The Starbase One Astronomy & Space Collection/STARBASE_ONE.ISO/a96/disk07/plt.exe/PLTVER41.EXE/ACTIVITY.TXT

Text File | 1993-12-06 | 38KB | 828 lines

                         An Activity Guide to Accompany
                                 PLANET TRACKER
                                   Version 4.1

                      by David Chandler and Michael Zeilik
                 (c) 1993 by David Chandler and Michael Zeilik

This software and activity guide are specifically designed to be used with
CONCEPTUAL ASTRONOMY (by M. Zeilik, 1st edition, 1993), ASTRONOMY: THE EVOLVING
UNIVERSE (by M. Zeilik, 7th edition. 1994), and ASTRONOMY: THE COSMIC
PERSPECTIVE (by M. Zeilik and J Gaustad, 2nd edition, 1990), all published by
John Wiley & Sons. Those using other texts will find it equally useful.

Directions for running the program and producing worksheets are provided within
the program itself. Select "Help Topics / Notes" from the main menu to read
selected information from the screen or print out all or part of the help file.

All computations in the program are based on Keplerian orbits using mean
orbital elements as described in Astronomical Algorithms by Jean Meeus. Given
the small scale of the charts, the algorithms are perfectly adequate for their
intended purposes. They are not suitable for critical uses such as navigation,
but they have more than sufficient accuracy for general observational purposes
well into the next century. For instructional purposes, to illustrate the
patterns of planetary motion, they may be run for several thousand years. The
algorithms lose validity and will eventually generate bizarre results if
allowed to run tens of thousands of years into the future.


                               Program Overview

The authors of "Planet Tracker" are both teachers of astronomy, and the program
was designed with the students in mind. "Planet Tracker" is a tool to
investigate the laws of planetary motion create printed planet charts and
worksheets in a variety of useful formats. The program is sharply focused on
concepts of planetary motion that most of our students find difficult to grasp.

You can think of the program as a simulation of the "raw" data from which
models of planetary motion were derived. The key to the program's usefulness,
however, is the way it displays this information. It allows us to see planetary
motion from vantage points that were available to Copernicus and Kepler only in
their imaginations. You will find that this program is very easy to learn as we
have been very selective in its capabilities. All screens have instructions at
the bottom. You can leave any screen by hitting the "ESC" key.

The collection of exercises and activities that follow is presented only to
suggest a few of the many possibilities. This file (ACTIVITY.TXT) is straight
ASCII text. You are encouraged to import it into a word processor and modify it
to meet your own needs. You may also print it out from the "Main Menu" of
Planet Tracker. The exercises are divided into two categories: those using
printouts only and those requiring direct student access to computers. We
envision that this program will be used in a laboratory or small class setting.
If you have enough computers for a small class, you will want to instruct the
students in running the animations themselves. In that case, you will need a
site license to run the program at the same time on multiple machines. For
information on site licenses, which cost an additional $50, contact David
Chandler Co., P. O. Box 309, La Verne, CA 91750. However, it is possible to
develop "short" activities to use in larger classes. I (M.Z.) have done so with
classes of 200 to 300 students at a time.



                             Suggested Exercises
                   (Student access to computers NOT required)

1. Planet Calendar

Introduction

The simplest use of the heliocentric planet charts is to pin them on the
bulletin board and keep track of the positions of the planets from week to
week.

Text References

Conceptual, Sections 1.2 and 1.3; Evolving, Sections 1.2 and 1.4; Cosmic,
Sections 1.2 and 1.4.

Procedure

Use the heliocentric charts as a bulletin board display and update the planet
positions daily or weekly. Using transparencies, the orbits can be projected
onto butcher paper and traced at a larger scale. With the right adjustments,
both the inner and outer planets can be combined into a single diagram.

