SUN-CENTERED PHYSICS

OUTREACH THEMES:

• Career awareness
• Information technology
• Organizing data
• Problem solving
• Teamwork
TEACHING OBJECTIVES:
Outcome:
Students will demonstrate their acquisition and integration of major concepts and unifying themes from the physical and Earth/space sciences.
Concept Indicators:
Most of what goes on in the universe involves one form of energy being transformed into another.
Everything in the universe is in constant motion; changes in that motion are due to the effects of forces.
All matter in the universe exerts gravitational forces.
Although energy is conserved, the total amount of energy available for transformation is almost always decreasing.
Energy is required for all technological processes.
Complicated motions are best described in terms of patterns, such as waves and vibrations.
Fission and fusion involve far greater energy changes than chemical reactions
Summary
The Sun is essential to life as we know it. Many of the physical phenomena that occur on the Earth are a direct result of the Sun-Earth interaction. These lessons are an attempt to bring the Sun into the foreground of a physics class. The first lesson involves the student in a calculation of the velocity and acceleration based on the position and time of a coronal mass ejection event. A series of photographs mark the motion of the mass as it is thrown into space.

The motion of the planets around the sun is typically used in the study of circular motion. In the next lesson, the students will be asked to determine the force of the sun on the earth, the force of the earth on the sun and finally, the mass of the sun from the information provided.

The movie "Independence Day" has once again raised the issue of alien life. Recent reports have indicated that four extrasolar systems have been discovered. The method used in all cases involves the motion of the star with respect to the center of mass of the system. A short compilation of three articles from Astronomy acts as a motivator in the calculation of the center of mass of the solar system. A further extension of the material includes a calculation using the Drake Equation.

The energy released from the Sun encompasses the entire electromagnetic spectrum. What is visible with the naked eye is only a tiny fragment of the energy released. Many features of the Sun become visible when other wavelengths are used. Students will read an educational brief from NASA on the electromagnetic spectrum and then compare images of the Sun in white light, the H-alpha wavelength, the calcium II K line, extreme ultraviolet, and radiowaves.

LESSON PLANS:

Position, Velocity and Acceleration
Centripetal Force and the Law of Universal Gravitation
Center of Mass of the Solar System
Introduction to the Electromagnetic Spectrum

LESSON 1: Position, Velocity, Acceleration and Force

Objective:
To use a coronal mass ejection (CME) to determine the relationship between position, average velocity and average acceleration and to analyze the motion of the coronal mass in terms of the forces acting on the body

Background:
Traditionally, students use a uniformly accelerated body (such as a cart on an incline) whose displacement is marked with a ticker or spark timer to calculate the average velocity and acceleration of the body. Frequently students are asked to plot a position vs time and a velocity vs time graph of this event. By providing the student with a series of images of the Sun showing a coronal mass ejection taken at known times and providing the information needed to determine the position of the mass, students can perform a similar manipulation of the data. The difference being that they are given real data which might not demonstrate uniform acceleration. This will help students realize that uniform acceleration is a special case NOT the standard.

A coronal mass ejection occurs when a "significant amount of cool dense plasma or ionized gas escapes from the normally closed, confining, low-level magnetic fields of the Sun's atmosphere to streak out into the interplanetary medium, or heliosphere." (SOHO....The Unquiet Sun) In other words, a large quantity of mass is accelerated by the magnetic field of the corona and travels through space eventually reaching the Earth. "Eruptions of this sort can produce major disruptions in the near Earth environment, affecting communications, navigation systems and even power grids. SOHO, with its uninterrupted view of the Sun, can observe such events continually, and allow us for the first time to get a better understanding of how such violent events occur."

