Challenges of Astronomy: Hands-on Experiments for the Sky and Laboratory

244 Pages·1991·17.89 MB·English

by  W. Schlosser

Challenges of Astronomy
w.
Schlosser T. Schmidt-Kaler E.F. Milone
Challenges of Astronomy
Hands-on Experiments
for the Sky and Laboratory
With 190 Illustrations
Springer-Verlag
New York Berlin Heidelberg London
Paris Tokyo Hong Kong Barcelona
W. Schlosser T. Schmidt-Kaler E.F. Milone
Universitiit Bochum Universitiit Bochum Department of Physics and Astronomy
Bochum, FRG Bochum, FRG The University of Calgary
2500 University Drive, NW
Calgary Alberta T2N IN4
Canada
Library of Congress Cataloging-in-Publication Data
Schlosser, W. (Wolfhard)
[Astronomische Musterversuche. English]
Challenges of astronomy: hands-on experiments for the sky and
laboratory / W. Schlosser, Th. Schmidt-Kaler, and E.F. Milone.
p. cm.
Rev. translation of: Astronomische Musterversuche.
Includes bibliographical references and index.
ISBN-13:978-1-4612-8769-8 e-ISBN-13:978-1-4612-4434-9
001: 10.1007/978-1-4612-4434-9
I. Astronomy-Experiments. I. Schmidt-Kaler, Th. (Theodor),
1930- II. Milone, E.F., 1939- III. Title.
QB62.7.S3713 1991
522' .078 -dc20 90-43848
CIP
Printed on acid-free paper.
© 1991 Springer-Verlag New York Inc.
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ISBN 0-387-97408-3 Springer-Verlag New York Berlin Heidelberg
ISBN 3-540-97408-3 Springer-Verlag Berlin Heidelberg New York
Contents
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1. The Vault of Heaven. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. Astronomy of the Spheres. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3. Early Astronomy .......................................................... 9
4. The Earth's Radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5. The Distance of the Moon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
6. Measuring Lunar Mountains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
7. The Phases of Venus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
8. Saturn's Parallax and Motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
9. The Astronomical Unit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
10. The Moon's Orbit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
11. The Galilean Moons of Jupiter ............................................... 54
12. Planetary Packaging: Mean Densities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
13. Earth Satellites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
14. Orbits and Space Travel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
15. Photography of the Sun and Stars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
16. The Speed and Color of Light. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
17. Planetary Surface Temperatures .............................................. 88
18. Planetary Atmospheres ..................................................... 94
19. Atmospheric Effects on Starlight and Sunlight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
20. Sources of Cosmic Radiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 106
21. Optical Aids and Their Limitations ........................................... 113
22. Laser Light and Speckle Interferometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 119
23. Photometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 124
v
VI Contents
24. Spectral Analysis .......................................................... 135
25. The Doppler Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 147
26. Binary Star Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 152
27. Fundamental Properties of Stars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 161
28. The Face of a Star: The Sun. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 169
29. Star Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 178
30. Olbers's Paradox: Cosmology and the Night Sky. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 187
Appendices
A Coordinate Systems and Spherical Astronomy. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .. 194
B A Brief Summary of Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 203
C Constructing a Cross-Staff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 208
D Julian Day Number Table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 210
E Planetary Position Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 214
F Photographic Targets ....................................................... 221
G Topics Guide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 223
Index. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 224
Introduction
This book began as a series of laboratory exer principles; it finishes with Olbers's paradox and a
cises in astronomy and related physical sciences by glimpse of the revelations of cosmology. The exer
the authors on both sides of the Atlantic. The bulk cises tend to become more demanding as one
of it is translated from the German work, Astro progresses. Thus the first six chapters or so are
nomische Musterversuche, a compendium of useful suitable for bright high school students while later
and interesting laboratory exercises developed chapters usually require a fuller background. The
mainly for teachers in the German public schools. chapters on celestial mechanics (14), photometry
Its revision and translation arose from the recogni (23), spectroscopic analyses (24), and the Sun (28)
tion by the third author of the unique character of are exceptionally detailed and are suitable for
the exercises, which resemble a series of chal advanced astronomy undergraduates, as well as the
lenges to the dedicated amateur and student as well dedicated amateur instrumentalist. Chapter 14 will
as to the professional (observer, experimentalist, be especially interesting to students with computer
or theoretician), rather than the rote activities of programming skills; but those with less interest in
most laboratory manuals. Accordingly, encouraged the calculational procedure will find a shortcut
by Theo Schmidt-Kaler, I sought a publisher with early in that chapter. The topics table provides a
connections in Germany who might be sym rough guide to the suitability of the material in a
pathetic to the enterprise. In Springer-Verlag I given chapter for a particular learning situation. In
found such a publisher, and in its (former) physics short, the early chapters stress mechanics and
editor, Jeffrey Robbins, both a kindred soul and trigonometry; the later chapters involve light and
a strong supporter of the project. The present atomic physics as basic tools.
