AST 309-TIME
Comparing Two Clocks

Procedure:

At the beginning of each class period we will do a time check between your watch (Clock A) and the standard (Clock B). I will tell you what my clock is going to read at the next whole minute, which you will write down on the accompanying table. I will then count down to that minute, and at the instant I say "Mark!" you should note the exact reading of your watch, to the nearest second (or tenth of a second, if you want to try estimating that), and write that information on the table. You can then calculate the offset between our two clocks by subtracting B from A, and entering that in the table. If the offset is more than one minute, write it down in seconds, e.g., if the offset is +1 minute 8 seconds write down +68 seconds.

Example: Suppose at 12:33:00 by the standard clock (B) your clock (A) reads 12:31:32. Then (relative to my clock) your clock is 1 minutes 28 seconds slow, or 88 seconds slow. Write down -88 seconds in the last column.

You may not get every reading because of class periods missed; That is not terribly important, but you should get as much data as you can.

Writing up your results:

If you are working with a classmate, you will be using the same data, but you should each write up your results independently.

For your convenience, I have included a column in the data table that gives the number of days since the start of the experiment. This will make it easier for your to graph your results. Take a piece of graph paper, and set up horizontal and vertical axes on it. Mark the horizontal axis in days, and the vertical axis in seconds of offset. Be sure that the scales on the axes are chosen so that all of your data can be plotted! Plot the offsets against the day, from your table. You will probably find that the data lie approximately on a sloping line. By eye (using a ruler to keep the line straight) draw the straight line that best fits the points on your graph (see example, last page of write-up). Then answer the following questions, and turn everything in, including your graph.

1. If you took data with another student, please write down the name and social security number of that student:
   
   
2. What kind of clock are you using (digital, analog, mechanical? Brand name?)
   
   
3. Did your clock, on average, gain or lose time, relative to my clock, during the course of the experiment?
   
   
4. On average, how many seconds per day did it gain (+) or lose (-)? Hint: Use the straight line you drew on the graph as a guide for estimating the average number of seconds gained or lost during the whole period of time. Divide that by the number of days the experiment lasted.
   
   
5. If the straight-line approximation is a good one, then your clock gained or lost at a nearly constant rate relative to mine. Is this what actually happened? Or is there evidence that the gain or loss was erratic? If it was erratic, do you have any guesses as to what might have caused it to be erratic?
   
   
6. How good is your data? Estimate this by looking at the average deviation of the points you plotted from the straight line you drew.
   
   
   
7. Please identify any points where you could have inserted or deleted "leap minutes" in order to keep your clock reading within +/- 45 seconds of mine. Would they have been positive "leap minutes" (insert an extra minute) or negative "leap minutes" (delete a minute)?
   
   
   

SAMPLE GRAPH

From this sample graph I determine that my clock is gaining on the standard clock. In 40 days it went from being 2 minutes behind to 1.1 minutes ahead, a total of 3.1 minutes, or about 3.1x60 = 186 seconds. This took 40 days, so that is about 4.6 seconds per day.

The average deviation of the points from the line on this graph is about 20 seconds.

The normal scientific practice is to let a clock run continuously without ever resetting it. Resetting can never be done perfectly, and each time we reset a clock we would introduce a new error. Instead of resetting the clock, we keep a record of the offset between our clock and the standard clock. Usually the standard is something like WWV (a radio signal transmitted by the National Bureau of Standards), LORAN-C, or a satellite standard such as GPS (Global Positioning System, a set of special satellites maintained by the Department of Defense). During the course of this experiment, this is the procedure you should follow.

TABLE FOR RECORDING YOUR DATA