Key Concepts

Through daily contact with this display, your students should learn to:
=> associate the length of a year with the orbit of the earth.
=> become familiar with the relative speed of the solar system orbits.
=> notice the high speed of the inner planets compared to the slow movement of
   the outer planets.
=> recognize that the planet orbits are not concentric circles.


2. Identifying the Planets in the Sky Using the Zodiac Time Line

Introduction

The planets are easy to pick out because they are as bright or brighter than
any of the stars. Once the planets are found the first time they are easy to
pick out on subsequent nights and their motions can be followed.

Text References

Conceptual, Sections 1.2 and 1.3; Evolving, Sections 1.2 and 1.4; Cosmic,
Sections 1.2 and 1.4.

Procedure

Start by locating the zodiac in the sky. One way to do this is to watch the
moon. It follows the zodiac from one night to the next, although it strays
farther from the ecliptic than most of the planets. Locate the sun on the
zodiac chart. The half of the zodiac to the left of the sun (wrapping around if
need be) is the portion visible in the evening. Identify the bright stars that
lie along the zodiac. Any bright star out of place in this region of the sky is
most likely a planet.

Venus is the brightest starlike object in the sky, whenever it is visible.
Jupiter is also brighter than any star. Saturn is about the brightness of the
brightest stars and is a pale yellow color. Mars can be as bright as Jupiter or
as faint as a second magnitude star depending on its distance from the earth.
Mercury is as bright as the brightest stars, but it is usually only visible in
the twilight. Checking the chart is critical to success in identifying Mercury.
If several planets are visible in the evening at once, notice that they, along
with the moon (if it is up), form a line close to the ecliptic.

Once the planets are identified they are easy targets for small telescopes.
Saturn shows its rings in even the smallest telescopes. Jupiter's moons are
visible in small telescopes or even binoculars, changing positions from one
night to the next. Mars looks like a tiny orange dot, but still clearly
different from a star, which appears as a point of bright light. Venus and
Mercury show phases but no surface details in a telescope. Crescent phases
occur as they are moving retrograde (left to right on the chart), crossing
between the earth and the sun.

Key Concepts

After completing this exercise, students should be able to
=> gain familiarity with the constellations and bright stars.
=> recognize planets as bright "starlike" objects that progress through the
   sky.
=> gain experience using a telescope.
=> recognize the difference between a star and a planet in a telescope.



3. Translating Heliocentric Orbit Diagrams to Earth's Perspective

Introduction

The heliocentric view of the solar system is the simplest way to describe
planetary motion, but at first it seems unrelated to the complex way the
planets move in the sky from earth's perspective. This exercise helps form a
bridge between the two.

Text References

Conceptual, Sections 2.2 and 2.3; Evolving, Sections 2.4 and 3.2; Cosmic,
Sections 2.4 and 3.2.

Procedure

Print out a heliocentric orbit chart for the current date. Draw an arrow from
the earth, passing through the sun, all the way across the page. Mark this
arrow with heavy lines. Now draw lines from the earth to each of the planets.

Face south and point the sun arrow of the diagram to where the sun is at noon.
Hold the paper roughly parallel to the ecliptic plane. Each of the other arrows
should now be pointing at its respective planet, but the planets cannot be seen
easily in daylight. Now rotate the sheet in the plane of the paper so that the
sun arrow points toward the western horizon. Any planets to the left of the sun
will still be up after the sun has set. Continuing to rotate the paper until
the sun arrow points to the eastern horizon, you can see that any planet to the
right of the sun should be up in the morning sky.

Key Concepts

Many students keep information about 3-dimensional "space" and their direct
perceptions of the 2-dimensional "sky" in separate compartments in their minds.
Any exercise that links the two will help clarify their understanding of both.


4. Relating the Heliocentric Orbit Diagrams to the Time Lines

Introduction

The previous exercise uses the heliocentric charts to relate the positions of
the planets in their orbits with where they appear in the sky at night. The
heliocentric charts can also illuminate the time lines, which in turn clarify
how the planets move in the sky.