physics editor, Tom von Foerster has maintained All three authors have had the opportunity to
that strong support. review the manuscript at intermediate stages and
The work commenced in 1987 and was com all chapters have been field-tested, either at the
pleted except for suggested revisions, figures, and University of Bochum or at the University of Cal
tables, in 1989. Its timely completion is due for the gary. It is a pleasure to acknowledge the help and
most part to the award of a Killam Resident Fellow advice given by three colleagues at the University
ship in the fall, 1988, for which my co-authors and of Calgary, Dr. Hans Laue, Dr. David Fry, and
I are grateful. The final result provides not only a Prof. T. Alan Clark, and the encouragement of
rich resource for teachers and instructors in plan Prof. Harlan 1. Smith of the University of Texas.
ning their own laboratory courses, but a work more University of Calgary students Gaston Groisman
directly accessible to the student and to the ama and Steven Griffiths provided several computer
teur astronomer and physicist as well. graphics figures. Finally, the readability of the
The exercises are arranged in chapters. They are manuscript has been much improved by the sharp
intended to be self-guiding but not self-standing: eye of my wife, Helen. Notwithstanding all this
the terminology of later chapters depends strongly assistance, errors in the final text are the responsi
on familiarity with astronomy or on a thorough bility of the third author alone.
working of the earlier chapters. The progression is
from ancient astronomy, emphasizing phenomena, E.F. Milone
to more modern astronomy, involving physical Calgary, 1989 Sept. 29
vii
Plate 1.1. The Temple of Heaven, section of ceiling and upper wall,
Beijing, China.
1
The Vault of Heaven
1.1 The Shape of Heaven 1.2 Determining the Shape
of the Sky
Many observers of the sky in early civilizations,
such as ancient China and Greece before the Chris
In a series of measurements made at a rooftop loca
tian era, depicted the sky as a great spherical
tion just south of the University of the Ruhr at
chamber on which the stars were emblazoned and
Bochum (in the industrial heartland of Europe),
within which the Sun, Moon, and planets moved.
at 1430 Local Civil Time (LCT)? July 14, 1981,
~ut not all ancient observers agreed on that percep
the results listed in Thble 1.1 were obtained for the
tion. The shape of the sky is a subjective notion,
measured altitude of the estimated halfway point of
con~itioned by cultural, psychological, and physi
vertical circle arcs made at various azimuths. The
ologIcal factors. It has sometimes been depicted
mean altitude was 30.2° and its uncertainty
as a flat concave bowl, as in Fig. 1.1.
The perceived shape of the sky is connected the standard deviation of the mean3-was 1.3°.
