# Astronomy 300: Homework Assignment #1

Due: Friday, Feburary 2

1. Order-of-magnitude estimate. Complete this problem WITHOUT using calculator, and without looking up anything online. Show all your steps in detail.

Estimate how long it takes the Sun to set. Use only the fact that the angular width of the Sun is 1/2 of 1 degree, and other generally known information.

Calculators may be used for the remainder of the homework.

2. One of the few surviving manuscripts from the Ancient Mayan Civilization of Mesoamerica is called the Dresden Codex. This document includes mathmatical tables describing 65 apparitions of the planet Venus in the sky, and repeatedly mentions the number 584. Given Venus' orbital period (See Appendix C of C&O) and Earth's orbital period, what could be the significance of this number in the Dresden Codex? (Hint: Look at the first equation in C&O)

3. Define the Solar Day and the Sidereal Day, and explain in your own words why they are different.

When is this difference minimized?

4. What are the right asencion and declination of the Sun on the: Vernal Equinox, Summer Solstice Autumnal Equinox & Winter Solstice.

(All observational astronomers know or can deduce these coordinates quickly. One of them is easy to remember!)

5. On January 9, 2018 Venus reached Superior Conjunction. Draw a diagram showing Earth, Sun and Venus on this date. (The ecliptic plane should coincide with your paper). Would this be a good time to observe Venus?

6. In "Alchemy of the Heavens" p. 2, Croswell describes a scale map of the Milky way. What is the scale ratio of this map? He then casually states : "On such a map, the Galactic center would be 27,000 miles from the Sun, for the Sun lies 27,000 light years from the center of the Galaxy." This implies that using the same scale, one mile would (coincidentally) map to one light year. Confirm that this is true.

7. Why are there so many bright stars visible in winter? Include a diagram to illustrate.

8. Copernicus is given credit for instituting the Heliocentric Revolution in scientific thought with his book De Revolutionabus Orbium Celestium, and clearly specifying the order of the planets from the Sun. But many misconceptions remain.

A.) Was Copernicus the first to propose a Heliocentric universe?

B.) Was the Sun at the exact center of Earth's orbit in Copernicus model? Compare & contrast Figs. 1.4-1.7 in C&O with Figs. 3,4 & 5 in The Watershed.

C.) Does Copernicus' model include the dreaded epicycles present in Ptolemy's geocentric model?

9. Why did Kepler consider it a great fortune that he was assigned by Tycho to understand the orbit of Mars? Why would the discovery of his first and second laws have been much more difficult if he had been assigned the orbit of Venus instead?

Observing Project

If possible, do this project in groups of 2 or 3. List the names of your partners.

10. Make your own attempt to measure the position of a planet in the sky with respect to the Sun or the fixed stars. Express your measurement as a number of degrees plus or minus some margin of error. There are three planets visible in the morning sky before dawn: Saturn, Jupiter & Mars. You'll need to be observing at about 6:00 AM, or slightly before. Look east and find Jupiter (brighter) and Mars just above the stars of Scorpius. Using the fact that a fist placed at arms length is about 10 degrees, estimate the angular distance from both Mars and Jupiter to Antares (Alpha Scorpii). Also compute the angular distance between the two planets. (on Jan. 6 this disance was minimized and Mars was in Conjunction with Jupiter)

Alternate Project (for late risers): Measure the angular distance from the Moon to a given star on two or three consecutive night. Hint: start on a night when the Moon is to the west (right) of a star.