Text References

Conceptual, Sections 1.2, 1.3, and 2.3; Evolving, Sections 1.2, 1.4, and 3.2;
Cosmic, Sections 1.2, 1.4, and 3.2.

Procedure

Draw arrows from the earth through the sun and from the earth through each of
the planets on a heliocentric chart as in the previous exercise. Measure the
angle of each planetary arrow from the arrow pointing at the sun. This tells
how many degrees left or right of the sun to look to find each planet.

Find the corresponding date on the solar time line and mark it with a dark
horizontal line across the page. The total width of the chart represents 360
degrees wrapped around the sky, so each quarter of the chart represents 90
degrees. Mark the location of each planet for that date and compare with the
angles measured from the heliocentric chart. They should agree.

Now compare the positions with the same date on the zodiac time line. The view
may be shifted, but the positions of the planets relative to the sun should be
the same.

From the heliocentric chart you can find the distance of a planet from the
earth, whereas the time lines show the planet's position projected onto the
sky. From the heliocentric charts, where would you expect Mars to appear it's
brightest? What is the elongation angle at that point? Where would it be on the
time lines at that point? Where should you look to find Mars in the sky when it
is at its brightest?

As a final check, print out a heliocentric chart and block out the data at the
top of the page. From an extended zodiac or solar time line the student should
be able to figure out the date of the chart to within a few days.

Key Concepts

The different charts present similar information in different forms. The
heliocentric charts preserve the 3-dimensionality and indicate distances,
whereas the time lines do not. On the other hand, the times lines better show
how the planets move with time. These charts illustrate how similar information
can be represented in very different formats.

5. Planetary Aspects

Introduction

The terms conjunction, greatest elongation, quadrature, and opposition are
called planetary aspects. They have to do with the angle between the sun and a
planet along the ecliptic. Note: None of Zeilik's textbooks use the term
"quadrature" in an effort to keep technical terms to a minimum. You may,
however, want to introduce it in your class.

Text References

Conceptual, Sections 1.2, and 2.3; Evolving, Sections 1.4 and 3.2; Cosmic,
Sections 1.4 and 3.2.

Procedure

On a heliocentric chart of the inner solar system, plot the two points where
Venus would be in line with the sun. When Venus is between the earth and sun it
is said to be at inferior conjunction. When it is behind the sun it is a
superior conjunction. Is Mars ever in conjunction with the sun? Is Mars ever at
inferior conjunction with the sun? Would you ever be able to see any planet at
either kind of conjunction with the sun?

Opposition occurs when a planet is opposite the sun in the sky. Locate the
points on the heliocentric chart where Mars would be at opposition. How do you
expect the viewing of Mars would be in a telescope when it is near opposition
compared with elsewhere in its orbit?

Is Venus ever at opposition? What would be the aspect of earth as seen from
Venus (if you could see through the clouds on Venus) when Venus is at inferior
conjunction? What would be the aspect of earth as seen from Mars when Mars is
at opposition?

Greatest elongation occurs when the elongation angle of an inferior planet is
maximum. Locate the points of greatest elongation for Venus. Does the line from
earth to Venus hit tangent to the orbit of Venus? If not, is there a greater
angle of elongation for Venus than the one you chose?

Quadrature takes place when the elongation of an outer planet is 90 degrees.
(The elongations of the inner planets never reach 90 degrees. Why?) Find two
places on the orbit of Mars when it is at quadrature. If you were on Mars
looking at the earth, in what aspect would the earth be? In what aspect would
you see earth from Venus when Venus is at greatest elongation?

Finally, identify on the zodiac time line or the solar time line the points
where Venus is at superior conjunction, inferior conjunction, and greatest
elongation. Identify points where Mars is at quadrature and opposition.

Key Concepts

Understanding planetary aspects involves spatial perception skills. Some
students may need coaching to answer how the earth would appear from some other
point of view. Acting out these relationships with the aid of the heliocentric
charts can be a significant aid to understanding.