Explanation for the teacher:
Students will use a series of images of the Sun showing the movement of the CME to calculate the average velocity and acceleration. They will be given the problem and asked to come up with their own solution. For students who have no clue, giving them the diameter of the Sun could point them in the correct direction. The following is an outline of one possible solution to the problem. Using proportions, the students will determine the position of a point of the mass for each frame and record the values in a table. To find the position from the surface of the Sun, students need to measure the diameter of the Sun and the distance of the mass from the surface. Knowing the actual diameter of the Sun, a proportion can be set up:

dsun1/dsun2 = smass1/smass2

where:
dSun1 is the diameter of the Sun measured on the screen
dSun2 is the actual diameter of the Sun
smass1 is the position of the mass as measured on the screen
smass2 is the actual position of the mass
Using the position and time, the students will first graph the data and then calculate the average velocity . Velocity is defined as the rate of change of position. Using the change in position and the change in time, the average velocity for the time period can be calculated using the following equation:
v = (s2 - s1)/(t2 - t1)

where:
s2 is the position at time, t2
s1 is the position at time, t1

Using the velocity obtained, the students can plot an average velocity vs time graph of this event. From the graph, students should be able to determine if the acceleration is uniform. (Uniform acceleration is indicated if the velocity vs. time graph is a straight line.) If the graph is a curve, the acceleration changes with time. The average acceleration, defined as the rate of change of velocity, can be calculated in a similar manner using the following equation.
a = (v2 - v1)/(t2 - t1)

where:
v2 is the velocity at time, t2
v1 is the velocity at time, t1

There is a problem with calculating the acceleration from the average velocity. If the acceleration is constant, the instantaneous velocity is equal to the average velocity in the middle of the time interval. (Or: the instantaneous velocity at the end of the time interval is twice the average velocity.) This might be an area where the students will require a little guidance.

Discussion of results:
The average acceleration obtained by the student will depend on how he/she decided to determine the position. It is clear from the images that a plume of gas is moving faster than that of the body. Should the student chose to follow the plume instead of the center, the average velocities and accelerations will be greater.

Student Handout:

PROBLEMS:
To use a coronal mass ejection (CME) to determine the relationship between position, average velocity and average acceleration.
To analyze the motion of the coronal mass in terms of the forces acting on the body

REQUIREMENTS:

1. A brief statement of how you determined the position, velocity and acceleration with equations and sample calculations.
2. A completed data table
4. A conclusion discussing the results of the experiment. You need to explain what type of motion the mass has undergone and account for any changes in the velocity.

Materials

SOHO CME IMAGES
ruler
calculator

DATA TABLE:
Universal Time Time Interval PositionAverage VelocityAverage Acceleration
08:05 _ ___
08:36 ____
09:27 ____
10:25 ____
11:23 ____

Questions:

1. Identify the forces acting on the mass.
2. As the gas bubble moves away from the sun, how does the size change?. Account for this.
3. In the second frame, there is a portion of the gas that appears to be separating from the rest. In terms of forces, account for this motion.
4. Would you expect the acceleration of the main body and this other portion to be the same? Why or why not?

LESSON 2: Centripetal Force and the Law of Universal Gravitation

Objective:
Students will use astronomical data to calculate the centripetal force of the Sun on the Earth.
Students will use the law of universal gravitation to calculate the mass of the Sun.

Background:
Traditionally, the movements of the planets around the Sun and the moon around the Earth have been used in the study of centripetal forces and the Law of Universal Gravitation. The first step is to have the students calculate the centripetal force exerted on the Earth by the Sun and the force of the Earth on the Sun. Students will be given the mass of the Earth and its average distance from the Sun. The next step is to have the students determine the mass of the Sun from the period of revolution around the Sun and the average distance of the Earth from the Sun by equating the centripetal force with the gravitational force as shown below.

Fcent = Fgrav
4(pi)2mer/T2 = Gmems/r2
ms= 4(pi)2r3/(GT2)
where:
me is the mass of the Earth
ms is the mass of the Sun
r is the average distance from Earth to Sun
T is the time for the Earth to move around the Sun
G is the universal gravitational constant

STUDENT HANDOUT:

PROBLEM 1:
What force does the Sun exert on the Earth?
What force does the Earth exert on the Sun?
PROBLEM 2: What is the mass of the Sun?

REQUIREMENTS:

1. Show the equation(s)
2. Solve the equation(s) for the unknown
3. Identify any values not given to you
4. Substitute the variables

USEFUL INFORMATION:
mass of the Earth: 5.974 X 1024 kg
average Earth-Sun distance: 1.496 X 1011 m
Note: this information may be useful for both problems.

