"Stargazers" in the Classroom
Outline of the material
"From Stargazers to Starships" is meant as an introduction to space, both for the inquisitive non-scientist and for students and teachers in schools. It is best viewed in a large font, e.g. 14 point size or even 18 point (in "Netscape", use "General Preferences" in "Option" menu to select size). You may also remove the background for better legibility: see hints for users.
In the classroom setting, "Stargazers" uses space and spaceflight to introduce students to two areas of the mainline science curriculum:
It consists of three main parts, which overlap slightly:
- The motion of the Earth in space (e.g. why summers are hot, winters cold), and
- Newtonian mechanics.
- Stargazers (sections 1-12)--a study of the Earth's motion in space and of the solar system to which it belongs, almost entirely in the framework of pre-telescope astronomy. Much of the material relates to phenomena which the student could observe directly.
- Orbits and Spaceflight (sections 9-25)--an introduction to the Newtonian theory of motion and is applications to spaceflight.
- Starships (sections 23-34)--a historical overview of space vehicles, their current uses and future promise.
In addition, this site includes a math refresher (sections M-1 to M-11), a quick self-contained introduction to algebra and trigonometry, with some tidbits on the beginnings of algebra and the discovery of Mt. Everest.
Parts (1) and (2) can be taught separately or together and are largely independent of each other. Part (3) is more of a "fun part", the dessert which follows the main course. While part (2) does not cover all of Newtonian mechanics--conspicuously absent are momentum, friction, harmonic motion, torques, rigid-body motion and rigid-body equilibria--it does provide a reasonable grounding in the fundamentals, and hangs together as a single unit. One wonders if any more could be covered within the time constrainst of a high school.
A selection of problems for the students is also provided. Teachers using this material in class may obtain a list of solutions by regular mail, by sending a personal request on school letterhead to Dr. David P. Stern, Code 695, Goddard Space flight Center, Greenbelt, MD 20771, USA.
Teachers whose courses cover any of this area would be well advised to make a hard copy for their own use and read it at their leisure. Even if their courses follow different texts and sequences, they will find here many ideas and examples which will enrich their teaching and give it variety. Each of the three parts can be read largely independent of the others.
In addition to "Stargazers" being used to guide a sequential course, it can also serve as source for student projects, large (L) and small. Many items contain links to other relevant web sites, which such students may also consult. Some topics, with numbers of the relevant sections in parentheses, are:
The sundial (2a)
Shape and size of the Earth (8)
Distance of the Moon (8b, 8c).
From Ptolemy to Copernicus and Kepler (9-12, 20, 21)(L)
Newton's laws (16-18, 24)(L)
Mass measurements in space (17-17a)
Universal Gravitation (16-20) (L)
Frames of reference (22a, 23, 24)
Centripetal and centrifugal forces (19,20,22, 23)(L)
The Coriolis force (24)
Robert H. Goddard (25) (can be L)
History of Rocket Flight (24, 25, 26, 27) (can be L)
Types of spacecraft and what they do (29) (L, or can be subdivided)
Unconventional spaceflight: Cannon (30, 30a)
Unconventional spaceflight: Nuclear power (31; can be L)
Unconventional spaceflight: Solar sails and ion rockets. (32-33)
(supplement with sections on ions and plasmas from "Exploration")
Satellite orbits (12a, 21, 21a, 34) (L)
Lagrangian points (34, 34a, 34b)
Planetary encounters (35, 35a)
(L if supplemented by material on specific missions)
The legacy of Al Khorezmi (M-2 and additional sources)
Trigonometry and the discovery of Mt. Everest (M-6, 8d)
The ideas "Stargazers" tries to transmit
"From Stargazers to Starships" was preceded by a slightly larger web site "The Exploration of the Earth's Magnetosphere" covering the magnetic environment of Earth in space--the polar aurora, radiation belts, magnetic storms. cosmic rays and much more. Non-mathematical and self-contained, 'Exploration" begins with an outline of the physics involved, much of it relevant to the high-school curriculum. Teachers who wish to introduce their classes to magnetic fields, electrons, ions, plasmas, the Sun and its eruptions, the solar wind and discoveries made by unmanned satellites, will find there a great deal of useful material.
"Stargazers" shares many of the ideas which guided "Exploration":
- Use of history of science as a unifying framework. By tracing the evolution of ideas, a logical framework is established in the mind of the student. The personalities of the discoverers, the twists and turns which may precede a discovery, all these help bring the subject to life.
The students will realize that old-time scientists could be quite ingenious--Eratosthenes in estimating the size of Earth, Hipparchus using eclipses to locate the Sun's place in the sky and estimate the distance of the Moon, and even Ptolemy's epicycles make sense when one is faced with the retrograde motion of the planets. They will find that the arguments of Columbus were in fact false, that his opponents never claimed the Earth was flat, and that were it not for the rocket nozzle which Goddard adapted from steam turbines, space flight might have remained an impossible dream. They may then decide that science isn't such a boring business after all!
