# Instructor: Dr. Korpela

## Due Jan 29, 2004

Much of the information required to complete this homework assignment is contained in the handouts. The remainder is available either in your text or at http://www.astronomynotes.com (a useful web resource if for some reason you don't yet have a text).

1. ### Numbers Big and Small (12 points)

Let's get a little practice using scientific notation. All the necessary information is contained in the handouts. This is simply to familiarize yourselves with this type of notation - you will never do complicated calculations.
1. Write the number 232,898.232 in scientific notation with only 3 significant digits.
2. Write the number 7.321 x 10-5 as a normal string of digits.
3. What is (6 x 10274)/(3 x 10268)? 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)?

2. ### Galactic Messages (20 points)

To help you become familiar with the idea that a light-year is a unit of distance, and what it tells you...

Let's assume you live on the planet Pong where the only means of communication is by bicycle messenger. All bicycle messengers travel 60 km/hour (this would be pretty fast on earth, but hours on Pong aren't the same). There are only 10 hours in a Pongian day, but 100 days in a Pongian year. Now suppose your parents live three bicycle-days away (1 bicycle-day = the distance a messenger can travel in a day, analogous to 'light-year'). You shouldn't need a calculator to do this question! Use scientific notation to help you.
1. How far away (in km) do they live? (Hint: How far is a bicycle-day?)
2. If they win the lottery, how long before you can hear about it? (Hint: No calculation should be required!)
Now assume that your civilization has somehow colonized other planets in your solar system, but the speed of communication is still the same. You get the news that a child is born on the planet Quong which is 6x1011 meters away (~4 AU, or the approximate distance between Earth and Jupiter at closest approach).
1. How far is a bicycle-year (in meters or km)? (Hint: This is just a conversion of units)
2. How far away is Quong in bicycle-years? (Use scientific notation to do the calculation).
3. How old is the child when you get the news? (Hint: No calculation should be required!)

Note that in our solar system, Jupiter is over 30 light-minutes from Earth, so even with a MUCH faster speed of communication, there is a significant lag! Since the nearest stars are several light-years away, interstellar communication and travel are impractical without faster-than-light technology (which violates physics as we understand it).

3. ### The Universe We Live In (8 points)

1. What is the difference between our solar system, our galaxy, and the universe, and how do they relate to one another?
2. Do people in other (northern hemisphere) cultures on earth see the Big Dipper (even if they call it something else)? What about people on planets circling other distant stars?

4. ### Sky Motion (20 points)

In the following question, remember that the stars appear to move in circles around the celestial poles, which are the projections into space of the Earth's north and south pole!
1. Where would you see the NCP if you were standing at the Earth's equator?
2. Where would you see the SCP if you were standing at the Earth's South Pole?
3. Now imagine you're at the South Pole in winter. You're cold in your parka, but do you see the stars rise and set each day?
4. Now imagine you're at the equator looking South. You've taken off your parka. Do the stars rise to the right or the left of the southern point on the horizon (ie. where is East)? Do they rise straight up, or at an angle with the horizon?
5. Assume it is nighttime and clear, and that you are standing on the equator looking west. Sketch the star trails that you would see. Include a horizon, compass direction, and the North or South Celestial Pole if they are relevant. Samples for some other situations are displayed in the star trail figures on p. 16 of your text.

5. ### Nature of Science - Doing Science (25 points)

For this question, you're going to be a scientist!
Newton's Theory: Newton's theory of gravity predicts that all objects experience the same acceleration due to gravity. This means that if you drop any two objects from the same height, the theory predicts that they will reach the floor at the same time, regardless of their mass/weight.
In a few minutes, you will take your textbook for this class in one hand, a flat piece of paper in the other, and drop them from an equal height.
1. Prediction: Based on your experience, what do you think will happen (ie which, if any, will hit the floor first)?
2. Prediction: What does Newton's theory of gravity predict will happen? Does your prediction match the prediction of Newton's theory?
3. Experiment: Drop the book (take out the CD first!) and the paper! Describe the results of the experiment.
4. Outcome: Do the results of the test match your predictions of parts (a) and (b)? ie. Do the results support (not prove/disprove) your prediction and/or Newton's theory?
5. Can you think of any reason that this experiment does not completely test the predictions of Newton's theory? How might you modify the experiment to more completely test the predictions of that theory?

6. ### Nature of Science - Designing an Experiment (15 points)

You're all familiar with the horoscopes in the daily paper! Basically, astrology says that human events are influenced by the apparent positions of the Sun, Moon, and planets among the stars in our sky, particularly at the time of one's birth. After all, the Sun's position in the sky determines the seasons, and so the times of planting, harvesting, warmth, cold, daylight, and darkness. Why shouldn't the other heavenly bodies that move among the stars affect our lives as well?

Design a scientific test of astrology. In other words, design an experiment whose results will either support the assertions of astrology, or conflict with them.

1. Clearly define the methods you would use in your test, outlining all the steps involved (1 paragraph). You will not be required to carry out the experiment, but it should be one that is feasible.
2. Include a description of how you would evaluate the results (1 paragraph).
3. You do not need to carry out the experiment you have designed. If you did carry out the test, do you think it would confirm the tenets of astrology, or conflict with them?