6. Phases of the Planets

Introduction

Planets have phases just like the moon. Phases are caused by the varying angle
of lighting from the sun. Many students misunderstand the phases of the moon;
they believe that they are seeing the earth's shadow on the moon (as in a lunar
eclipse). Introducing the phases of the planets may be an alternative approach
to the same conceptual problem.

Text References

Conceptual, none; Evolving, Section 4.1 (see Figure 4.5); Cosmic, Section 4.1
(see Figure 4.5).

Procedure

Find a day on the solar time line (or any other resources of the program) when
Venus is closer to the earth than the sun and Mercury is farther from the earth
than the sun, or vice versa. Print out a heliocentric chart for that day. For
each of the two planets, draw a line from the planet to the sun and from the
planet to the earth and extend those lines across the page so they form an
angle whose vertex is at the planet. One line represents our line of sight, the
other represents the direction of lighting.

In a darkened room with a bare light bulb and a tennis ball, place the ball in
the position of the planet. Place the bulb so it illuminates the planet along
the line from the sun to the planet. Place your eye at the level of the table
so that you are looking along the line of sight from the earth toward the
planet. Sketch the shape of the illuminated portion of the ball from this
perspective. Repeat for the second planet. Move the ball representing the
planet to various positions around the bulb representing the sun. When is it
gibbous and when is it a crescent? Is it ever truly full when it can be seen
from our point of view?

Ptolemy thought Venus went in a circle centered at a point between us and the
sun. How would the cycle of phases look if that were the case? Would Venus
ever have a full phase? Galileo was the first one to observe the phases of
Venus with a telescope. How could his observations tell if Ptolemy were
correct? Or wrong!

Does Mars have changing phases? (Yes!) Does it go through crescent phase? (No!)

Key Concepts

=> Phases are not logically limited to the moon, but rather apply to any object
   illuminated by an outside source where the direction of lighting changes
   over time.

=> Inferior planets

7. Inferior and Superior Planets

Introduction

Inferior planets are defined as the planets whose orbits lie within the earth's
orbit. Superior planets lie outside the earth's orbit. This is the determining
factor in how the planets appear to move in the sky. Note: None of Zeilik's
textbooks use the terms "inferior" and "superior" in an effort to keep
technical terms to a minimum. You may, however, want to introduce them in your
class.

Text References

Conceptual, Section 1.2; Evolving, Section 1.4; Cosmic, Section 1.4.

Procedure

On the heliocentric charts find the largest elongation angle possible for
Mercury and again for Venus. When a planet is to the left of the sun it remains
in the evening sky after sunset. Will either Mercury or Venus ever be found in
the eastern evening sky or in the western morning sky? Will either planet ever
be visible at midnight? Why are Mercury and Venus referred to as morning and
evening stars? Does either planet ever go through opposition? Do any of the
superior planets ever pass in front of the sun?

On the solar time line the paths of the inferior planets behave very
differently from the paths of the superior planets. The superior planets move
continuously from left to right, pass behind the sun, and wrap around at the
opposition point behind the earth. The inferior planets, on the other hand,
move right to left behind the sun and left to right as they cross back in front
of it from our point of view on earth. Can you explain why they behave
oppositely? (Hint: who passes whom in the race among then planets to get around
the sun?)

Key Concepts

=> How a planet appears to move depends on whether we view it from outside or
   inside its orbit.
=> The earth moves faster than the superior planets and slower than the
   inferior planets. This affects their apparent direction of motion through
   the sky.
=> Superior planets never pass between the earth and the sun and inferior
   planets never circle to the far side of the earth from the sun.


8. Regularities of Planetary Motion

Introduction

Planetary motion as observed from the earth is well represented by the zodiac
time line. The regularities in the motions on this chart are clues to the
motions we would observe from space.

