Astronomy homework - week 3

Due Tues.14.April in class

Due Thus.26.April in workshop:

(Extra: try Ch.3 OP#20-21 if you can get up before dawn)

These are not full solutions. You may use these answers to check your results, but your homework should also include clear explanations of methods, meanings, and relationships between quantities, written in your own words. Show your work on all numerical problems, including intermediate steps such as algebra and units conversions. If you turn in homework as sketchy as the answers below, the grader will remind you to "explain more," "draw a diagram," and/or "show your work."

Every numerical answer needs units and a referent - a bare lonely number is meaningless.

Crowe P.7 (p.15) Suppose that on the night of 13 August 1301, a lunar eclipse occurred that was seen in London. What was the phase of the moon on the night of 12 Aug 1301?

A lunar eclipse is when Earth's shadow falls on the Moon. This can occur only when the Earth is directly between Moon and Sun, that is, when the moon is FULL (and at the line of nodes, where the ecliptic intersects the plane of the moon's orbit).

Crowe P.9 (p.15) The attempt has sometimes been made to account for the darkening of the sky during Christ's crucifixion by attributing the darkening to a solar eclipse. According to the Synoptic Gospels, the crucifixion occurred on the afternoon after the Jewish Passover meal, when meal was set on the 15th day of the month Nisan. The Jewish calendar being a lunar calendar, the first day of each month coincided with a new moon. Use this information to comment on the acceptabilty of the proposed explanation.

A solar eclipse is when the Moon's shadow blocks sunlight from a narrow path on Earth, and can occur only when the Moon is between Earth and Sun. So solar eclipses correspond with New Moons (and only those at the line of nodes).

If the first day of a lunar month is counted from the New Moon, then the 15th day is about at Full Moon.

A Solar Eclipse is impossible on the 15th day of a lunar month, so that explanation for the darkening of the sky during Christ's crucifixion FAILS. There could have been a Lunar Eclipse that evening, but that wouldn't darken the afternoon sky, as the Christian myth reports.

K2, AQ#12 (p.53) A line joining the Sun and an asteroid was found to sweep out 5.2 square AU in 1994. How much area was swept out in 1995? Same: 5.2 AU². In five years? 5*5.2=26 AU²

If the asteroid's ordit s not significantly perturbed by planets or other asteroids, it will be an ellipse and obey Kepler's laws, including equal areas in equal times - even if it slows down (further away) or speeds up (closer).

K2, AQ#13 (p.53) A comet moves in a highly elongated orbit about the Sun with a period of T=1000 years. What is the length of the semimajor axis a? a³(AU)=(1000 yrs)² so a= 10^6/3=2= 100 AU. What is the farthest the comet can get from the Sun? For a highly elongated orbit, the distance c from center to focus is nearly the distance a from center to edge, so the maximum separation a+c is nearly 2a, or a little less than 200 AUfor this comet.

Draw a diagram of an elliptical orbit to see this.

Kepler's law in the form T²(yrs) = a³(AU) applies only to objects orbiting the Sun (1 year for 1 AU, for the Earth).

K2, AQ#14 (p.53) The orbit of a spacecraft about the Sun has a perihelion distance (d_min = closest approach) of 0.5 AU and an aphelion distance (d_max = furthest separation) of 3.5 AU. What is the spacecraft's period?

Draw a diagram of an elliptical orbit to see that d_min + d_max = 2a. Then a=2, and T²(yrs) = (2AU)³, which yields T<3 years.Similar analyses helped astronomers figure out the orbit of Hale-Bopp a couple of years ago.

K2, AQ#15 (p.53) Suppose the Earth were moved from R=1 AU to 10 AU from the Sun. Since the gravitational force is inversely proportional to R², the Sun's pull on Earth would be 10²=100 times weaker.

The year would be much longer, but we would weigh the same and the tidal range would not be much less, if the Moon followed us.

Observing exercises (if possible):

K3, OP#26 (p.79) On a clear night (morning), view the Moon, a planet, and a star through a telescope, using eyepieces of various focal lengths. How does the image seem to change as you view with increasing magnification? Does it degrade at any point?

(Extra: try Ch.2 OP#20-21 if you can get up before dawn)

CONTINUE K1, OP#48 (K.35) Observe the moon on each clear night over the course of a month. Note the Moon's location among the constellations and record that location on a star chart that also shows the ecliptic. After a few weeks, your observations will begin to trace the Moon's orbit. Identify the orientation of the line of nodes by marking the points where the Moon's orbit and the ecliptic intersect. On what dates is the Sun near the nodes marked on your star chart? Compare these dates with the dates of the next solar and lunar eclipses.

Maintained by E.J. Zita

Last modified: 16.Apr.98