The Luminosity of the Sun – due Mar 1 if we observe on Feb 22

IF THE WEATHER IS BAD ON THE DAY OF THE LAB SESSION (Feb 22), we will have a lecture instead. The lab session woul d then occur at a later date, to be announced.

“The Sun, with all the planets revolving around it, and depending on it, can still ripen a bunch of grapes as though it had nothing else in the Universe to do.” --Galileo Galilei

Before you arrive for the lab session, be sure to read the entire handout. Make sure you understand 1) the quantities that will be measured, 2) what a photometer is, and 3) how to calculate the surface area of a sphere. On the day of the lab, you will be provided with hard copies of the data entry sheets at the end of this

READ THIS HANDOUT BEFORE THE LAB SESSION!

During the lab session, you will make some measurements. All of your data should be recorded in the appropriate places on sheet given out during the lab . At the end, you will be asked to answer relevant questions and perform some calculations using the data. Please place your answers in the spaces provided in the handout. You will share data with members of your observing group but all calculations and answers to questions should be done by you alone.

Checklist for work to be completed during the lab session: (order of the activities is not important)

1) With members of your observing group, set-up your light bulb, baffle, and paraffin block facing the Sun as sketched in Figure 4. Page 3 gives detailed instructions. 2) With members of your observing group, make the measurements to fill in the table the data sheet passed out at the start of the lab. 3) Look through the telescopes that are set up just outside the lecture hall. Answer questions and make the drawing on the data sheet.

Due date for turning in the lab assignment is one week after the lab session (March 1, if it is clear on February 22 ).

1. Introduction

The temperature of the Earth is determined by the luminosity of the Sun. Although Earth has a hot molten core, the Sun contributes 99.98% of the energy that heats our planet. The next largest heat source (< 0.02%) is the decay of long-lived radioactive isotopes in Earth's interior. If the Sun were to turn off suddenly, the Earth's surface temperature would drop by ~ 250oC and all the water on Earth would turn to ice. On the other hand, if the Sun were much brighter, or much closer to the Earth, solar radiation would raise the planet's surface temperature and all our rivers, lakes and oceans would vanish in a puff of steam.

The total amount of energy that the Sun radiates into space per second is called the solar luminosity (Lsun), which is measured in energy per unit time, or Watts, just like a light bulb. The solar energy reaching the Earth is measured by the solar constant, Isc. The solar constant is defined as the total amount of solar energy that enters the top of the Earth's atmosphere per unit time per unit area, with an average distance of the Earth from the Sun

1 of ~ 1.5 X 108 km or 1 astronomical unit (1 AU). The solar constant is measured in units of energy per unit time per unit area, or Watts per square meter (W/m2).

The solar constant is not a true constant because the luminosity of the Sun fluctuates by a tenth of a percent or so. Scientists who study the Earth's climate and the greenhouse effect continuously monitor the solar constant because changes in Isc cause changes in the temperature of the Earth's atmosphere. Although the changes in the solar constant appear to be very small, only by monitoring it can we learn whether changes in the Earth’s temperature are due to the changes in amount of solar energy we receive or some other cause.

Both the solar constant and the solar luminosity are fixed by the total amount of energy produced by thermonuclear reactions in the core of the Sun, so they can be related by a simple formula. Imagine a sphere with a radius of Dsun = 1 AU, centered on the Sun. The solar constant is the number of Watts that pass through each square meter of this sphere every second. All of the energy radiated by the Sun must pass through our 2 imaginary sphere, which has a surface area of 4π Dsun , so L sun I SC = 2 (1) 4π Dsun

Therefore, the total amount of energy produced by the Sun each second (that is, the solar luminosity, Lsun) can be determined by measuring the solar constant (Isc), knowing the distance from the Earth to the Sun (Dsun).

During the lab activity you will measure the solar constant and calculate the solar luminosity. You will determine the solar luminosity by comparing the power output of the Sun to the known power output of a light bulb. Near the end of this lab, with help from Einstein's relation between mass and energy, E = mc2, you will calculate the rate at which nuclear reactions in the core of the Sun consume mass. The total mass of the Sun is 2.0 X 1030 kilograms (or 2.0 X 1027 tons!), of which about 10% can sustain these reactions. You can predict the lifetime of the Sun by calculating how long it would take the Sun to burn all of this Figure 1: Photometer Components mass. You'll then compare these answers to the current age of the Sun, 4.5 billion years. It may come as a surprise to you that even with such simple experiments you can learn about processes occurring in the center of our Sun!