Text References

Conceptual, Sections 1.2 and 1.3; Evolving,
Sections 1.4 and 3.2; Cosmic, Sections 1.4 and 3.2.

Procedure

Print out a Zodiac Time Line covering at least three years. Find a date when
one of the superior planets is at opposition and another is behind the sun.
Print out an outer solar system geocentric and matching heliocentric plot for
that data. (Use a multiple of ten days as the plotting interval, since the
zodiac time line is plotted in multiples of ten days.) When does retrograde
motion occur on the zodiac time line? What is occurring on the heliocentric
and geocentric charts at that time? When does maximum prograde motion occur?

Note the orbit of Mars in particular. How long does it take to move from behind
the sun to quadrature (half way to opposition)? How long does it take to move
from quadrature to opposition? Compare these times for Jupiter and Saturn as
well. What progression do you observe? Plot the points of quadrature for Mars,
Jupiter, and Saturn on the heliocentric chart. Are we as off center with
respect to Jupiter or Saturn as we are for Mars?

Speaking of asymmetries, can you explain why the inferior planets take longer
to go from right to left than from left to right across the sun on the time
lines? (Consider where the points of greatest elongation are on the
heliocentric chart.) Why is Venus' path more asymmetric than Mercury's?

9. Sidereal versus Synodic Periods

Introduction

How long does it take the hands of a clock to move from one alignment to the
next? Consider their angular rates (the reciprocals of their periods). The fast
hand moves at 1 rev/h, the slow hand moves at 1/12 rev/h, therefore the fast
hand gains on the slow hand at a rate of 11/12 rev/h. Taking the reciprocal of
the relative rate gives 12/11 h/rev, or 65.4545 minutes as the time between
alignments.

If the clock hands were the earth and another planet, the absolute rates would
be the sidereal rates and the relative rate would be the synodic rate. The
relation in terms of the periods is 1/Te - 1/Tp = 1/Tsyn for superior planets,
or 1/Tp - 1/Te = 1/Tsyn for inferior planets. Since our observation point is on
the earth, one of the planets participating in the race, it is only the synodic
periods of the planets that are directly observable. Given the synodic period
of a planet and the sidereal period of the earth (365.25 days), the problem is
to find the sidereal period of the planet.

Text References

Conceptual, Section 2.3; Evolving, Section 3.2 and Focus 3.1; Cosmic, Section
3.2.

Procedure

Print out either the zodiac or solar time line for several years. Measure
synodic periods of each planet by counting the number of days from one
alignment with the sun to the next, preferably averaging over several cycles.
Calculate the sidereal period for each planet using the formulas above.

As a complementary exercise, use a heliocentric chart generated for the day of
an alignment between the earth, some other planet, and the sun. Count the days
until the next alignment by stepping each planet forward the same number of
days. Compute the synodic period from the two sidereal periods using the
formula and compare your answer with the direct count.

Key Concepts

=> The sidereal period of a planet is a fundamental astronomical measurement,
   but it must be found indirectly from earth-based observations.
=> The measurement of the sidereal period of Mars is the first step in Kepler's
   method for determining the orbit of Mars.



10. Determining the Orbit of Mars

Introduction

Determining the orbit of Mars is the key in Kepler's discovery of elliptical
orbits. The method consists of finding the position of Mars on pairs of dates
687 days apart, preferably close to opposition. Since the sidereal period of
Mars is about 687 days, Mars would be at the same point in its orbit on both
days. The earth, however, would be at different locations on those two dates.
Constructing the line of sight from the earth to Mars on both dates locates the
actual position of Mars in space by triangulation.

Text References

Conceptual, Section 2.5; Evolving, Section 3.2 (see Figure 3.7); Cosmic,
Section 3.2 (see Figure 3.9).