The uncertainty is several times smaller than the
to estimated angles of elevations (astronomical
largest deviations from the mean; the largest devi
altitudes) from the horizon.! The summer midday
ations in this case possibly reflect the difficulties of
Sun (or winter full moon) is typically estimated
making the eye estimate for the arc midpoint and
to be close to the zenith, or point overhead, even
of setting a hand-held sextant to such a point.
at high-latitude locales such as northern Europe
Nevertheless, the experiment was successful, and
or Canada, where the latitude is in the range 50
the precision clearly was improved by the use of
to 65°. Over this range of latitude, the maximum
several measurements. In this particular experi
altitude of the midsummer Sun is about 63 to 48°.
ment, as in others, the observer, sighting along a
The midpoint altitude of any vertical circle arc
line at 45° altitude, was startled at how close to the
from the zenith to the horizon will be under
zenith this line appeared to run.
estimated by many people by as much as 15°
The measured result suggests that the horizon
from the true value of 45 A related perception is
that. of the impressively la0.r ge disk of the rising or app~ars to be twice as distant as the zenith. Figure
1.2 IS a sketch of the cross section of the perceived
settmg Sun or Moon. It is striking, unmistak
sky in the plane defined by the observer and a par
able, and yet purely illusory. In fact, the low
ticular azimuth direction. The arc ZMH is bisected
altitude disks are slightly flattened in the altitude
at the point M, which is therefore the midpoint of
direction (i.e., toward the zenith) because atmos
that arc. The mean measured altitude < h > of that
pheric refraction bends light up toward the zenith,
and the bending is stronger for the lower limb than
for the upper.
2This is the time in effect at that location. It is usually a
~ype of ~ean sol~r time, e.g., EST, Em, GMT (UT).
~ppendlx B reviews error analysis and defines terms
lAltitude, azimuth, zenith, etc., are defined and illus s~ch as mean, standard deviation of a single observa
trated in Appendix A. tIOn, and standard deviation of the mean.
2 1. The Vault of Heaven
FIGURE 1.1. An Egyptian depiction of the sky as a some Earth and thus created the present universe. After a frieze
what flattened shell. Seen in cross section is the person of at Luxor, 1300 B.C., courtesy of Fr. Becker (1980). As
the sky goddess, Nut, raised up by her father, Shu, god of with all cosmic myths, a literal interpretation of this depic
the atmosphere, whose action separated the sky from the tion is not necessarily what the depictors had in mind.
point is indicated also. The observer is at point O. follow the instructions for making one in Appendix
The ratio r == OHIOZ = 2.33 is a measure of the C, and calibrate it. If you are hopeless as an instru
apparent distortion of the sky. Note that if OZ = ment maker, you may use the increments of an
OH, the altitude would measure 45°. equatorial telescope's declination setting circle, or
even a blackboard protractor.
With such a device, you can make your own
1.3 Activities
determination of the shape of the sky by replicating
the experiment described previously. It is impor
The perception of the sky as a flattened bowl varies tant to try to make the observations at a level site to
from person to person. Let us find out how this avoid excessive horizon dip or obscuration. Keep a
shape appears to you. record of the location, sky condition, date, and
A cross-staff is a simple instrument consisting of time at which the observations are made, the
essentially two sticks, a long one along which you azimuth (bearing from the north, through the east
sight and a shorter one held perpendicular to the directions), as well as the measured altitude of
first and slid along the first until the object to be your best estimated halfway point, for each obser
measured is matched in angular size. Make a cross vation. It would be best to make several observa
staff (or sextant, a more elaborate but perhaps tions at the same azimuth before moving to another
more familiar instrument) of your own design, or (if this is possible at the observing site), and
arrange your data in tables to facilitate analysis.
After the data have been collected, and you are in
a warm, well-lighted place with calculator at hand,
TABLE 1.1. Sample measurements of midarc altitudes. compute the altitude means and their uncertainties
Measure Altitude (0) for each azimuth. Thenr ,b y geometric construction
determine the quantity and describe the apparent
1 27
2 28 shape of the sky. Table 1.2 will be needed.4 We will
3 30
4 34
5 32
4Similar tables were developed in antiquity by, for exam
Mean 30.2 ± 1.3
ple, Ptolemy.