ASTR 1010 – Homework Assignment 3 – Spring 2009

 

Chapter 3

1)   Question 5 – A lunar calendar has 12 months, some with 29 days and some with 30 days (recall that the period for the phases to cycle is 29.5 days).  The problem with this approach is that these calendars end up with a yearly total of 354 or 355 days, while the year has 365 or 366 days in it.  So, with a lunar calendar, the months cycle through the seasons as the years go by.  The Muslim calendar follows the lunar cycle which is why the Muslim holidays cycle over the seasons.                                                                                            The Metonic cycle is the smallest period of time that has nearly an integral number of months and years in it (19 solar years are almost exactly 235 months).  If each of these 19 years contains 12 months, that would be 228 total months.  To get to 235, you would have to have 7 of the 19 years made up of 13 months instead of 12 (228 + 7 = 235).  Thus, lunar calendars that follow the Metonic cycle have 7 out of each 19 years with 13 months while the remaining 12 years have 12 months.  This keeps the calendar in sync with the seasons and the holidays in a Metonic-based calendar (like the Jewish calendar) do not cycle over the seasons.

 

 

2)   Question 6 – A model in science is a conceptual representation of nature whose purpose is to explain and predict observed phenomena.

 

3)   Question 8 – The Ptolemaic model is a geocentric model of the Solar System that uses epicycles (smaller circles orbiting on the main orbital circle or sphere for each planet) to explain retrograde motion.

 

4)   Question 9 – The Copernican Revolution was the shift in the 15th and 16th centuries from a geocentric to a heliocentric model of the Universe.  This is a fundamental change in the geometric relation between the bodies in the Solar System.  When coupled with the advances in understanding why planets move made by Galileo and Newton, this revolution culminates in a renewed confidence by western scientists in understanding and controlling nature.

 

5)   Question 10 – CopernicusŐ insistence on using circular orbits for the planets forced him to use epicycles to make the planets move at different velocities during their orbital motion.  Thus, his system was nearly as complex as that of Ptolemy.

 

6)   Question 11 – An ellipse is a geometric figure of oval shape that is symmetric about its major and minor axes.  There are two foci along the major axis equidistant from the origin.  The line segment from one focus to a point on the ellipse to the other focus has the same length for all points on the ellipse.  Almost all bound orbits are elliptical (the ones that arenŐt elliptical are circular).

 

7)   Question 12 – KeplerŐs First Law: planets move around the Sun in elliptical orbits with the Sun at one focus.  This allows the planets to sometimes be nearer and sometimes be farther from the Sun.          KeplerŐs Second Law: Equal areas of an orbit are swept out by the orbital motion of a planet in equal periods of time.   This means that planets change speed during this orbital motion going faster when near the Sun.         KeplerŐs Third Law:                          p2 = a3 Planets near the Sun go around it more quickly than planets farther away.

 

8)   Question 13 – A tentative explanation for a natural phenomenon is a hypothesis.   A theory is a powerful yet simple model that makes predictions about nature that have survived repeated and varied testing.

 

9)   Question 16 – The basic idea behind astrology is that the stars and planets control fate and can reveal the characteristics of a person or even future events.  This belief can be understood when the heavens seemed to be impossible for man to understand.  Now that we have understood that the same physical processes that work on Earth work Ňin the heavensÓ, it is more difficult to ascribe mystical powers to the objects there.  In recent times, whenever astrology has been tested rigorously, it has failed the tests.  See http://skeptico.blogs.com/skeptico/2005/02/what_do_you_mea.html                     for more details.

 

10)                   Question 49 – An object at 80 degrees altitude is 10 degrees from the zenith.  So, set up the following relation:

 

                                    10ˇ / 360ˇ    =    1000 km / x   km

                                    x =  36,000 km

            So, the circumference is 36,000 km.                 

 

11)                   Question 51 – Need a and e for Mars:

                        a = 1.524 AU

                        e = 0.093

 

            perihelion = a(1 – e) = 1.38  AU

            aphelion = a(1 + e) = 1.67  AU

 

12)                   Question 54 – Use KeplerŐs Third Law. 

                        a = 68  AU

                        Pluto has an average distance of 39 AU

 

13)                   Question 55              a = 112 x 106 km = 1.12 x 108 km = 0.75 AU

                                                e = 0.3

                        perihelion = 0.75 (1 – 0.3) = 0.52  AU

                        aphelion = 0.75 (1 + 0.3) = 0.98  AU

                        p2 = a3         

                        p2 = (0.75)3

                        p = 0.65 years

 

14)                    Question 56 – Use KeplerŐs Third Law

                        a = 18  AU

                        perihelion = 18 (1 – 0.97) = 0.54 AU

                        aphelion  = 18 (1 + 0.97) = 35.5  AU

            HalleyŐs comet spends most of its time near its aphelion distance.