Name: Class: Date: Assignment #13 Roemer s measurement of the speed of light Part I: Purpose, Goals, and Objectives This assignment will give you some observational experience associated with what I consider the first measurement of the speed of light. The quantity is key in our understanding of the world. It is thought that information cannot be transmitted any faster. It is constant in all reference frames, thereby tying together 3-dimensional space and time. For us, it seems almost instantaneous. For example, when we measure the distance to a lightening flash, we count the time since the flash to the boom of the thunder. You may remember that Galileo suggested (or performed) an experiment to measure light speed. He and an assistant would each take a lantern and a timepiece, and stand on a hilltop. They both started with covers over the lanterns. They would cover the lantern until they saw that the other lantern uncovered. By measuring the time it took to uncover the second lantern, they would deduce the speed of light. The result was that it s exceedingly fast, at least 10 times the speed of sound. This was 1638. Figure 1 - portraits of Galileo, Cassini, and Roemer This was the time of great explorations by the Europeans of the world around them. Naturally, if you want to explore, then you must know where you are. Latitude is easy to determine, just look at the north star. Longitude is much more difficult and requires a clock. It wasn t until John Harrison in 1764 had a good clock that you could take with you. Galileo had suggested that one could use the moons of Jupiter as timepieces. Kepler s Laws showed that the orbital periods would be constant perfect for a timepiece. It was Cassini that was the first to perform these measurements, determining longitude by using the eclipsing Jupiter s moons as timepieces. This methodology allowed Cassini to measure the size of France for the first time. It was much smaller than assumed. So much so that the king quipped that Cassini had taken more of his kingdom from him than he had won in all his wars. 1
The next step in the measurement was only 40 years after Galileo s measurement. Roemer had access to Cassini s measurements. Remember, these data were extensive in order to measure the entirety of France. Roemer noticed that the orbital periods for the moons varied as a function of position relative to earth. Part II: Terms to Review Look up the following words and provide an appropriate definition of the word in the space provided. 1) Astronomical Unit 2) Eclipse 3) Ephemeris 4) Satellites 5) Jupiter 6) Galilean Satellites 7) Latitude 8) Longitude 9) Conjunction 10) Opposition 11) Orbit 12) Period of an Orbit 13) Speed of Light 14) Julian Day 15) Universal Time 16) Shadow 17) Transit 18) Occultation 19) Percent Difference 20) Field-of-view (FOV) Part III: Stellarium observations of Jupiter/Solar conjunctions and oppositions In this part, you re going to determine when the next conjunction of the Sun and Jupiter will be, and find the following opposition between these two objects. Of course, these events are assuming that you re standing on Earth. Still it is easiest to first get an estimate of these events by looking at the entire solar system. Then we ll move back to Earth and get a better estimate by comparing the Right Ascension of the Sun and Jupiter. This is the method that follows. Unless 2
you ve been told differently, choose a date of conjunction and opposition different than your classmate. 1) Turn on Stellarium. Turn off the ground, fog, and atmosphere. 2) Go to the Sky and viewing options, and click the simulate-light-speed button. Also, you may want to a) move the Planet slider over to the right, b) show planet orbits, and c) show planet markers. 3) Select the solar system observer, and move your position to it (cntrl-g/cmd-g). Now select the Sun. Change the field-of-view (FOV) so that you can observe the Earth and Jupiter. For me, the Solar System Observer is 46AU away from the Sun. So, I feel comfortable with about a 10 o FOV. 4) Find the approximate date and time for the next conjunction of Jupiter and the Sun, and provide it in the space provided: 5) Find the approximate date and time for the following opposition of Jupiter and the Sun, and provide it in the space provided: 6) Now select the Earth, and move back to the Earth (cntrl-g/cmd-g). Now move back to Los Angeles. 7) Now go back to the dates and times you provided in item 4. Set Stellarium for this date and time. a. For conjunction, how will the Right Ascension for the Sun compare to that for Jupiter? b. Move time back and forth, until the Right Ascension is where you want it. What is the date and time for Solar/Jupiter Conjunction? 8) Now go back to the dates and times you provided in item 5. Set Stellarium for this date and time. a. For opposition, how will the Right Ascension for the Sun compare to that for Jupiter? b. Move time back and forth, until the Right Ascension is where you want it. What is the date and time for Solar/Jupiter Opposition? Part IV: Determining Eclipse Observation Dates The best observation times for observing the Galilean Eclipses is not when we have a conjunction or an opposition. In fact, the best time is about 2 or 3 months after the conjunction, and about 1 month before opposition. We will now take your dates from Part III item 7b and 8b, and determine the FAR and NEAR eclipse observation dates. Put these dates into the space provided. The FAR date is 2 or 3 months after conjunction: The NEAR data is 1 month before opposition: 3
