HOMEWORK 1

Hand in at the beginning of class on Wednesday September 6th

• You may study with your friends but the work you hand in should be your own. The main purpose of the homework is for you to learn the material - on which you will be tested later. You cannot learn by others doing the work for you.
• Write your answers on a regular 81/2" x 11" paper. PLEASE STAPLE TOGETHER. Don't forget your name!
• A single number or word on its own is not an answer. You must show HOW you came to your answer and give the units of quantities.
• This homework will probably take at least 2 hours.

1. Astronomical Accuracy.
   Estimate the circumference of the Earth in kilometers, as follows: The circumference of a circle is 2 R and the radius R of the Earth is 6374 km, and is about 3.14. (a) Estimate in your head - to 1 significant figure only. (b) Calculate with a calculator - keeping only an appropriate number of significant figures.
    
2. Scales in the Universe.
   This problem should help you see the need for scientific notation of numbers and give you a feeling for the large and small scales of the universe. Use your calculator, and express all answers to no more than two significant figures.

   (a) Grains of sand are very small, there being about 3000 grains in one cubic centimeter (cm³) of sand. A cm³ is a small cube measuring one cm on each side and is about the size of your little finger from the fingernail onward. Given that there are one million cubic centimeters (cm³) in one cubic meter (m³), how many grains are there in 1 m³ of sand?

   (b) If you counted one grain of sand each second, how many seconds would it take you to count all the grains in one cubic meter?

   (c) We want to change this to years: how many seconds are there in one year?

   (d) How many years would it take to count all the grains of sand in one cubic meter?

   (e) One can estimate the total length of coastlines along all the beaches in the world using a globe, a piece of string, and a ruler. Roughly, there are 200,000 km of beach in the world. How many meters is this?

   (f) We now want to calculate the total volume of sand on all the world's beaches. Remember that volume is length x width x depth. Use the length of beach from part (e), say that the average width of a beach is 15 meters, and that the average depth of sand is 2 meters. What is the total volume of sand, in m3, adding up all of the world's beaches?

   (g) Using parts (a) and (f), estimate how many grains of sand there are on all the beaches of the world.

   (h) There are something like 100 billion (10¹¹) stars in a typical galaxy, and there are about 100 billion galaxies in the universe. How many stars are there in the universe?

   (i) You should have found that the number of stars in the universe is greater than the number of grains of sand on all the beaches of the world. Divide the number of stars by the number of grains of sand to figure out how many times more stars there are than grains of sand.

   (j) Thinking about this incredible number of stars in the universe, and that our Sun is but one of them, consider the possibility that many of those stars have planets, and perhaps some of them have "people". (Do you think there is intelligent life in the universe?)

   (k) Now we consider the very small. Each of us is made of a very large number of atoms, each atom being only about 1/100,000,000 cm (10^-8 cm) in diameter. There are about 10²³ atoms in a cubic centimeter, and about 10²⁸ atoms in our bodies. How does this compare with the number of stars in the universe (i.e. how many times more atoms are there in your body than stars in the universe)?

   (l) A typical star, such as the Sun, has about 10²⁹ times as many atoms as your body. How many atoms are there in a star?

   (m) Now let's go for the big one.... How many atoms are there in all the stars of the universe?
    

3.  Space is BIG and EMPTY:

    

   (a) The distance between the Sun and the Earth (1.6 x 10⁸ km) is call an Astronomical Unit (AU for short). The distance to Alpha Centauri is about 280,000 A.U. How many km is this?

   (b) The diameter of the Sun is 1,400,000 km. How many Suns, placed side by side, could you place between us and Alpha Centauri?

   c) How many Suns could you put in a cube where each side of the cube is the distance to Alpha Centauri? This should give you an idea of the emptiness of space.

    

4. Apparent vs. Actual Motions.
   Describe and distinguish between the apparent and actual motions in the following two cases:

   (a) The daily motion of the stars.
   (b) The annual motion of the Sun.

    

   (c) You are on a merry-go-round (carousel, roundabout) at a fair, looking outwards. You see a friend standing at a nearby stall buying sugar-candy (candyfloss). The merry-go-round is revolving anti-clockwise (that's the same as counter-clockwise) looking down from above. Which way does your friend appear to move - left-to-right or right-to-left? (Drawing a picture or acting out the situation may help).