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PHYS1650 - Nature of the Universe

Assignment 1

Due date: 5:00pm, October 3, 2023

Submit to Moodle.

Give answers and explanations for the following questions.

1. (10 marks) Give that the Earth-Sun distance is 1.5 × 108km and diam-eter of the Sun is 1.4 × 106km. Use the formula

angular size in radian = diameter of the Sun

                                   Earth-Sun distance            (1)

to find out the angular size of our Sun viewed from the Earth. Express your answer in two significant figures in degrees.

Given that the Earth-Moon distance is 3.8×105km and diameter of the Moon is 3500 km. Find out the angular size of the Moon and compare it to that of the Sun.

2. (20 marks) (a) What is the rotating direction of the Earth if we look down from the north pole? (b) If both the rotation of the Earth and the revolution about the Sun changed to the opposite directions, how would the ecliptic change, if any? (c) Would the Sun rise from the west or from the east? Explain. (Note that we do not change the definition of directions, which means, Lantau island is still west of Hong Kong island.)

3. (20 marks) What is the angle between the southern horizon and the Sun at noon on the day of summer solstice in Hong Kong? (Hint: The figures in lecture notes are not accurate enough.)

4. (10 marks) For Hong Kong (latitude 22.5 ◦N) and Beijing (latitude 40◦N), in which city can we see more circumpolar stars? What are the inclination angles of Polaris above the horizon in the two cities?

5. (10 marks) Astrononmy news reported that the Comet Nature is pass-ing nearby Earth. John and Mary decided to observe it on Christmas Eve. The position of Comet Nature on that day is (R.A. = 5h30m, dec. = −68◦ ). Which of the following place is best choice for the ob-servation? Please Explain.

(a) City H: Lat. = +45◦ , Long. = 63◦E;

(b) City G: Lat. = +10◦ , Long. = 71◦W;

(c) City K: Lat. = −68◦ , Long. = 102◦E.

6. (10 marks) Andrew wants to take a photograph of a constellation that near the celestial equator by placing a camera on the ground pointing to this constellation. Because the stars are dim, he has to leave the shutter open to have a longer exposure time. Then, due to their motion on the sky, the stars will leave a trail on the films. Andrew finds that the images of the stars are still point-like if the stars just move for 15” , then what is the maximum time of exposure?

7. (20 marks) Let’s assume for simplicity that the orbital plane of Mars is the same as the orbital plane of Earth, and the angle between its rotational axis and revolution axis is 25◦ . For observers on Mars, is their north celestial pole same as ours? Does their apparent path of the Sun pass through the same constellations? (Same zodiac?) Hence, is their ecliptic same as ours? Can they observe retrograde motion of the Earth?