- Both sites tried to transmit the spirit of scientific inquiry. There is no prescribed road to discovery, and Nature often poses puzzles more intricate than textbooks suggest. The student will come to understand that science is an extension of common sense and rests on a network of logical deductions. Wild theorizing has no place in it--rather, explanations are accepted as true only after nothing else makes sense, and unsolved problems still exist that stymie the sharpest minds.
- "Stargazers" and "Exploration" also try to provide a balanced view of what scientists are like. Not nerds in white labcoats, out of touch with the "real world," but active individuals who form very much part of society. And furthermore, science is an important part of the world's cultural heritage. Al Khorezmi writing on laws of inheritance, the story of trigonometry and mapmaking (and the word "benchmark" entering our language), the daydream of Robert Goddard and the strange tales of Gerald Bull and of "Project Orion"--they all belong.
- We hope that acquainting the student with the ideas and arguments behind accepted scientific "facts" will deepen their understanding, even when limitations imposed by time and by the nature of the material do not allow a "hands on" experience. Both "Stargazers" and "Exploration" have tried to avoid "book knowledge"--facts the student learns from the book alone, without a clear idea of why they are held true.
For instance, "Stargazers" does not give the students any mnemonic for remembering the names and order of planets, but it does dwell on where the planets appear in the sky, how they seem to move and how Ptolemy and Copernicus regarded such motions. It would be great if students actually went outdoors at night to examine the sky, and some might be motivated by this material to do so, but within the limitations of the web, it would be hard to go beyond the present coverage.
Some of the details differ. "Exploration" was completely non-mathematical, while "Stargazers" included some mathematics, especially concerning Newtonian mechanics. The math was kept to a minimum, and a "mathematical refresher" was provided, covering the tools used here. We named it "refresher" to attract students unsure of their own skills, but actually it is a complete (though brief) self-contained course, and sould provide a patient and motivated student, even one unfamiliar with algebra and trigonometry, with all the required tools.
A high-school course would also need problems, and those (at least for now) teachers would have to provide from their own resources. In a later version of "Stargazers", a list of problems will be provided.
What is covered
--The celestial sphere, its apparent rotation and its relation to the rotation of the Earth.
--The annual path of the Sun around the ecliptic.
--The daily path of the Sun in different seasons, and
the consequent variation of its heating ability.
--The principle of the sundial, with instructions for a paper model.
--Different calendars--Julian, Gregorian, Metonic and Muslim.
--The precession of the equinoxes.
--Variations of the Earth-Sun distance and the Milankovich theory of ice ages.
--The size and shape of the Earth, and the Columbus controversy.
--The distance to the horizon.
--The calculation by Hipparchus of the distance to the Moon, using
(1) An eclipse of the Sun (2) An eclipse of the Moon
--The notion of parallax, and its use in estimating distances to the stars.
--The theories of planetary motion by Ptolemy and Copernicus.
--The work of Tycho Brahe and Kepler, and Kepler's laws,
with illustrations and explanations.
--An optional section on the way orbits are calculated,
including orbital elements and Kepler's equation.
--Free fall and its acceleration g.
--The motion of thrown objects
--Simple vectors and the way they are added.
--Energy--potential, kinetic and other kinds.
--Newton's laws of motion, in their conventional form.
Action and reaction.
--The concept of mass and the distinction between inertial mass
and gravitational mass.
--An illustration of inertial mass: how astronauts "weighed"
themselves in a "zero g" environment, aboard space station Skylab.
--Newton's second law in Mach's formulation.
--Concept of moving frame of reference, and its application to
swept-back airplane wings and aircraft propeller operation.
--Motion in a circle and centripetal acceleration.
--How Newton showed a connection between g
and the distance and period of the Moon.
--Kepler's 3rd law for circular orbits, in particular
for Earth satellites.
--Motion in a circle as seen from the rotating frame of reference:
centrifugal forces and "zero g."
--Coriolis forces aboard a spinning space station
and on the spinning Earth.
--Center of gravity and the principle of rocket action.
--How Robert Goddard used a ballistic pendulum to measure the efficiency of a rocket engine, and how he greatly improved that efficiency.
--(Sect 34a) Approximate derivation of the distance to the L1 Lagrangian point.
--(Sect 34a) Approximate derivation of the location of the L5 Lagrangian point.
--(Sect. 35 at the end) Elastic collisions and close encounters between
spacecraft and planets (or the Moon). Also (sect. 35a) the operation of the Pelton water turbine.
--Robert Goddard's pioneering work
--The contributions of Von Karman, Von Braun, Korolyov and others.
--The V2 rocket in WW II, Sputnik, Explorer 1, the space race.
--The staging of rockets.
--Manned spaceflight and the problem of safe reentry into the atmosphere.
--Types of unmanned spacecraft: looking up at the sky, looking
down at Earth, sampling the space environment, serving mankind and exploring distant space and planets.
--The light-gas cannon as a possible space launcher.
--Nuclear propulsion in space and the Orion project.
--Ion rockets and their current status.
--Orbits in space--synchronous, sun-synchronous, Lagrangian pts.
--Planetary encounters and their use in flights to distant destinations.