Astronomy 300: Homework Assignment #1

Due: Wednesday Feburary 1

Reading: C&O, Ch 1..

  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. Explain in your own words why the Solar Day is different from the Sidereal Day.

    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 Jan 12, Venus reached greatest elongation East, an excellent time to observe the planet. Draw a diagram showing Earth, Sun and Venus on this date. (The ecliptic plane should coincide with your paper).

    Reading: Croswell, Ch 1.

  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.

    Reading: The Watershed, Ch. 6

  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 angle between the Sun and Venus. One way to do this is to measure Venus shortly after sunset, when the Sun is about a few degrees below the horizon. Discuss your methods, and estimate the error with which you measured this angle. Compare this error to that of Tycho, whose observational precision was two minutes of arc or better. Revisit your drawing for problem 5, above, and try to sketch in the location of Venus on the date of your observation.