer: The angular size of the Moon as viewed from Earth's surface is approximately 0.517°. When viewed through the telescope, the angular size is approximately 20.7°.

Step-by-step solution

Part (a): Finding the Angular Size of the Moon from Earth's Surface

To find the angular size, we use the formula: Angular size = \(\frac{\text{Actual size}}{\text{Distance}}\) We are given the necessary information at the back cover, which is: - Distance from Earth to the Moon: 384,000 km (3.84 × \(10^8\) m) - Actual size (diameter) of the Moon: 3,475 km (3.475 × \(10^6\) m) Now, we can plug in the values to find the angular size: Angular size = \(\frac{3.475 × 10^6 \text{ m}}{3.84 × 10^8 \text{ m}}\) = 0.00904 rad We can convert radians to degrees, as people are more familiar with degrees: Angular size = 0.00904 rad × \(\frac{180^\circ}{\pi \text{ rad}}\) ≈ 0.517° The angular size of the Moon as viewed from Earth's surface is approximately 0.517°.

Part (b): Finding the Angular Size of the Moon Through a Telescope

To find the angular size of the Moon as viewed through the telescope, we first need to determine the magnification of the telescope. The magnification formula is: Magnification = \(\frac{\text{Focal length of the objective}}{\text{Focal length of the eyepiece}}\) We are given the focal lengths: - Objective: 80 cm (0.8 m) - Eyepiece: 2.0 cm (0.02 m) Now, we find the magnification: Magnification = \(\frac{0.8 \text{ m}}{0.02 \text{ m}}\) = 40 The telescope magnifies the image of the Moon 40 times. Therefore, the angular size of the Moon as viewed through the telescope is 40 times larger. Angular size through the telescope = 40 × Angular size from Earth's surface Angular size through telescope = 40 × 0.517° ≈ 20.7° The angular size of the Moon as viewed through this telescope is approximately 20.7°.