Homework #1

Homework #1

Due on Wednesday, May 31st at the beginning of class (10:10 AM)

100 points total (individual point vaules will be determined at the time of grading)

1. Numbers Big and Small

Let's get a little practice using scientific notation and converting units. (Refer to pg. 544 of your text for conversions between metric and English units.)
1. Write the number 238,793.387 in scientific notation with only 3 significant digits.
2. Write the number 5.765 x 10-7 as a normal string of digits.
3. What is (6 x 104)/(3 x 10-6)? Do not use a calculator. Show your work. What's the name of this number (i.e., how many million, billion, trillion, etc. is this)?
4. A light-year is the distance light travels in one year. If light travels at a speed of 186,000 miles/second how many miles are there in a light-year? How many meters is this? Give all answers in scientific notation and show all work.

2. Scale Models

Suppose you wish to construct a scale model of the Universe. The Sun has an actual diameter of about 1.5 x 106 km, and you represent it by a dot the size of a period (0.5 mm in diameter). The average distance between stars in our region of the Milky Way Galaxy is about 5 light-years. (1 light-year = 9.5 x 1012 km)
1. What is the average distance between stars on the scale of your drawing? (Hint: use ratios, and keep track of your units!)
2. The Galaxy is about 105 light-years in diameter. How large is this on your scale?
3. On this same scale, what is the distance to the Andromeda galaxy, about 2 million light-years away? (This is the nearest large galaxy.)
4. On this same scale, what is the distance to the most distant objects we have seen (quasars and very distant galaxies), about 13 billion light-years away?
5. Compare your scaled answer in part (d) with the true diameter of the Solar System (as defined by Pluto's orbit), about 12 billion km. Which is larger, and by roughly what factor?
Now let's make a scaled down cosmic calendar. Evidence suggests that Earth is about 4.6 Billion years old. Let's scale this to one day (24 hours).
1. How many seconds ago did the USA achieve independence (1776 A.D.)?
2. How long ago did Rome fall (around 476 A.D.)?
3. How long ago was the first city, Jericho, built (about 10,000 years ago)?
4. How long ago did the first modern Homo Sapiens show up in the fossil record (about 100,000 years ago)?
5. How long ago did the Dinosaurs go extinct (65 Million years ago)?
6. How long ago did the first plants appear on dry land (250 Million years ago)?
7. How long ago was the origin of life on Earth (about 3.8 Billion years ago)?

3. How Far is the Horizon?

As we discussed in class the horizon is the place where the Earth meets the sky, and the horizon is farther away the higher you get above the surface of Earth. The mean radius of Earth (sea-level) is 6,371 km.
1. Let's say you are standing on a small (10-foot) boat out in the ocean. Your feet are essentially at sea-level. Estimate or measure the height of your eyes above your feet while standing. Calculate the distance to the horizon.
2. Now you hike up to Volmer peak (elevation 1,913 ft). Neglecting your own height, how far away is the horizon?
3. Finally, you are flying out east to see a friend. During the flight the captain tells you that you are flying at a height of 35,000 ft. A young child is sitting in the window seat next to you looking out and wondering how far she can see from way up here. What's the answer?

4. National Lampoon's: Vacation on the Moon

Let's say that you took a trip to the Moon. After checking in to your hotel room you walk out onto your balcony to check out the view. It's rather spectacular. Earth is up in the Southwest sky and it's a waxing gibbous, nearly full.
1. You want to call your friends back in Berkeley on Earth to tell them about the awesome view. What phase will they see the Moon to be in?
2. The phone company will only allow you to make the call when the Moon is directly overhead in the location you are calling on Earth. What general time of day will that be in Berkeley? (i.e. noon, midnight, dawn, dusk, or sometime between those)
3. You're kinda tired and would like to take a nap, but the Earth is pretty darn bright and is shining a lot of light into the room. You have difficulty sleeping with that much light in the room. How long will you have to wait until Earth sets over the horizon?

5. Eclipse

1. During an annular eclipse of the Sun, the observer sees a ring (Latin annulus) of light, which is the rim of the Sun's photosphere. In other words, the Moon's angular size isn't quite as large as that of the Sun, so one gets a special kind of partial eclipse. When in Earth's elliptical orbit around the Sun and the Moon's elliptical orbit around Earth would this phenomenon reach an extreme (i.e., Sun's angular size is as large as it gets at the same time the Moon's angular size is as small as it gets)? Explain.
2. When people in New York see a total lunar eclipse, what type of eclipse do people one-fourth of the way around Earth see? (Assume that the Moon is visible in both skies.)

6. Where in the World is Gilligan?

In a forgotten episode of Gilligan's Island the Professor finds a magical goat that can communicate via radio signals. They use the goat to make contact with civilization. They are saved! But first they must give someone their coordinates so that they can be found. Not much survived the Minnow's demise, but they do have a watch that is still running on Pacific Standard Time. Plus they have a sextant and can measure angles in the sky with high accuracy.
1. First they wait for nightfall and locate the Big Dipper and use the pointer stars Merak and Dubhe to locate Polaris. They know that Polaris is about 1° from the North Celestial Pole (I should say the professor knows that, the magical goat might also). They measure the angle of the North Celestial Pole above the horizon to be 28°. What is their latitude?
2. On the next day they wait for the Sun to cross the local meridian, this happens at 3:04 PM PST, by their watch. Recall that Pacific Standard Time is the Mean Solar Time at a longitude of 120° West of the Prime Meridian. What is their longitude?

7. Hey Baby, What's Your Sign?

As we discussed in class the Sun signs of Astrology are out of date. The precession of Earth's axis has altered the constellation that the Sun is in during any given month. Additionally, the International Astronomical Union recognizes 13 constellations in the Zodiac.
1. Using an online star map generator, or the planetarium software provided with your text or in class, determine what constellation the Sun was in at the time of your birth. Is this the same as the Sun sign given for you in the newspaper (check out any newspaper and site the source)?
2. Read the Horoscope of your real Sun sign from at least three different newspapers or websites. If you are an Ophiuchus (Nov. 30th - Dec. 17) just read the one for the date of your birth printed in the paper (either Sagittarius or Scorpius). Make a copy of the three horoscopes and turn them in. How well do they agree? Do they actually make any predictions? If so, did they come true?
-Links to Astrology sites from Yahoo!.

8. Going Retro

1. In words and in pictures show how both Ptolemy's model of the Universe and Copernicus' model of the Universe explained the retrograde motion of the planets.
2. In Copernicus' time measurements of the Planets' positions were not sufficient to be able to differentiate one model from the other as being more accurate. Explain why, using modern scientific reasoning, we would have to go with Copernicus' model as the best explanation of nature if we lived then.