2. How We Use a Photometer to Measure the Sun's Luminosity A photometer is a device to measure the apparent brightness of a source of light, by detecting the amount of light falling on the device. In this experiment, we will use a simple photometer made with two blocks of paraffin wax and which uses your eyes as the detectors. The two blocks are separated by a sheet of aluminum foil and held together by rubber bands. (See Figures 1 and 2.) These photometers will be supplied to you already assembled. Figure 2: A completed When a light source shines on one side of the photometer, the paraffin photometer block on that side glows because it absorbs and scatters the light shining

2 on its surface. The closer the light is to the photometer, the brighter the wax block will appear to be. The apparent brightness (I) of the paraffin block is determined by the inverse square law kL I = (2) 4π d 2 where d is the distance from the light source to the photometer, measured in meters, L is the luminosity of the light bulb in Watts and k is a factor that account for absorption in the paraffin.

The block on the opposite side remains dark because the light is reflected by the aluminum foil and cannot pass through. (See Figure 3.) If another light source is placed on the opposite side of the photometer, then that side will also glow and the apparent brightness of that block can also be calculated using the inverse square law.

Now suppose that we want to measure the luminosity of Sun and we know how far it is from the photometer. The side of the photometer that faces the Sun will glow. If we place a light bulb with a known luminosity on the other side, then that side of the paraffin block will also glow, but not with the same brightness. However, if we move the light bulb so that the apparent brightness of both sides of the photometer are the same, then we can calculate the luminosity of the Figure 3. The side of the paraffin facing the light glows. Sun. (See Figure 4.) We are in effect using the photometer to compare the brightness of the Sun to a light bulb with known output.

When the two sides of the photometer glow with the same brightness, the apparent brightness of the paraffin on the light bulb side is equal to the solar constant, or I = Isc, where I is the apparent brightness from the light bulb and Isc is the apparent brightness of the Sun. Substituting the inverse square law into this equation we find that

LLBulb sun 2 = 2 (3) 4dπ Bulb 4Dπ sun where LBulb and Lsun are the luminosities of the light bulb and the Sun, respectively, and dBulb and Dsun are the distances of these two sources from the photometer. Assuming the paraffin blocks on either side of the aluminum foil are similar, the factor, k, cancels out. We already know LBulb and Dsun, and we can measure dBulb, so this equation can be manipulated to give the luminosity of the Sun, Lsun.

The experiment works better if the paraffin block is partially surrounded by a baffle to keep stray sunlight from reaching it. You can use pieces of black cardboard to make a baffle, as indicated in Figure 4.

3. Measuring the Sun's Luminosity in Watts

1. This is an outside activity. Each group of students will be given a 300-watt bulb, an extension cord, a photometer, a ruler, and a large piece of black poster board.

3 2. Turn the light bulb on.

3. Hold the photometer between the Sun and the bulb with the bulb's filament parallel to the face of the photometer. Hold the other face of the photometer towards the Sun (see Figure 4). One of you should hold the cardboard baffle around the paraffin block. Try to point the face of the paraffin block directly at the Sun.

4.

Figure 4. Comparing the brightness of the Sun to a 300-Watt light bulb.

Move the photometer toward and away from the Sun, stopping when the two sides have the same apparent brightness. The color difference between the Sun and the bulb will cause a color difference on either side of the paraffin. Just keep in mind that the apparent brightness on both sides of the paraffin should be similar in intensity rather than color.

5. Hold the photometer steady while a member of your group measures the distance in centimeters between the bulb filament and the aluminum in the photometer. Assume that the filament is at the center of the bulb. Make observations as carefully and consistently as you can. Record each measurement on the data sheet passed out in class (also shown below).

6. As a check on your first value, repeat the above step four more times, switching responsibilities with your group members each time. Also, try reversing the paraffin block so the sun and light bulb shine on the opposite sides from where you started. Again, record your measurements in the table below. If there is a major discrepancy between any of the measurements (more than a couple of centimeters), then additional measurements are needed. On the other hand, if the five measurements are fairly close in value, average them to yield a single measurement. (The table below will be distributed on a sheet in class).

Bulb distance, dBulb (cm) Measurement #1 Measurement #2 Measurement #3 Measurement #4 Measurement #5 Average Value = Table 1: Photometer measurements. Weather Conditions: (circle best choice) A. Clear B. Some thin clouds away from the Sun 4 C. Some thin clouds covering the Sun D. Some thick clouds away from the Sun

Name:______Section:______

Print out this page and the following two pages. Please turn in these three pages as well as your data sheet from the lab.

