Labs from Chicago, Summer 1993 :
Measuring the Wattage of the Sun and a "Standard Candle."

Dr. Jim Sweitzer
Labs written for the CARA Space Explorers, Summer 1993

This is meant to be handed out to the students.

Introduction

By now you should now know quite a bit about light and the way it behaves. Last week you determined the distance between the Earth and the Sun. This distance is called the astronomical unit and is equal to 150,000,000 kilometers(*). Today you and your partner are going to put this knowledge together to actually determine the power (in watts) radiated by the Sun. Think of it, by simply applying the "inverse square law" you will be able to determine the energy output of the greatest powerhouse in the entire Solar System!

* Footnote: Let's put this in some other forms. Since there are 1,000 meters in a kilometer and 100 centimeters in a meter, the distance to the Sun in centimeters is = 150,000,000 X 1,000 X 100 = 15,000,000,000,000 cm. A good shorthand is to write this distance as = 15 x 10^12 cm. Where you simply count the number of zeros and place them in the exponent after the 10. This is called scientific notation and sure makes life easier.

But we're not going to stop here. Using the same technique used to get the wattage of the Sun, you will also determine the wattage of a very small light bulb. The reason for this is that we will then take this very small light bulb up to Yerkes Observatory and compare it to stars in the sky. It will be our reference standard. Astronomers sometimes call such things "standard candles," so that's what we'll call it. Once we know it's wattage along with how far away it is, we will be able to get the distances of a star like the Sun, by simply assuming that the star is the same wattage as the Sun. It seems odd, but with just a couple of measurements today, we will be all set to determine some of the greatest distances in the Universe.

Inverse Square Law (again)

Our theoretical tool will be the Inverse Square Law. It is very powerful, even though it seems quite simple. For today's lab we will write it as the following equation:

[Intensity of source of light at a distance] =[Power output of source]/[Distance to source]^2

Written as symbols this is: I = W/D^2

To use this equation today, we will want to solve for W. That is actually very simple. All we have to do is multiply both sides of the equation by D^2. Thus, the wattage of the sources of light we are investigating is simply W = ID^2. This would be great if we could just directly measure I, the intensity. Well, it's not that easy. What is simple, however, is to compare the light from two sources and determine that the intensity is the same from both sources. So, we'll build a comparison photometer to tell us when the light from two sources is the same. That way, if we know the wattage and two distances, we can solve for the other unknown wattage.

It works like this: Suppose we have two sources of light that are in the right place to emit the same amount of light. If source number 1 is given by the equation below with 1's in parentheses and the quantities for source 2 are shown with 2's in parentheses, then: I(1) = W(1)/D(1)^2 and I(2) = W(2)/D(2)^2

But, since we will match the two intensities so that they are equal with the comparative photometer, then I(1) = I(2). This allows us to write just one equation from two, but setting the I's equal to one another. We get W(1)/D(1)^2 = W(2)/D(2)^2

This equation allows us to solve for a wattage (W(2)) if we know the two distances and the wattage of source 1 (W(1)). All we have to do is multiply by the denominator on the right side. That gives us the final equation we will use today. [W(1)/D(1)^2] * D(2)^2 = W(2)

Procedure

To make life easier, you'll find a table to fill in your work as you go along. Here's the basic procedure.
  1. First do the activity labeled Part A CONSTRUCTING A SIMPLE PHOTOMETER.
  2. Then, place the 100 watt bulb about 2 meters away from the two bulbs together and measure the wattage of the 2 bulbs with the photometer.
  3. Then, take your photometer and a short ruler up to the penthouse level of the building and measure the Sun's wattage in using the activity labeled Part B. Again, use your work sheet.
  4. Finally, come back inside and measure the wattage of the little "standard candle" using the same procedures. Record your results on the work sheet.
  5. When you've taken all the measurements and done all the computing, then average your results for each source and write the averages at the bottom of the page.

Connections to Yerkes Summer Institute

Once you have done all this, then you are ready to make more similar measurements at Yerkes. We will keep using the Inverse Square Law, but this time will solve it for the distance. If there's any time left today, take the second to last equation above and see if you can't solve it for D(2). Write your work in the space below.

Work Sheet

[The worksheet doesn't translate into hypertext very well at all. I've tried to make clear what it used to look like. -- ed.]

Recall how the different symbols are defined:
W(source) = the power output of "source" -- units are watts
D(source) = distance from photometer to "source" -- units are centimeters
I(source) = intensity of light from "source" -- units are watts/(cm2)

Record your observations, computations and results in this table. Note that you must repeat your observations four times for each set of sources. Average your final results for each of the three unknown sources and write the final answers in the table at the bottom of the page

source 1       D(source 1)   D(source 1)^2  I(source 1) =
                  (cm)          (cm^2)        W(1)/D(1)^2.
                                            (Watts/cm^2)
100 watt bulb
   trial 2
   trial 3
   trial 4
200 watt bulb
   trial 2
   trial 3
   trial 4
100 watt bulb
   trial 2
   trial 3
   trial 4
source 2       D(source 2)   D(source 2)^2  W(source 2) =
                  (cm)          (cm^2)        I(1)*D(2)^2.
                                              (Watts)

2 bulbs together
   trial 2
   trial 3
   trial 4
Sun
   trial 2
   trial 3
   trial 4
"standard candle"
   trial 2
   trial 3
   trial 4


Summary Results (Average wattage) for each source:
2 BULBS TOGETHER = ________WATTS,
SUN = ______________WATTS,
STANDARD CANDLE= ______ WATTS

Important Disclaimers and Caveats


Go back to the Chicago Summer 1993 home page.