Solution set, homework 1
Chapter 1 (page 35): Review 1 (5 pts)
Chapter 2 (page 59,69): Review 9 (5pts), Problem 10 (5pts)
Chapter 3 (page 83): Review 11 (5pts)
Due: Tuesday, Feb 10
Chapter 1, Review 1: What do we mean by geocentric universe? In broad terms, contrast a geocentric universe with our modern view of the universe.
In a geocentric universe, the Earth is at the center, everything else revolves around the Earth. In this picture, we have so called spheres for the planets, the Sun and an outermost sphere for the stars, at a certain distance from Earth. The Earth is in the center of all those spheres. In our modern view, we live in a heliocentric cosmology. The Earth is just one planet among 8 others, they all revolve around the Sun. The Sun is part of the Milky Way galaxy, orbiting its center, and all the stars are grouped in galaxies, in very different distances from the Milky Way in the universe.
Chapter 2, Review 9: Describe the Moon’s cycle of phases and explain why we see phases of the Moon.
The lunar cycle contains the New Moon, the Waxing Crescent, the 1st Quarter Moon, the Waxing Gibbous, the Full Moon, the Waning Gibbous, the 3rd Quarter Moon, and the Waning Crescent. Half of the Moon is always lit up by the Sun, but as the Moon goes around Earth, our viewing angle changes, and we see different combinations of the lit and the dark parts of the Moon. So we see the different phases over the course of approximately one month, the time of one lunar orbit around the Earth.
Chapter 2, Problem 10: Your view: a) Find your latitude and longitude, and state the source of your information. b) Describe the altitude and direction in your sky at which the north or south celestial pole appears. c) Is Polaris a circumpolar star in your sky? Explain. d) Describe the path of the meridian in your sky. e) Describe the path of the celestial equator in your sky.
a) Latitude: 39°00’50” N, longitude: 76°55’18” W for College Park
Source of information: http://www.rei.com/stores/collegepark/
b) In the northern hemisphere, we don’t see the south celestial pole. The north
celestial pole is visible due North, at an altitude of 39°, which is equal to our latitude.
c) Polaris, or the North Star, is a circumpolar star in our sky. It is very close to
the north celestial pole, circling it so closely, that it never sets below the
d) The meridian is a half-circle, coming from the horizon due South, through the
Zenith, the highest point in our sky, to the horizon due North.
e) The celestial equator is a half-circle stretching from the horizon due East,
going through its highest point at an altitude of 51° to the horizon due West. Its altitude is equal to 90°minus our latitude, because the celestial poles and the celestial equator are separated by a 90° angle.
Chapter 3, Review 11: Was Copernicus the first person to suggest a Sun-centered solar system? What advantages did his model have over the Ptolemaic model? In what ways did it fail to improve on the Ptolemaic model?
The first person to suggest a heliocentric cosmology was Aristarchus about 260 B.C.
Advantages of Copernicus’ model: 1) Sun – centered which is more aesthetic
through explaining retrograde motion as result of lapping (more natural
than epicycles), and explaining the orbits of Mercury and Venus as
orbits of planets interior to Earth’s orbit around the sun (more natural
than keeping orbits aligned)
2) predicts mathematical relationship between true orbital period of a
planet and time between successive appearances of planet at position
opposite the Sun in sky
3) allows to find distances between Sun and planets in terms of Earth’s
distance from Sun by geometrical methods
4) predicts parallax and full range of phases for Mercury and Venus –
both of those are observed later
Failures: 1) assumes perfectly circular orbits – still needs epicycles to account for
difference of orbits, which are ellipses in reality
2) did not predict planetary positions more accurately than Ptolemaic