LESSON 3: Center of Mass of the Solar System

Objective:
Students will calculate the center of mass for the solar system and explain how this concept is being used to search for planets outside our solar system.

Background:
As a result of the movie "Independence Day", one of the hottest topics of conversation is the possibility of Earth being visited by aliens. For years, scientists have been searching for evidence that there are in fact other solar systems. Just recently, four extra-solar planetary systems have been discovered. This was done by looking for regular changes in the Doppler shift of stars caused by the motion of the star around a center of mass of the star-planet system (which is not at the center of the star). The off-set of the center of mass is caused by the presence of another body (the planet) moving around the star. Thus far four stars or star-like objects outside out solar system have been found to have planets orbiting them. The first to be discovered consisted of three planets revolving around a pulsar (which is a rapidly turning neutron star). The second is a planet two times the mass of Jupiter in an orbit that is closer to the Sun-like star than Mercury is to our Sun. The conditions on these planets make them hostile to life as we know it. Two other Jupiter-sized planets were found which are in a better position to yield life. The first is orbiting the star 47 Ursea (approximately 40 light-years away) which has a mass of about 3.5 Jupiters and an orbit somewhere between that of Mars and Jupiter. The second is the planet around 70 Virginis (about 70 light-years away) which is about 8 Jupiters in mass and 4/10 the distance of the Earth from the Sun.

References:
Stephens, Sally: "Second Chance Planets", Astronomy, Jan 1996.
Naeye, Robert: "Is This Planet for Real?", Astronomy, Mar 1996.
Naeye, Robert: "Two New Solar Systems", Astronomy, Apr 1996.

Calculation of the center of mass of a system is generally a part of the introductory physics class. Calculation of the center of mass of the solar system and a discussion about how astronomers are making use of this value in prospecting for planets outside the solar system add a motivational factor to the calculation.

Procedure:
To spike the student's interest, the reading "Planets Found Outside the Solar System!" will be given to the students. It is a summation of the three articles on extra-solar planets.

After students are familiar with the concept of center of mass, a list of the planet's masses and distances from the Sun will be displayed. The students will be asked to predict which of the planets will have the greatest impact on the position of the center of mass of the solar system. It is hoped that they will pick Jupiter as it is the most massive of the planets. Students will probably be surprised that the center of mass of the solar system lies within the surface of the Sun yet this causes the Sun's position to vary slightly with time.

Calculation of the probability of finding life is an interesting open-ended question that will demonstrate to the student that there are some problems for which there is no known "right" answer. Their estimations are as good as the next as long as they can support their answers with logical reasons.

STUDENT HANDOUT

PROBLEMS:
1. Which planet has the greatest influence on the center of mass of the solar system? WHY?
2. Calculate the center of mass of the solar system given the following data.
3. Using the equation supplied, calculate the probability of finding life in the universe. The equation was written by Frank Drake (and is known as the Drake Equation) to estimate the number of civilizations in our galaxy that would be able to contact each other.
REQUIREMENTS:
Problem 2:
1. Show the equation(s)
2. Solve the equation(s) for the unknown
3. Identify any values not given to you
4. Substitute the variables
Problem 3:
1. identify the value for each variable
2. State a reason for your choice in number one.
3. Show substitution into the equation
DATA:
Name of Planet Mass of Planet X 10 23 kg Distance of Planet from Sun X 10 9 m
Sun 19910000 ------
Mercury 3.30 57.9
Venus 56.7 108.2
Earth 59.7 149.6
Mars 31.8 227.9
Jupiter 669 778.3
Saturn 562 1427
Uranus 245 2871
Neptune 233 4497
Pluto .199 5914

DRAKE EQUATION:

N = (R*)(fp)(ne)(fl)(fi)(fc)(L)
where:
N = number of civilizations in our galaxy able to communicate
R* = the rate at which stars form in our galaxy
fp = the fraction of the stars that have planets
ne = the number of planets per solar system that are suitable for life to survive
fl = the fraction of these planets on which life actually arises
fi = the fraction of these forms that develop intelligence
fc = the fraction of intelligent species who choose to communicate
L = the lifetime of such a civilization

Planets Found Outside The Solar System!

