Homework Set 2 -- Solutions
DUE: Tuesday, June 11
NOTE: There was mistake in the first problem on the paper copies handed out on Friday. The problem should refer to a star near the SOUTH celestial pole, not the north celestial pole. It is corrected here.
Please use a separate piece of paper for your answers
1) Suppose you are standing in the Southern hemisphere, facing south at night. Describe, as a consequence of the Earth's rotation, the apparent direction of motion of each of the following:
a) A star just above the south celestial pole
b) A star just below the south celestial pole
c) A star to the left of the south celestial pole
d) A star on the southern horizon
a) right
b) left
c) up
d) left
2) If a given star, say, Sirius, rises at 6 pm one night, when will it be rising 3 months from now?
Stars rise in the East 4 minutes earlier every day. So in 90 days, Sirius will be rising 90 x 4 = 360 minutes earlier. Therefore it will be rising at noon 3 months after being observed to rise at 6 pm.
3) Which planet has the shortest year?
Mercury
4) Assuming we have no data from Apollo, propose another theory for the origin of the Moon
One theory was that the Moon is a captured planetesimal.
Another was that a piece of the Earth broke off due to a rapidly spinning Earth. Still another is that they formed together as a double planet.
From the orbital evolution of the Moon, as well as compositional considerations, these theories can be ruled out. From Apollo, we know the Moon is similar in composition to the Earth's mantle, and is almost totally dry.
5) What causes the volcanoes in Hawaii? How are they different from volcanoes you find, say, in Japan? What makes them different?
Volcanoes in Hawaii are shield volcanoes. They are broad mountains with gentle slopes that are formed by a plume of hot mantle material impinging beneath the lithosphere. Magma works its way to the surface through cracks in the lithosphere. In Japan, the volcanoes are steep-sided, typical of volcanoes formed near subduction zones. Here, volcanoes are formed due to the heating and melting associated with the subduction of an oceanic plate beneath a continental one.
6) Draw an ellipse, and indicate the semimajor and semiminor axes. Draw in the center and both foci. If this is the orbit of the Earth, draw in the correct location of the Sun. Indicate the direction the Earth moves in its orbit, and the direction the Earth revolves on its axis.
An ellipse is an elongated circle, with half the long axis called the semimajor axis and half the short axis called the semiminor axis. The foci are labelled F1 and F2 in the diagram. The Sun is at one focus, and the Earth rotates in the counterclockwise direction as seen above the north pole. The Earth also spins in this direction on its own axis .
7) Draw a picture with the Moon in orbit around the Earth at 4 equally spaced locations along its orbit. Pick a direction that sunlight is coming from and draw it in with arrows. Show how the sunlight falls on each of the 4 Moons you've drawn, and label each of the 4 Moons with 'Full Moon', 'First Quarter', 'New Moon' and 'Last Quarter' Indicate which direction the Moon revolves in its orbit, and which direction both the Earth and Moon spin
The Moon revolves around the Earth in the counterclockwise direction as seen above the north pole. The phases result from how the moon gets illuminated by the Sun, and our perspective on Earth.
8) For June 7 through June 11, 1996, find out the exact rising and setting times of the Moon. Calculate exactly how long the moon is up. Is the moon staying up longer as the days progress, or staying up less long? Make a table with day, moonrise time, moonset time, duration in the sky, and phase. When is the next full moon, and what time of the day, approximately, will it rise and set? You can look in local newspapers.
Date Rise Set Duration Phase
June 7 11:11 am 11h 38 min
June 8 12:09 am 12:17 pm 12h 8 min 3rd quarter
June 9 12:43 am 1:21 pm 12h 38 min
June 10 1:17 am 2:24 pm 13h 7 min
June 11 1:51 am 3:26 pm 13h 35 min New Moon June 16
The Moon is staying up longer as the days progress. The next full Moon is on July 1, 1996. It will rise at 7:58 pm and set at 5:23 am.
7/1/96