This article describes a new educational resource, a book-sized site on the world wide web covering astronomy, Newtonian mechanics and spaceflight. Written at the high-school level and titled "From Stargazers to Starships" (http://www.phy6.org/stargaze/Sintro.htm), it continues the style of "The Exploration of the Earth's Magnetosphere" [Stern and Peredo, 1997; http://www.phy6.org/Education/Intro.html]. However, where much of "Exploration" (especially its second half) is relatively specialized, most of "Stargazers" tries to cover subjects relevant to high-school physics. It could well serve as the framework of a one-year course, but it is equally suitable for individual study by any person interested in space, and it contains material for a variety of student projects, as well as a section directed at teachers.|
A Space Oriented Curriculum
With so many high-school texts in print, why add yet another one--even one in the new medium of the web? Two main reasons. First, today's high school physics curriculum is sadly out of date, consisting almost entirely of material from the 19th century. Modern material, unfortunately, tends to be mathematical, requiring familiarity with Maxwell's equations and quantum theory. How then can students in a pre-calculus course be given the feeling that their science is up-to-date?
In "Stargazers" (and to some extent in "Exploration") this is achieved by making the curriculum space-oriented. Spaceflight and space exploration are still evolving and contain many open ends and unanswered riddles, yet much of their physics is "classical," explainable on the high school level. Moreover, spaceflight has glamor, it draws the interest of young people. That is the second reason: at a time when motivating students towards science has become a major challenge, a space-oriented curriculum may be at least part of the answer.
Written by a space scientist with a strong interest in science history, "Stargazers" not only covers the better known facts of space, but also more exotic aspects--e.g. unconventional ideas of spaceflight (cannon, nuclear, solar sails and ion drives) and Robert H. Goddard's introduction of the DeLaval nozzle to rocketry.
If high-school physics seems somewhat short on up-to-date material, the astronomy curriculum has an over-abundance. It is rich in recent discoveries and ideas--the big bang, black holes, the evolution of stars and their ultimate fates, etc., but all this comes to students as "book knowledge," material found only in the textbooks, not related to any direct experience. Indeed, students growing up in today's brightly lit cities rarely see much of the sky or pay much attention to what can actually be seen there.
The astronomy of "Stargazers" takes a big step backwards, to pre-telescope astronomy. Some basic aspects covered in lower grades--the apparent motion of the Sun and stars, seasons of the year and the calendar--are expanded here and covered more thoroughly. Other subjects may be new--the ecliptic and the zodiac, coordinates, size and shape of the Earth, the precession of the equinoxes and more. The student will find here that the critics of Columbus did not argue that the Earth was flat (and they were right, while Columbus was wrong), will learn to construct a sundial, calculate the distance to the horizon andget to know calendars different from ours.
"Stargazers" can be divided into three parts, of comparable size--on astronomy, Newtonian mechanics and spaceflight. With some additional material, each of these could in principle be studied by itself. The first two are linked by a discussion of Kepler's laws, the last two by the story of R.H. Goddard. Altogether the site contains the following 35 main units, with 13 additional ones expanding the discussion:
Astronomy of the Earth"s motion in space
1. The Sky Above Us
2. The Path of the Sun, the Ecliptic
2a.--Building a Sundial
3. Seasons of the Year
4. The Angle of the Sun's Rays
5. Maps of the Heavens
6. The Calendar
8. The Round Earth and Christopher Columbus
8a--Distance to the Horizon
9. Discovery of the Solar System
10. Kepler and his Laws
11. Kepler's First Law of Planetary Motion
12. Kepler's Second Law
12a--How Orbital Motion is Calculated.
13. The Way Things Fall
16. Newton and his Laws
17a.--Mass Measurements aboard Space Station Skylab
18. Newton's Second Law
19. Motion in a Circle
20. Newton's theory of "Universal Gravitation"
21. Kepler's Third Law
21a.--Applying Kepler's Third Law
22. Frames of Reference: The Basics
23. Frames of Reference: The Centrifugal Force
24. Rotating Frames of Reference in Space and on Earth
Spaceflight and Spacecraft
25. The Principle of the Rocket
26. Robert Goddard and his Rockets
27. The Evolution of the Rocket
29a.--Satellites observing the Sun, solar system and the universe
29b.--Satellites observing Earth from above
29c.--Satellites which observe the local space environment
29d.--Satellites for commercial benefits
29e.--Missions to planets and distant space
30. Far-out Pathways to Space: Great Guns?
;30a.--Project HARP and the Martlet
31. Far-out Pathways to Space: Nuclear Power
32. Far-out pathways to Space: Solar Sails
31a.--Early Warning of Interplanetary Disturbances
33. Ion Rockets
34. Orbits in Space
35. To the Planets, To the Stars
35a. --Planetary Swing-by and the Pelton Turbine.
