Download HOMEWORK #1

HOMEWORK #3 (due start of class September 15)
My Messier object is ____________
(copyright D. McCarthy)
LEARNING GOALS:
1. Continue practicing Polya’s 4-step plan in “How to Solve It.”
2. Continue practicing with astronomical coordinate systems.
3. Continue deriving useful, and fun, mathematical formulae.
4. Practice the concept of scaling.
TO RECEIVE FULL CREDIT:
1. Write your Messier name at the top of your homework.
2. If you submit multiple pages, staple them together.
3. To receive any credit on these problems, you must show how you derived your answer by writing
all the logical steps that led you to it.
4. All sentence responses must be typewritten and in complete sentences. You may handwrite any
arithmetic. Use good English grammar.
5. If you work more than three hours on this assignment, you should stop, record your work
here, and contact Dr. McCarthy.
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1. Optional:
a. Liquid nitrogen ice cream and movie night
September 29 (Thursday; 6-9 pm) in Steward Observatory’s auditorium (N210). We will watch the movie
“Contact” concerning communication with an extraterrestial civilization. The movie is based on a living
woman astronomer (Dr. Jill Tarter; SETI Institute) as well as the late astronomer/educator Dr. Carl Sagan.
b. Want to be a better problem solver? Here are three short articles to read.
“Why Floundering is Good” (Time magazine; A. Paul on April 25, 2012)
http://ideas.time.com/2012/04/25/why-floundering-is-good/
“Want to be Creative? Take a Walk” (New York Times; G. Reynolds on April 30, 2014)
http://well.blogs.nytimes.com/2014/04/30/want-to-be-more-creative-take-a-walk/?src=rechp
Take courses in classics and language.
“An Open Letter to SUNY Albany” (G. Petsko on November 22, 2010)
https://www.insidehighered.com/views/2010/11/22/petsko
c. Observe an “Iridium flare”
A really neat Web site (http://heavens-above.com/) predicts that a “flare” from an Iridium satellite will
occur Wednesday evening (September 14) with the specifications below. Practice your skills in AZ/ALT
coordinates and report your observations and impressions (perhaps even pictures!) of the flare to Dr.
McCarthy immediately via email or Twitter (hashtag #TucSky).
This flare should be ~100x brighter than any visible star (visual magnitude -4.8), but it will only last ~15
seconds so you must be looking near the correct location at the correct time:
Iridium flare (Sep 14): 7:27 pm local time; azimuth = 141deg; altitude = 56 deg
d. Practice with astronomical coordinate systems
Pretend you are planning to observe at the MMT Observatory this coming Thursday (Sep. 15) and wish to
study “Campbell’s Hydrogen Star” (aka, HD 184738 or BD+30 3639) with equatorial coordinates ( =
19h:34m:45s; = +30o:30’:59”). The Local Sidereal Time (LST) at midnight will be 23:19:06. The Sun sets
at 6:28 pm. Over what time period could you observe this object within an hour angle of 2h and hence
over a relatively low air mass?
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3. Required: How well do you know planet Earth?
a. “Meteors” (aka, ‘shooting stars’) are exciting to observe at night. They are simply small particles of
dust that heat up quickly as they collide at high speed with our atmosphere, leaving a streak of light in the
sky. Some of the vaporized debris falls to the Earth. “Meteorites” are much larger chunks of material that
hit the ground. The Earth gains ~2 x 105 kilograms (~220 tons) of material per day from such debris. The
Earth’s current mass is 6 x 1024 kilograms. Estimate the Earth's mass one million years from now. Do you
believe your answer is correct? Why or why not? Describe your reactions in several sentences.
Answer one of the following two questions.
b. The diameter of the Earth is 7926 miles at its equator. The highest point on Earth (Mt. Everest) is 5.5
miles above sea level; the lowest point (Mariana Trench in the Pacific Ocean) is 6.8 miles below sea level.
Hence, the "roughness" of the Earth’s surface is 5.5+6.8 = 12.3 miles. For comparison, a basketball has a
diameter of about 25 centimeters (cm). The bumps on a basketball’s surface are about 1 millimeter (mm)
high. Percentagewise, would you characterize Earth’s surface as rough or smooth vs. a basketball’s?
Justify your answer in several sentences by discussing, and incorporating, the numbers in these questions.
c. “Scaling” is an important tool in science. Pretend the Earth were scaled down to the size of an egg.
Estimate the volume of water on the egg’s surface that would represent the oceans. According to
Wikipedia, the average depth of water in Earth’s oceans today is ~ 3,682 meters.
4. How far away is the horizon?
Use geometry to derive a formula for the distance (“d”) to the horizon while standing at height (“h”) on a
spherical object (radius “r”). Ignore atmospheric effects. Justify any assumptions or approximations.
Assume Earth is a sphere of radius (“R”) 3960 miles and apply your formula in two cases. (A) If a tall
adult (h = 6 feet) looks out to sea, how far away can s/he see? (B) How far away could you see from an
airplane at altitude 30,000 feet?
5. Optional: Challenge Question
Eratosthenes was very resourceful in measuring Earth’s circumference. You can be resourceful, too!
Compute the Earth's radius using the picture of the cruise ship’s wake. If Earth were flat, the wake would
converge to a single point. You may assume the picture is taken from a height of 30 meters, the width of
the wake at the ship is also 30 meters, and the angle of the wake at the convergent point is 4.5 arcmin.
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