The first confirmed "sighting" of a planet outside the solar system occurred in the most unlikely place: around a pulsar. A pulsar is a very massive, very small, rapidly-spinning neutron star which forms as a result of the star running out of fuel and going supernova. A supernova explosion is very violent as the star's outer layer is ejected and sweeps out the region around the star leaving it free of debris. The core of the star collapses to the point where protons and electrons are squeezed together to make neutrons. The angular momentum of the star is conserved in the explosion so the new, much smaller star spins very rapidly. (Most pulsars rotate at a rate of less than one second per spin.) The rapidly-spinning star generates a large amount of energy which is ejected through the magnetic poles of the star. If the star is oriented so that the pole is pointed toward Earth during part of the spin, we see a pulse of energy much like a sailor sees the light house beam sweep past; thus the name pulsars.

Despite the unlikelihood of finding planets around pulsars, that is exactly what has happened. Four years ago, radio astronomer, Alex Wolszczan (pronounced VOL-shtan), found three and perhaps four small planets orbiting the millisecond pulsar PSR 1257+12 which he and a colleague had just discovered. Millisecond pulsars rotate hundreds of times per second and are more precise that atomic clocks. It is possible to predict arrival times of the radio pulsar to an accuracy of 3 milliseconds. PSR 1257+12 is a relatively old pulsar which should have a very regular pulse. Wolszczan noticed that the signal would sometimes arrive a few milliseconds early or a few milliseconds late. He also realized that there was a pattern to the variations that seemed somewhat periodic. After further analysis, he discovered two periods; one of 66.6 days and the other lasting 98.2 days which lead him to theorize that there are planets around the pulsar. The variation in the arrival times being caused by the planet's gravitational tug on the pulsar causing it to move ever-so-slightly toward and away from us. After publishing his results, many astronomers remained skeptical, theorizing a wobble in the axis of rotation or something strange happening inside the star. In 1994, after continuous monitoring, the perturbations caused by the gravitational interaction of the two planets was observed and the doubts were removed. These observations revealed the presence of a smaller, third planet and perhaps even a fourth one. The other half of the question is how the planets came to be orbiting a pulsar and many theories have been put forth to explain them. If you are interested in the explanation, refer to the article cited below by Sally Stephens.

The next extra solar planet was discovered by Michel Mayor near the Sun-like star, 51 Pegasi, located 55 to 60 light-years away. Based on the amplitude of the star's motion, the planet is one-half to two times the mass of Jupiter in an orbit that is 1/20 of the Earth's distance from the Sun. The orbital period of the planet around 51 Pegasi is 4.2 days. The temperature on the planet is estimated to be about 1000oC, much too hot for life as we know it.

Viewing the planets directly is not possible because the star is about a billion times brighter than the planet. The only way to "see" the planet is through the gravitational pull it exerts on the star. The rotation of the system about a common center of gravity, causes a repeating pattern in the position of the star which is detected in the spectrum. By repeatedly observing a star, this pattern becomes apparent. In the case of 51 Pegasi, the pattern repeats every 4.2 days like clockwork.

The next two planets were discovered by Geoff Marcy and Paul Butler who have been observing 120 solar-type stars since 1987. The team has been putting its effort into improving the detector and software rather than analyzing the data. After the announcement by Mayor, the team decided that their data might be good enough to detect large planets so they borrowed six powerful computers that they ran day and night analyzing 60 stars. Early in January 1996, the telltale patterns of two planets around two stars popped up. Both planets are more massive than Jupiter and are thought to be giant gaseous planets with rocky cores. The first is orbiting the star 47 Ursea (approximately 40 light-years away) which has a mass of about 3.5 Jupiters and an orbit somewhere between that of Mars and Jupiter. This planet has roughly Jupiter's mass and a Jupiter-like orbit that looks like it could fit into our solar system. The second is the planet around 70 Virginis (about 70 light-years away) which is about 8 Jupiters in mass and 4/10 the distance of the Earth from the Sun. Because of its distance from the star, the temperature at the cloud tops is estimated to be about 85oC which is "just right" for liquid water and has been dubbed the "Goldilocks" planet

Excerpts from:
Stephens, Sally: "Second Chance Planets", Astronomy, Jan 1996.
Naeye, Robert: "Is This Planet for Real?", Astronomy, Mar 1996.
Naeye, Robert: "Two New Solar Systems", Astronomy, Apr 1996.