It is not possible to do justice to all this material (especially to the mechanics) without some mathematics, and a moderate amount of calculation is included. To make the material self-contained, a "mathematical refresher" was added, actually a short course on basic algebra, trigonometry and the theorem of Pythagoras:
Elements of Algebra
(M-1) Basic ideas
(M-2) How it all started
(M-5) The Theorem of Pythagoras
Elements of Trigonometry
(M-6) What is it good for?
This part can also be studied independently, e.g. by students covering these topics in their math classes.
(M-7) How to tell sines from cosines
(M-8) Deriving Sines and Cosines
(M-9) Going past 90 degrees
The most substantial part of "Stargazers" is the middle one, on Newtonian mechanics. This is by no means a complete coverage: not only is calculus absent, but so are momentum, torques, rotating rigid bodies and friction. At the college level such omissions would be inexcusable, but in high school one can hardly expect to cover more. On the other hand, we strove to clarify the basic concepts, especially the two frequent stumbling blocks, mass and the centrifugal force.
The distinction between mass and weight is intimately linked to Newton's laws of motion, and these are carefully introduced,using an approach similar to that of Ernst Mach. To underscore the distinction between mass and weight, and to use an example relevant to spaceflight, two sections describe the way astronauts aboard the 1973 space station "Skylab" monitored their masses in a "zero-g" environment.
The centrifugal force is sometimes dismissed in physics class as "nonphysical," with only the centripetal force considered legitimate. While this is strictly true, the use of the centrifugal force often helps intuition and simplifies calculations."Stargazers" begins this subject by deriving and using centripetal acceleration, but then frames of reference are discussed, the invariance of the laws of motion in uniformly moving frame and their modification in a rotating frame. This leads to a discussion of the "zero-g" environment and the realization that the "artificial gravity" in a spinning space station contains an extra complication, the Coriolis force.
Other subjects include free fall and its generalization, with a brief introduction to vectors, then energy, and somewhat more briefly, centers of gravity and rocket motion. Newton's discovery of "universal gravitation" is carefully explained, pointing out how Newton, using the inverse-squares law, managed to connect two seemingly unrelated quantities--the acceleration g of free fall and the orbital period of the moon (a web site telling the story of Newton's apple tree is also linked). At this stage Kepler's laws are further discussed, in particular the 3rd law, relevant to the Lagrangian points L1 and L2 described at a later stage.
History as a framework
The way knowledge is arranged in a student's mind is as important as the knowledge itself: a jumble of remembered facts does not add up to useful information. Like "Exploration" before it, "Stargazers" follows a historical thread, because the sequence in which ideas actually evolved is often also the one in which they naturally hang together.
In addition to serving as a framework, history also brings up details which help students understand and appreciate the ideas of science and the problems encountered by the pioneers. Ptolemy's epicycles seem senseless unless the student is aware of the retrograde motion of the inner and outer planets. Only then canthe student appreciate how the heliocentric theory of Copernicus, assigning longer orbital periods to more distant planets, led to a more rational explanation.
History also brings life to the study of science. Arab mathematics, the voyage of Columbus, the story of Tycho and Kepler, the discoveries of Pike's Peak and of Mt. Everest, all these make cameo appearances. So does Roland (or Lorand) Eötvös, a Hungarian physicist at the turn of the 19th century, who not only demonstrated the equality of gravitational and inertial mass to a high level of accuracy, but also helped establish the renowned high schools of Budapest, one of whose alumni was Theodore Von Karmán, an important pioneer of rocketry. And students may resonate with Robert H. Goddard who, in a visionary moment at the age of 17, resolved to devote himself to achieving spaceflight, and who kept the anniversary of that day--19 October, 1899--as an annual personal holiday.
If astronomy and mechanics are the main courses of "Stargazers," spaceflight is the dessert. Ranging from "the rockets' red glare" of William Congreve's early military rockets, to the V-2, Sputnik and today's satellite orbits, the part devoted to spaceflight tells how rocketry developed and describes the roles of Goddard, Von Braun, Von Karmán and Sergei Korolev. Most of the material is qualitative, but some extensions of Newton"s mechanics are included--the ballistic pendulum used by Goddard, Lagrangian points L1 and L2, and the way spacecraft gain energy from planetary encounters, in what are essentially perfectly elastic collisions, which has an interesting connection with the Pelton turbine.
In addition to all these, "Stargazers" also contains a timeline and a detailed glossary, as well as links to many web sites which extend the material. It cites relevant books, among them the science fiction of Jules Verne, H.G. Wells, Arthur Clarke, Robert Forward and Larry Niven. For a hands-on project, a template of a paper sundial is provided--it can be downloaded and duplicated on an office copier--together with instructions and explanations.
This is just the first step, version 1.0 of "Stargazers," and additions are in preparation, e.g. a collection of problems and a hands-on section involving a cross-staff. Look it up--you are likely to find material you can use in your classroom, or some of interest to yourself (both, I hope). Look it up, browse through it, and let me know of any thoughts or suggestions you may have, to help make version 2.0 even better.
Stern, David P. and Mauricio Peredo, Space Physics for Poets, The Physics Teacher, January 1997.