# Inventory of "From Stargazers to Starships"

### Sect.             Concepts

1    Celestial sphere and its pole.
Equatorial and alt-azimuth mounting, coordinates.
2    The ecliptic and the zodiac.
Planets in the sky (also in #1)
2a   Sundial construction
3    Seasons of the year and inclination of the Earth's axis.
4    Seasonal changes in the position of the Sun
5    Declination and right ascension, first point in Aries

6   Calendar: solar and sidereal day
Julian and Gregorian calendar
Lunar calendar--Metonic and Moslem.
7   Precession of the Earth, shift of pole star
Milankovich theory of ice ages.
8   Longitude and latitude
Why existence of horizon suggests the Earth curves.
8b, 8d  Parallax, and its use estimating distances--to Moon, Stars, outdoors.
9a, 9b    Aristarchus and his estimate of the size and distance of the Sun
9c   Retrograde motion of inner and outer planets.
Ptolemy's theory of epicycles.
Copernicus model--planets overtaking or being overtaken.
10   Conic sections

11   Orbital elements: Semi-major axis, eccentricity.
Center of motion is not Sun but mutual center of gravity.
12a   Concept of solving an equation by iteration [see M-2 for "Algorithm"]
13   Acceleration, in particular acceleration g of free fall.
14   Concept of vector
vector addition and resolution into components.
15   Energy, kinetic, potential and other kinds.
Conversion of energy from one kind to another,
special role of heat [in 27, heat engines].

16   Newton's 1st and 3rd laws: steady motion in a straight line, reaction
17   Concept of mass--gravitational vs. inertia.
18   Concept of equilibrium, and reaction forces in equilibria.
19   Centripetal acceleration and force.
20   The force of gravitation and its inverse-squares variation.

21   Escape velocity from Earth.
22   Concept of frame of reference: constant motion makes no difference.
23   Motion in a circle as sensed in rotating frame: centrifugal force.
24   "Zero g" in orbiting spacecraft: gravity is still present.
Coriolis force and inertia, on a rotating space station.
25   Concept of center of gravity
Principle of rocket motion.

26   Ballistic pendulum
De-Laval nozzle as a heat engine, rocket design.
27   Staging of rockets, its reasons. Proportion of fuel in a rocket's weight.
28   Problems of atmospheric re-entry, shock wave.
29   (a-e)--- 5 classes of unmanned spacecraft.
30   About using cannon for space launches, need for on-board rocket

32   Solar sails.
33   Solar ion propulsion. Need to neutralize spacecraft.
34   Sun synchronous orbits
Lagrangian points
Escape velocity from the Sun
35   Elastic collisions with moving body can lose or gain energy
Rocket propulsion gains leverage if applied near planet or star.

### Sect.      Calculations and formulas

2a    (formulas for sundial--optional)
2a+  (reason why sundial must point at pole of the heavens--optional)
5     Cartesian and polar coordinates, in 2 and 3 dimensions (sine & cosine)

8     Calculation by Erastothenes of the Earth's size.
8a    Distance to the horizon (use the theorem of Pythagoras)
8b, 8c  Calculation of the distance to the Moon by Hipparchus
8d    Derivation of the parsec.
10    Kepler's laws, formula for the 3rd law and
examples from solar system.

11    Graphs of functions in rectangular and polar coordinates.
Graph of cosine and of ellipse, properties of ellipse.
12    Energy, and its conservation in free fall and in planetary motion.
(Mean anomaly, describing motion of a planet).
12a  Orbital elements, Kepler's equation.(optional extension)
13    Motion of falling or thrown object.
14    Vector addition and resolution into components
Acceleration down an inclined plane.
15    Equation of energy for falling object and pendulum
Units of energy.

16    Newton's laws.
18    Argument why "F=ma" is by itself meaningless.
Newton's 2nd law--its consistent formulation by Mach.
19    Derivation of centripetal acceler. (using the theorem of Pythagoras).
20    How Newton tied the acceleration g due to gravity
to the Moon's period.

21    Orbital and escape velocities.
Kepler's 3rd law for Earth satellites.
21a  A practical equation for circular orbits around Earth, applied in 34.
22a   Sweep-back of airplane wings
Operation of variable-pitch propeller on an airplane.
(this item & next illustrate frames of reference
and resolution of vectors).
23    Variation of gravity observed from poles to equator. "Loop the loop"
on a roller coaster. Analysis in rotating and static frame.
24    Coriolis force due to Earth's rotation.
Estimate effect in bathroom sink.
25    In 2-body interaction, center of gravity does not move.