Part V: Stellarium observations of Jupiter eclipses of IO at the FAR position 1) Turn on Stellarium. Turn off the ground, fog, and the atmosphere. 2) Set the Stellarium date and time so that it matches the FAR date that you just determined in Part IV. Turn the passage of time off. 3) Select Jupiter and set the FOV to about 0.2 o. Most of the Galilean Moons should be visible. Switch the Equitorial/Azimuthal mount. This will orient the moons on the screen more along our horizontal. Now set the FOV to about 0.03 o. Io will be now be off-screen. 4) Advance time until Io becomes visible on the screen. Click on Io and find out its magnitude. It should be about 6.5. As it approaches Jupiter, it will suddenly wink out and go to a magnitude of about 29. This is the moment that Io has gone into Jupiter s shadow. Record this time accurately to within a couple of seconds. This may take a couple of runs back and forth. Place this date and time information in the top box. 5) Select Jupiter again and record the distance between the Earth and Jupiter and put it in the box to the side (call this distance FAR_distance): PART VI: Estimation of Ionian Eclipse at the Near position In this part, we re going to calculate when Io will go into eclipse. We first will determine the number of orbits Io will make, and then add this to the observation we made in Part V. The equation is EclipseNearTime = EclipseFarTime + NumberOfOrbits*OrbitalPeriod. 1) Find the number of days between the approximate NEAR and FAR dates. These are the dates as determined in Part IV: 2) Find out and use the synodic period of Io (not the sidereal period): 3) Divide the number in item 1 by the number in item 2 (item 1/ item2):. 4) The number in item 3 is the number of orbits that Io will make around Jupiter between the FAR and NEAR dates. Round this number down to a whole number: 5) Multiply the number of orbits (in item 4) by the synodic period (item 2), DON T ROUND:. This is the amount of time to the predicted eclipse. 6) Add this number to the date and time boxed in Part V, and place it in the box below. Part VI: Stellarium observations of Jupiter eclipses of IO at Opposition 1) Turn on Stellarium. Turn off the ground, fog, and the atmosphere. 2) Set the Stellarium date and time so that it is about 10 hours prior to the time you boxed in Part V. Turn the passage of time off. 3) Switch to the Equitorial/Azimuthal mount 4) Select Jupiter and set the FOV to about 0.2 o. Most of the Galilean Moons should be visible. Switch the Equitorial/Azimuthal mount. This will orient the moons on the screen more along our horizontal. Now set the FOV to about 0.03 o. Io will be now be off-screen. 4
5) Advance time until Io becomes visible on the screen. Click on Io and find out its magnitude. It should be about 6.5. As it approaches Jupiter, it will suddenly wink out and go to a magnitude of about 29. This is the moment that Io has gone into Jupiter s shadow. Record this time accurately to within a couple of seconds. This may take a couple of runs back and forth. Place this date and time information in the top box to the side. 6) Select Jupiter again and record the distance between the Earth and Jupiter in the bottom box to the side (call this distance NEAR_distance). PART VII: Final Analysis Hopefully, you ve noticed that Io disappeared sooner than you predicted. The claim is that we should have expected this outcome, because light takes time to travel between sites. Since the FAR site is further away than the NEAR site, we ll notice the eclipse event sooner when Io and Jupiter are closer. Roemer deduced this way back in 1676. Here is the procedure: 1) Find the change in distance (Δd pronounced delta d, where the delta represents the change) a. Write out the FAR distance b. Write out the NEAR distance c. Subtract the two 2) Find the change in the times (Δt pronounced delta t) a. Write out the FAR time b. Write out the NEAR time c. Subtract the two (remember to convert units appropriately). 3) Now to find the speed of light, a. Divide the distance change by the time change, ( c = Δd/ Δt ) b. Show your result in meters/second. 4) Now the accepted value for the speed of light, c, is 3.00 10 8 m/s. So let s compare your calculated/measured value to the accepted value. a. Find the difference between your value and the accepted value: b. Divide this difference by the accepted value. c. Multiply by 100%. d. This is your percent error. Roemer measurement done in 1676 was 30% too low. How did you do? Conclusion Write a detailed conclusion, summary, and reflection about this exercise. 5