Procedure

Prepare several time lines (either kind) covering at least two years each
starting shortly before an opposition of Mars. Pick pairs of dates 687 days
apart and measure the elongation of Mars on each date. If the first date is
about 20 to 30 days after an opposition, the other date will be shortly before
the next opposition. (Use a scale factor of 360 degrees = 6", which converts to
2.36 degrees per mm. to measure angles horizontally across the time lines.)
Make a heliocentric plot of the earth's orbit at five day intervals starting
January 1. Use a protractor with the earth orbit plot to lay off the elongation
of Mars for each date. Where the lines intersect is one point on Mars' orbit.
Repeat for other pairs of dates to find more points on the orbit. Finally,
compare the plot with another heliocentric chart that contains the orbit of
Mars.

Key Concepts

=> This lab exercise uses the time lines to simulate the work of Tycho Brahe,
   but it presents the information in more concrete visual form.
=> The information that is so neatly summarized in tables of planetary data is
   often not directly observable. It must be deduced by observations from our
   earth-based perspective.

11. Determining the Orbit of Mercury

Introduction

Not all greatest elongations of Mercury are created equal. By scanning down the
time lines (the solar time line is best for this exercise) it becomes apparent
that evening elongations are smallest in the spring and largest in the fall.
When we are looking at Mercury at greatest elongation we are looking tangent to
its orbit. If we construct enough tangents to Mercury's orbit, the shape of the
orbit is revealed.

Text References

Conceptual, Section 2.3; Evolving, Section 3.2 (see Figure 3.6); Cosmic,
Section 3.2 (see Figure 3.8).

Procedure

Print out several years worth of solar time line and an orbit of the earth at 5
or 10 day intervals starting January 1 without the planets. Using the same
angle measuring techniques as in the Mars orbit lab, find the elongations of
Mercury at each greatest elongation and plot the lines of sight on the orbit
diagram. Compare the results with a heliocentric inner planet chart.

Key Concepts

This exercise illustrates another example of using indirect methods to
determine the nature of our solar system from our limited vantage point on
earth.



12. Kepler's Laws

Introduction

Kepler introduced three laws of planetary motion: 1) Planets move in elliptical
orbits with the sun at one focus. 2) A planets sweeps out equal areas in equal
times. 3) The square of the period of an orbit is proportional to the cube of
its semi-major axis.

Text References

Conceptual, Section 2.5; Evolving, Section 3.5; Cosmic, Section 3.4.

Procedure

Before Kepler, the orbits of the planets were thought to be off-centered, or
eccentric, circles. Kepler showed that they are actually ellipses, although
they are close to circular. See how close the circular approximation actually
is by finding the centers of the orbits and drawing the circular approximations
to the orbits. To the accuracy of simple drafting tools can you notice a
discrepancy between the circles and the orbits? Which planets have the worst
fit? If a is the semi-major axis of the ellipse and c is the distance from the
center to the focus, the eccentricity is defined by e = c/a. Measure the
eccentricities of each of the orbits.

To test the equal area law, use pairs of days close enough together that the
curvature of the orbit between them is not significant. Use the radius to one
point as the base, measure the altitude, and compute the area. Compare for
different parts of the orbit. How do the "area sweep rates" compare for
different planets?Kepler's third law can be verified directly using a numerical
table of orbital elements. An interesting consequence of the third law,
assuming circular orbits, is that the orbital speed of a planet is inversely
proportional to its orbital radius. The spacing of the dots lessens
dramatically with radius in the heliocentric plots. It is simple to check that
the speeds drop off inversely with the radius.



13. Distances to the Planets

Introduction

The heliocentric charts are scale drawings of the solar system. Distances
measured on the charts in centimeters are proportional to actual distances.
Knowing one distance, the distance from the earth to the sun, any other
distance can be determined.

Text References

Conceptual, Section 10.1; Evolving, Section 13.1; Cosmic, Section 8.2 (see
Figure 8.5).

Procedure

Taking the distance from the earth to the sun to be 93 million miles or 150
million km, find the: a) distances from the sun to the other planets. b)
closest approach of Venus and Mars to earth. c) range of distances between Mars
and earth. d) ranges of opposition distances of Mars from the earth.