26   Ballistic pendulum, used in determining the speed of a bullet.
27    Kinetic energy which needs to be dissipated in rocket re-entry.
30    Acceleration in a cannon for space launches.
Molecular veloc. inside cannon, reason for using hydrogen [also in 31]

34    Lagrangian points L1 and L2 (qualitatively)
34a    Calculating distance to L1, circular orbits.(optional)
34b    Calculating position of L5, circular orbits.(optional)
35    Elastic collisions between oppositely moving objects (by frames of ref.)
35-a  Estimate transfer of energy in elastic collision--
greatest loss when overtaking object moving at half the speed.

M-1    Basic ideas of algebra: (1) unknown numbers can be handled
as numbers. (2) Equal operations on both sides of
equality create new equality.
M-3    Formulas--equations can be given only in symbols.
M-4    Identities: distributive law and its consequences.
M-5    Approximations with small quantities; Newton's binomial theorem.
M-6    Theorem of Pythagoras, proof by identities for
the square of sum and difference.
M-7    Trigonometry: basic application, concept of baseline
M-8    Sines and cosines, sums of squares. (tan. & cotan., definition only)
M-9    Calculations: sines and cosines of complementary angles,
derivation for angles of (30, 60), 45, (0, 90) and (15, 75) degrees.
M-10    Sines and cosines past 90 degrees,
generalized using polar coordinates. Graph. M-11   Sine and cosine of sum of angles.

### Sect.      Stories, extensions and illustrating examples

1    Psalm 19
4    Orientation of solar panels
Design of house windows, taking advantage of the Sun's motion.
5    Rene Descartes

6    Lengthening of the day due to tides
Switch from Julian to Gregorian--
Washington's birthday, October Revolution.
7    Use of eclipses by Hipparchus to discover precession of equinoxes.
The evidence for ice ages on Earth.
The song "Dawning of ther age of Aquarius" and its background.
8   Size of Earth as estimated by the ancients and by Columbus.
8a  The story of Pike's Peak.
9    Story of Copernicus.
Galileo and his first-ever astronomical telescope.
10    Story of Tycho and Kepler

13    Stories of Galileo and tower of Pisa,
Galileo using slanted board to study ball rolling under gravity
Cartoon depiction of gravity suddenly taking over is incorrect.
The way a gunsight works
Air resistance, and story of
astronaut demonstrating free fall on Moon
15    Analogy of energy and money.
Calories in food.

16    Isaac Newton.
Examples of 3rd law: jumping from a boat, balancing a bicycle
17      Why mass explains the reason all bodies fall at the same rate.
Mass in the horizontal motion of a heavy wagon.
Measuring mass on the space station "Skylab," in "zero-g."
Analogy to the balance spring on a wristwatch.
17a   The complete story of mass measurement aboard "Skylab".
18    Roland Eötvös and the equality of gravitational and inertial mass.
(in 27, Eötvös and the high schools of Budapest)
20    Story of Newton's apple.

22a    Problems of flight near the speed of sound.
26    History of rocket: Ft. McHenry, Tsiolkovsky, Goddard
Detailed story of Goddard: vision as teen ager.
His use of a ballistic pendulum
Introduction of De-Laval nozzle, liquid fueled rocket.
27    History of rocketry--in Germany (V2) US. Von Braun, Oberth, Karman.
28    Stories of Sputnik and of Explorers 1 and 3.
29    Manned space flight--John Glenn, etc.
29a   Spacecraft for astronomy--Hubble, etc. Links to sites.
29b   Earth-monitoring spacecraft. Links to sites.
29c   Spacecraft observing the Earth's outer environment. Links to sites.
29d   Commercial use of space--comsats, GPS. Links to sites.
29e   Planetary and lunar exploration by spacecraft. Links to sites.

30   The SHARP cannon at Livermore National Lab.
30a   The HARP cannon and the story of Gerald Bull.
31    The NERV and Rover nuclear rocket projects.
"Project Orion"--spaceship propulsion by nuclear bombs.
32    Solar sail projects.
Robert Forward's visionary laser-drive space sail.
32a   Using light pressure for station-keeping beyond L1 Lagrangian pt.
33    Solar ion engines--DS1 mission, XIPS engine.
34    Energy gain of "Voyager", ISEE-3 etc. from close encounters.
35a    Story of Lester Pelton and his turbine--relate to Calif. gold rush.
NASA's solar probe mission.
M-2    History of algebra: Al-Khorezmi.
M-6    Story of how the height of Mt. Everest was first measured.

Author and curator: David P. Stern
Last updated 12 January 1999