Week 13 (Nov. 18 - 21)
Read: A new theory of gravity (Chap. 23). We'll spend some time on this reading from Einstein on Monday, and then move on to some light reading from Gamow's Mr. Tompkins in Wonderland for Wednesday.
Quiz: Monday. Covers Leavitt and Slipher.
Homework exercises:
Laboratory exercises: This week, we will do a solar eclipse laboratory experiment. The goal is to try to understand how solar eclipses work. You will need an optical rail (with a measuring tape), a ping pong ball, a white screen, a ruler, and two light sources: one small "point source" and one large bulb. You may need to recall some geometry and trigonometry formulae in order to do the calculations in this lab.
Begin with the point source on one side of the optical rail. This will represent a very small sun. Measure the diameter of the light source using a ruler. Place the ping pong ball somewhere in the middle of the rail. This will represent the moon. Measure the diameter of the ping pong ball. Now place the screen opposite the ping pong ball. This will represent the surface of the earth. Move the earth back and forth, closer to the moon and farther from the moon, and observe the size of the shadow cast by the moon on the surface of the earth. What do you notice?
Now be quantitative. Do at least 8 measurements of the size (diameter) of the moon's shadow as a function of the earth-moon distance. Keep the sun-moon distance constant during these measurements. Then make a plot of the shadow diameter (y-axis) as a function of the earth-moon distance (x-axis). Be sure to clearly label the plot, make a printout, and place it in your lab book.
Now use the large light source. This is a more realistic representation of the sun. Again, place the moon between the sun and the earth. Move the earth toward and away from the moon. Now you will notice that the shadow has a dark part (the umbra) and a kind-of-dark-part (the penumbra). Why is this? In particular, if you were standing on the earth (the screen) in the umbra, would you experience a total solar eclipse or a partial solar eclipse? What if you were standing in the penumbra? Explain clearly your measurements and how they are related to observations of solar eclipses.
Now be quantitative. Do at least 8 measurements of the diameter of the penumbra and the diameter of the umbra as a function of the earth-moon distance. What do you notice? Put all three data sets on a single plot. Use different symbols and a legend to indicate the appropriate data sets.
Let's try to relate our data to actual solar eclipses. First, suppose that the sun was a small point source. Look up (i) the distance between the sun and the earth (let's use the average distance), (ii) the (largest) between the moon and the earth (lunar apogee), and (iii) the diameter of the moon. Based on this data, how wide would you expect the umbral region to be on the surface of the earth? You will need to use a bit of geometry to calculate this. Show how you do the calculations in your lab notebook. How would your measurements change if the moon were closer to the earth (at perigee)? Would the shadow be larger or smaller?
Now, look up the diameter of the sun. Using the average earth-sun distance and the largest moon-earth distance (lunar apogee), what is the size of the umbral shadow on the earth's surface? Now use the smallest moon-earth distance (lunar perigee). What is the size of the umbral shadow in this case? What does this imply? Try to determine the maximum distance between the earth and moon so that there is, in fact, an umbra (not just a penumbra) cast by the moon.
Finally, can you calculate the size of the penumbra if the moon was at perigee? At apogee?
After you have recorded and analyzed your data in your lab notebook, be sure to scan and submit your lab book pages by noon Monday week 14.
A new theory of gravity (1 video):
Euclid, Gauss, and Mercury's orbit (no videos yet…):
A finite universe with no boundary (no videos yet…):
Homework exercises:
Laboratory exercises: This week, we will do a solar eclipse laboratory experiment. The goal is to try to understand how solar eclipses work. You will need an optical rail (with a measuring tape), a ping pong ball, a white screen, a ruler, and two light sources: one small "point source" and one large bulb. You may need to recall some geometry and trigonometry formulae in order to do the calculations in this lab.
Begin with the point source on one side of the optical rail. This will represent a very small sun. Measure the diameter of the light source using a ruler. Place the ping pong ball somewhere in the middle of the rail. This will represent the moon. Measure the diameter of the ping pong ball. Now place the screen opposite the ping pong ball. This will represent the surface of the earth. Move the earth back and forth, closer to the moon and farther from the moon, and observe the size of the shadow cast by the moon on the surface of the earth. What do you notice?
Now be quantitative. Do at least 8 measurements of the size (diameter) of the moon's shadow as a function of the earth-moon distance. Keep the sun-moon distance constant during these measurements. Then make a plot of the shadow diameter (y-axis) as a function of the earth-moon distance (x-axis). Be sure to clearly label the plot, make a printout, and place it in your lab book.
Now use the large light source. This is a more realistic representation of the sun. Again, place the moon between the sun and the earth. Move the earth toward and away from the moon. Now you will notice that the shadow has a dark part (the umbra) and a kind-of-dark-part (the penumbra). Why is this? In particular, if you were standing on the earth (the screen) in the umbra, would you experience a total solar eclipse or a partial solar eclipse? What if you were standing in the penumbra? Explain clearly your measurements and how they are related to observations of solar eclipses.
Now be quantitative. Do at least 8 measurements of the diameter of the penumbra and the diameter of the umbra as a function of the earth-moon distance. What do you notice? Put all three data sets on a single plot. Use different symbols and a legend to indicate the appropriate data sets.
Let's try to relate our data to actual solar eclipses. First, suppose that the sun was a small point source. Look up (i) the distance between the sun and the earth (let's use the average distance), (ii) the (largest) between the moon and the earth (lunar apogee), and (iii) the diameter of the moon. Based on this data, how wide would you expect the umbral region to be on the surface of the earth? You will need to use a bit of geometry to calculate this. Show how you do the calculations in your lab notebook. How would your measurements change if the moon were closer to the earth (at perigee)? Would the shadow be larger or smaller?
Now, look up the diameter of the sun. Using the average earth-sun distance and the largest moon-earth distance (lunar apogee), what is the size of the umbral shadow on the earth's surface? Now use the smallest moon-earth distance (lunar perigee). What is the size of the umbral shadow in this case? What does this imply? Try to determine the maximum distance between the earth and moon so that there is, in fact, an umbra (not just a penumbra) cast by the moon.
Finally, can you calculate the size of the penumbra if the moon was at perigee? At apogee?
After you have recorded and analyzed your data in your lab notebook, be sure to scan and submit your lab book pages by noon Monday week 14.
A new theory of gravity (1 video):
Euclid, Gauss, and Mercury's orbit (no videos yet…):
A finite universe with no boundary (no videos yet…):