Key Concepts

This kind of exercise reinforces math skills in proportional thinking,
scientific notation, and metric units.



14. How Big Would it Look in a Telescope?

Introduction

This question arose in class when I (DC) announced an opportunity to view the
1988 opposition of Mars through the telescopes of a local astronomy club.
Rather than give them the answer, we used the class time to figure it out
together.

Text References

Conceptual, Section 2.3; Evolving, Sections 3.2, 4.1, and Focus 6.1; Cosmic,
Sections 4.1 and 7.1.

Procedure

All you need to know is the distance to the planet and the size of the planet.
The diameter of a circle (measured in cm) representing a planer compared to the
distance of the paper it is drawn on (45 cm is typical reading distance) is
proportional to the actual size of the planet compared to its distance, as long
as the size and distance of the planet are measured in the same units. The dot
size computed in this way will be very tiny, as it would appear to the naked
eye. Multiply by 100 or so to get an idea of the size of a telescopic
image.

Different groups in the class could compute the sizes of various planets under
different circumstances. A revealing comparison is to calculate the apparent
size of a star. Assume the diameter of Alpha Centauri is comparable to that of
the sun, about 1.4 million km. It's distance is about 4.5 light years, and
light travels 300,000 km/s. From this data, you can be show that the image of
such a star on a sheet of paper would be about 1 millionth of a centimeter.
Even at a few hundred power the disk would not be discernible.

Key Concepts

Many students who ask simple quantitative questions do not realize that the
answers are within their own power to compute. Helping a student answer their
own questions with mathematics they already know can help motivate further
study of mathematics.



                   Suggested Exercises for a Laboratory Class
                (Where students have direct access to computers)

Motion Along the Ecliptic

1. Select Mercury and the sun only. Note the dates of several inferior
conjunctions (left to right crossing of the sun). What is Mercury's motion at
these times relative to the stars?

2. Select Venus and the sun only. Set the vertical exaggeration to 5. At what
point in its orbit does Venus stray farthest from the ecliptic? Why? Allow the
program to run through many years. (You may have to set the interval to 5 days
or more to speed up the program.) What evidence is there for resonances between
the orbits of Venus and the earth? Do other planets show similar resonances?
Hint: try Mercury!

3. Select Mars and the sun only. Watch Mars goes through a retrograde loop and
note the date when it is in the middle of a loop. What is happening in the top
view relative to the sun?

4. Starting with Mars, plot one planet at a time. Note how their positions
relative to the stars correlates with the position of the sun (compare top and
lower views). Note the sizes, elapsed time intervals, and the amount of drift
of the retrograde loops across the zodiac. Also note that the shape of a
retrograde loop is directly related to its position among the background
stars.

5. Find the synodic period of Mercury (or any other planet) in as many
different ways as possible. The Julian date makes finding the time interval
easy.

6. What happens when the calculation interval is set to 365.25 days? To 365
days?



Split Screen Animations


1. Apparent Dome of the Sky versus Zodiac as Seen from Earth

Note that in the left display, the sun is fixed. The little white dots
traveling around the dome represent stars in their seasonal motion with respect
to the sun. On the right, the stars are fixed. This pairing is almost identical
to the ecliptic views, but now the sky is wrapped around in a circle. Follow a
planet such as Mars and note where the sun is when Mars undergoes retrograde
motion in both views.

2. Apparent Dome of the Sky versus Earth and Sun Held Stationary

Note the basic similarity of the two views. When you go out every evening at
sunset, the earth is beneath you and the sun is at approximately the same
position relative to the horizon. The planetary orbits do NOT retrace
themselves exactly in the right view. (Why? Because the elliptical orbits are
rotating as seen from the earth.) The lack of depth in the left view is
dramatic in this comparison. But note that the angular speeds of the planets on
the left correlate with their distance from the earth on the right. For the
outer planets, note the large variation of the distance of Mars from the earth
compared to the relatively smaller variations of Jupiter and Saturn. That is
why Mars varies so much in brightness in comparison.


