a) Observe the sun at sunset on 3 occasions between now and
21, at the same location. (If sunset is not a convenient time for you,
sunrise will do just as well. A mixture of sunrises and sunsets WON'T
Stand in exactly the same
spot for each observation. Make sketches
clearly showing the position of the sun with respect to
foreground features. Be sure the same foreground features appear in
each picture. Note the date and
time of your observation
on each sketch. (Photographs are also acceptable.) Discuss how
the position of the sun at sunset changes from one observation to the
b) Make a sketch showing the position of the Earth in its orbit at this time. Show the position of the Earth, the Sun and the Earth's rotation axis clearly. Also show which way things are moving.
c) Explain your own observations in terms of the model shown in part (b). State clearly how the model is consistent with and explains what you saw.
1. Your bicycle wheel has a radius of 1 ft, and you are pedalling so
that the wheels turn once per second. How fast is the bicycle moving in
feet per second?
Extra credit: how fast is that in miles per hour?
2. The Earth rotates once per day (!) You may assume that the Earth is a sphere with a radius of 6378 km. San Francisco is at Latitude 38°, and so it moves around a circle whose radius is 5026 km.
(Reference: Ferris, Chapter 7 and your lecture notes. You'll need
Earth-sun distance from your units handout.)
2. Use the planetary data on your "Ellipses" handout to calculate T2 and a3 and show that all the orbits are consistent with Kepler's 3rd Law. (Note that the numbers given on your sheet are all rounded to two or three significant figures. You can show consistency only to 2 figure accuracy!)
3. Measure the length of the major axis of the ellipse on page 1 of that handout, and the distance between the two foci. Hence find the eccentricity of the ellipse. Compare with the values for the planets. (This should give you an idea of how circular the orbits are, and how careful Kepler had to be to find the differences.)
1. Use Newton's Law of gravitation and your results from problem 2, assignment # 3, to find the mass of the Sun.
The same principles are used in the following exercise:
2. The Sun orbits around the center of the galaxy in about 250 million years. The gravitational pull of the material interior to the Sun provides the force to make the Sun move in a circle. Use Newton's Law, as in Problem #1, to find the mass of the galaxy that is interior to the sun. (The distance of the Sun from the center of the galaxy is about 3x1020 m.)
(Material outside the sun has no effect and may be ignored.)
1. The Sun has a luminosity of 4x1033 erg/s amd a mass m
(The energy unit erg = 1 gram times (1 cm/s)2 and the speed of light is c = 3x1010 cm/s. See Ferris Chapter 10 and class handout.)
(a) By how many grams does its mass decrease per second? Is that a large or a small amount? For example, how many cars is that?
(b) By what percentage does its mass decrease per year? Is that a large or a small number? If 10% of the Sun's mass is available as fuel, how long can the sun shine before it runs out of fuel?
Einstein's discoveries also changed the way that we view the universe; in particular, he changed our understanding of time.
2.(a) Using graph paper, construct a space-time
diagram to illustrate the following events. Use light-days as your
unit of length, and days as your unit of time. Be sure your diagram is
LARGE enough for you to make measurements easily and accurately.
(Use a full 8x11 page.)
A rocket leaves Earth moving at 4/5 the speed of light. After 2 days Earth-time a radio signal is sent from earth to the rocket. Immediately after the signal is received at the rocket, a reply is sent to Earth.
(b) Use your picture to determine when the rocket receives the signal according to earth-bound clocks, and when the reply is received on Earth.
(c) Use the formula for time dilation to determine how long after departure in rocket time the signal is received at the rocket. Be careful here. For which observers, those on Earth or those on the rocket, do both events occur at the same place? Use your answer to decide which time interval is the smaller, the one in rocket time or the one in Earth time.
(d) Make another diagram showing events as seen by the rocket crew.
(In this diagram the earth moves away at speed (4/5)c.)
Comment! What have you learned?