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The Luminosity of the Sun – due Mar 1 if we observe on Feb 22
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)
- 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.
- 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.
- 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 ~ 250 o^ C 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 ( L (^) sun ), 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 , I (^) sc. 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
“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
IF THE WEATHER IS BAD ON THE DAY OF THE LAB SESSION (Feb 22), we will have a lecture instead. The lab session would then occur at a later date, to be announced.
Figure 1: Photometer Components
of ~ 1.5 X 10^8 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/m^2 ).
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 I (^) sc 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
imaginary sphere, which has a surface area of 4π Dsun^2 , so
( 1 ) 4
2 sun
sun SC D
L I π
=
Therefore, the total amount of energy produced by the Sun each second (that is, the solar luminosity, L (^) sun ) can
be determined by measuring the solar constant ( I (^) sc ), 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 = mc^2 , 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 10^30 kilograms (or 2.0 X 10 27 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 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.
When a light source shines on one side of the photometer, the paraffin block on that side glows because it absorbs and scatters the light shining
Figure 2: A completed
photometer
Figure 4. Comparing the brightness of the Sun to a 300-Watt light bulb.
Turn the light bulb on.
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.
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.
- 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).
- 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
Measurement
Measurement
Measurement
Measurement
Average Value =
Table 1: Photometer measurements.
Weather Conditions: (circle best choice)
A. Clear
B. Some thin clouds away from the Sun
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
Name:___________________
- 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 = mc^2 , 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:
2 Sun
Sun 2
Energy kg c
L _____ _______
sec ond sec ond
L kg
______
c sec ond
The value of c, the speed of light, is 3x10 8 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 x10^30 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 10^7 seconds/year).
Time to convert all the mass in the core = Mass of the core / Rate of conversion = ______________ seconds
= ______________ years
