ORBITS EXPLAINED
A Priori
In Chapter 36 we will develop a formula for areal velocity for elliptical orbits.  Our
scaling methods and knowledge of the behavior of the planets that we have
learned so far will lead to the formula which relates the semilatus rectum, the
Gravitational Constant, and the mass of the Sun to rate of area swept for a
planet in an elliptical orbit.
Chapter 36 GMP / PDF Format
In Chapter 37 we inspect the hodograph for elliptical orbits to obtain a formula
relating the radius of the hodograph circle to the Gravitational constant, the
mass of the Sun, and areal velocity.  This formula will be applied in Chapter 38
in order to develop an equation related to the energy of a planet.
Chapter 37 P Velocity / PDF Format
In Chapter 38 we inspect the hodograph to develop a formula relating the velocity
of a planet in an elliptical orbit to the Gravitational Constant, the distance to the
Sun, the mass of the Sun, and the semimajor axis length.  Chapter 37 was helpful
in demonstrating a mathematical relationship between the radius of the
hodograph circle and the Gravitational Constant, the mass of the Sun, and aereal
velocity.
Chapter 38 Total Velocity Squared / PDF Format
In Chapter 39 we derive in a priori fashion the Energy Equation for orbits.  It can
take many forms and indeed it does with several fascinating interpretations in
Chapter 39.  In one of its forms the Energy Equation relates escape velocity to total
velocity in terms of the mass of the Sun, the Gravitational Constant, the distance to
the Sun, and the semimajor axis length of the orbit.
Chapter 39 Energy Equation Derived / PDF Format
We have finished the proof portions of Orbit Explained. In the final chapters we
apply what we learned, for enjoyment, to orbital situations.  In Chapter 40 we
see some known properties of ellipses, particularly as they relate to the directrix.  
We will need this to understand the mathematics of polar coordinates for
elliptical orbits as demonstrated in Chapter 41.
Chapter 40 The Directrix / PDF Format
In order to apply our knowledge to actual orbital predictions, we need to be
able to express the position of the planet in polar coordinates.  We will do this
in Chapter 41 so that we can examine orbital situations in Chapter 42.
Chapter 41 Polar Coordinates / PDF Format
In Chapter 42 we see several orbital situations that we can analyze using
the equations we derived in Orbits Explained.
Chapter 42 Elementary Predictions / PDF Format
In Chapter 43, we take a brief philosophical glimpse of what has been
accomplished in Orbits Explained.
Chapter 43 Philosophical Metaphysical Orbits / PDF Format
All material copyright 2006 David S. Marlin
Permission granted to copy for study and teaching purposes.
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Orbits Explained.

Carry on and Fare Well.

-DAVID S. MARLIN