This portion of the lab is to be done on your own after class.

Answer the questions below. You can get views of the sun over the internet at the following URL: http://coolcosmos.ipac.caltech.edu/cosmic_classroom/multiwavelength_astronomy/multiwavelength_museum/sun.html and some individual examples at: http://sohowww.nascom.nasa.gov/sunspots/ for broad band visible http://www.bbso.njit.edu/Images/daily/images/hfull2.jpg H alpha emission line http://umbra.nascom.nasa.gov/images/latest_eit_171.gif for extreme ultraviolet/soft X-ray

Compare the appearance of the sunspots. Since we are near solar minimum, there may not be many now (but look carefully at the images at the links above). However, there is a collection at http://sohowww.nascom.nasa.gov/bestofsoho/ showing activity in previous solar cycles.

Use the images at these sites to answer the following questions (use the links to the H alpha and X-ray images):

Because they are cooler than the surrounding photosphere, they are dark in the ______a.) visible b.) H alpha emission c.) Ultraviolet/X-ray

Because they are the sites of high energy particles, they or the surrounding regions are bright in the ______a) visible b.) H alpha emission c.) ultraviolet/X-ray

Hot gas streaming out into the corona from active regions becomes clear in the ______a.) visible b.) H alpha emission c.) Ultraviolet/X-ray

5 Computing the Sun’s Luminosity and Lifetime

Name:______

1. Solving for the Sun's luminosity (or the solar luminosity) requires several steps, which are outlined below. (a.) What is the average distance between the 300-watt bulb and your photometer (in cm)? How many meters is 8 this? This distance in meters is the value of dbulb to use in (b.). The Sun is about 1.5 X 10 km from the Earth. How many meters is this? This distance is the value of DSun to use in (b.). Be careful to express these distances as a number with a unit (eg., 10 cm rather than just the number 10).

(b.) Equation (3) is reproduced below and then re-arranged algebraically to isolate Lsun which is the quantity we are measuring: LL Bulb= sun (3) 4dπ 2 4Dπ 2 Bulb sun LLBulb22 Bulb L4DDSun=•π=•2 sun2 sun 4dπ Bulb dBulb

So LSun =

Plug in the numbers on the right hand side of the equation and compute LSun. This will be your derived value of the Sun's luminosity.

26 2. (a.) The accepted value of the Sun's luminosity is Lsun = 3.8 X 10 W. How does your value compare to the accepted value (express this comparison mathematically by stating “My value is XX% greater [or smaller] than the accepted value).

(b.) Why do you think your derived values for the Sun's luminosity is different than the average accepted values? (Hint #1: The light bulb filament is cooler than the surface of the Sun, so it is only 1/3 as efficient in converting watts to visible light. Hint #2: Think about the sources of error in measurement, etc,)

6 Name:______

3. Use your derived value of the Sun's luminosity from Question #1 to predict how long the Sun will continue to burn. Recall that the Sun is converting 4 hydrogen atoms to one helium atom in its core, and that a small amount of matter is converted to energy in this process. Einstein’s famous equation, E = mc2, expresses how much energy is produced when mass is converted to energy. A Watt is the same as 1 Joule /second and a Joule is a unit of energy. The Sun’s luminosity can be equated to the energy produced from the rate at which mass is being converted in the core of the Sun: Fill in the blanks in the equations below:

Energy kg c2 LSun == ______second second L kg Sun = ______c2 second

8 The value of c, the speed of light, is 3x10 meters/second. Substitute for c and use your measured value for LSun to compute the rate at which mass is being converted to energy in the Sun’s core:

Rate of mass conversion to energy = ______kg/second

When hydrogen is converted to helium, only a small fraction of the original mass of hydrogen is converted to energy; most of the mass remains as helium. Only 0.7% of the hydrogen mass disappears and is converted to energy. At what rate is hydrogen participating in the conversion of H to He:

Rate of hydrogen conversion to helium = 0.007 x ______kg/second

Only the hydrogen in the core of Sun where the temperature and pressure are sufficiently high can be converted to helium. The core contains 10% of the mass of the Sun. The mass of the Sun is 2 x1030 kgs. Compute the mass of the Sun’s core.

Mass of the core of the Sun = ______kg

If hydrogen is being converted to helium at the rate you calculated above, how long will it take to convert all the mass in the core of the Sun to helium? (express your answer first in seconds and then convert to years; The number of years is the number of seconds divided by 3 X 107 seconds/year).

Time to convert all the mass in the core = Mass of the core / Rate of conversion = ______seconds

= ______years

7