3. Heliocentric versus Geocentric

Run first without trails and note the similarity of the motions. Add the trails
and note the great difference in the paths. Run Mars alone. Note that the loops
on the right correspond to oppositions on the left.


4. Zodiac versus Geocentric

Run Mars with a large calculation interval over hundreds of years. Not all the
oppositions are the same. Find the "most favorable" oppositions in terms of
time of the year and location among the constellations. Determine the next
opposition of Mars and the most favorable one within your lifetime.


5. Heliocentric versus Earth and Sun Held Stationary

The display on the right is a rotating frame of reference. Add trails. The
inner planets move at slower rate compared to the left view. But the outer
planets reverse their direction of motion! (Why? Because the earth's angular
speed is subtracted from that of the other planets. Since the outer planets
move slower than the earth, as viewed from the sun, in the right view they
appear to go backwards.)

6. Heliocentric versus Zodiac

Note that the "sky dome" appears to rotate synchronously in these views. The
stars are "fixed", and all local motions are relative to them. Find a time when
Mars and Mercury are in conjunction with each other. What is happening with
these planets in the heliocentric view?



               (Specific example for in-class or lab activities)

Note to the Instructor: For this activity, you will need to run a Zodiacal Time
Line and a Solar Time Line selecting Mercury and Mars for a period of about two
years each. (To get a continuous chart, note the last date printed at the end
of the first page and select it as the starting date for the second year. Trim
the heading from the second chart and fit them together.) Start with the date
of the class or some other convenient starting date. Be sure that the time span
includes one retrograde motion of Mars.


                                 Astronomy 101
                          Major Motions of the Planets
                               (c) 1993 M. Zeilik

Name:_______________________________Class/section:______________

Purpose: To describe the positions of the sun and selected, naked-eye planets
along the ecliptic and infer general patterns in their motions from
graphs.

Predictions: Write your responses to these questions on this page before you
look at the graphs:

1) In what one way does the motion of the sun along the ecliptic resemble that
of the planets?


2) In what one way does the motion of the sun along the ecliptic differ from
that of the planets?

Materials: Pencil, ruler, calculators, and graphs of planetary positions.

Text references: Section 1.2, Conceptual (1/e); Section 1.4, Evolving (7/e)

Procedure:

1. Examine carefully the graphs of the positions of the planets. They show time
running down the page, and the dates at the left are given in 10-day intervals
(the year is given on the right). Their vertical extent covers a little more
than a year, and their horizontal span is 360 degrees. The bolder line is the
sun. The angular distance between the sun and a planet on any given date is
called the planet's elongation.

The planetary positions run across the page horizontally through the
constellations of the zodiac (see the diagram at the top of the page; each
constellation of the zodiac is drawn and labeled). Once around the zodiac is a
complete circle of 360 degrees. The solid line through the center of the
constellations is the path of the sun in the sky relative to the star--the
ecliptic. The legend is in the upper right corner for the planets plotted and
the year. Note that east is to the left, and west is to the right.

Seek out patterns in the motions you see for Mercury and Mars. Answer the
following questions on this page:

3) Which planet always appears close to the sun in angle (elongation)?




4) How frequently does Mercury move from one side of the sun to the other? Is
this change more or less frequent for Mars?

5) For Mercury, does its maximum angular distance (maximum elongations) from
the sun remain constant or does it vary?




6) How does the sun's motion differ in this plot? In what direction does the
sun move relative to the stars? How long does it take to move 360 degrees?



7) How does the sun's resemble in general that of Mercury and Mars



8) How does the sun's motion differ from that of Mercury and Mars?



9) Note the cases when the planet's motion is toward the right (west) rather
than to the east. What is happening to the planets in the sky during these
times?