Discussion Questions:
1. Why has it taken so long for scientists to find planets?
2. Do you think there is life on 70 Virginis-B (the planet around 70 Virginis)?
3. Do you think there is intelligent life "out there"?

List of Lesson Plans

LESSON 4: Introduction to the Electromagnetic Spectrum

Objective: Students will be able to discuss the parts of the electromagnetic spectrum and give the relative energy of each part.

Background: In order to provide the student with an appreciation of the range of the electromagnetic spectrum, images of the Sun will be examined in the visible, H-alpha(red), Ca-K line (blue?), radio, and x-ray The images will be taken from the same day so that features visible in one wavelength can be compared to features in another wavelength. The differences in the Sun's image are caused by the fact that different parts of the Sun produce different frequencies of radiation. For example, x-rays are produced by the corona and so an image in x-ray wavelengths, will show the corona of the Sun. Since the photosphere and chromosphere do not produce x-rays, the disc of the Sun appears black in x-ray images.

Student Handout:

PROBLEM:

To compare images of the Sun taken in different wavelengths.
To discuss the relative energy of the regions of the electromagnetic spectrum.
REQUIREMENTS
1. Read and answer discussion questions on THE ELECTROMAGNETIC SPECTRUM found in the NASA Educational Briefs for Secondary Classrooms. Click here to go to the brief.
2. Look at the images of the sun as outlined below and write a statement comparing the images.

IMAGES OF THE SUN:

All images are from July 8, 1996. Since we are in a period of minimum sunspot activity, there are few features on the Sun. Read the description for each image and then click on the underscored section of the description to view the image. To return to this screen, click on the BACK button at the top of the screen.

1. The first image in white light taken at the Big Bear Solar Observatory shows a set of sunspots near the equator in the lower right quadrant.

2. The second image is from a very narrow band of visible light. The band corresponds to the red emission line from hydrogen and is called the hydrogen alpha (H alpha) line. The bright areas are plages (pronounced "plah'jes") which surround sunspots. The dark areas are filaments marking the location of zero magnetic field that separate regions of positive and negative magnetic polarities. When on the limb of the sun, they are called prominences

3. Another slice of the visible spectrum is the calcium II K-line which shows the chromosphere supergranulation features.

4. The Muana Loa Solar Observatory produced this H alpha coronagraph which shows a prominence at the edge of the Sun between 2 and 3 o'clock and a second feature between 4 and 5 o'clock. The corona of the sun is only visible during a solar eclipse because it emits little visible light and the photosphere outshines the corona. The corona is the hottest part of the sun and extends far out into the solar system. The corona is so hot it emits mainly X-rays.

5. The Mount Wilson Observatory Dopplergram shows the convection currents and granulation on the Sun.

6. The magnetogram image shows the polarity of the Sunspots. The polarity of the sunspots is determined from the direction of the Zeeman splitting and the strength of the field from the extent of the splitting. The Zeeman effect is the splitting of certain spectral lines when in a magnetic field. Since sunspots are magnetic in nature, the polarity and strength of the magnetic field can be determined by utilizing the Zeeman effect.

The next four images are from SOHO (Solar and Heliospheric Observatory) which is a satellite at the "L1 Lagransian point" between the Earth and the Sun. Each of the following images shows a small piece of the extreme ultraviolet region and are used to show detailed magnetic features.
Fe IX/X: wavelength = 17.1 nm
Fe XII: wavelength = 19.5 nm
Fe XV: wavelength = 28.4 nm
He II: wavelength = 30.4 nm

7. The Yohkoh Soft-X Telescope produces an image of the corona as seen in X-ray. The photosphere doesn't produce X-rays so the disc of the sun appears dark in contrast to the corona.

8. Nobeyama Radio Heliograph 17 GHz shows bright area over sunspots and the prominences visible on the coronagraph.