Chapter 7

The Path To Space 

The two previous chapters extended modeling of motion in Earth's atmosphere to two dimensions. This chapter extends the modeling to three dimensions. It contains four closely related topics.  

The first topic contains terms and relationships used in describing orbital motion, in or out of atmosphere and takes into account a rotating earth.

The second topic provides a detailed description of a spreadsheet macro suitable for modeling orbits and trajectories in and out of Earth's atmosphere.

The third topic is about determining past and future positions and their time of occurrence for an object in orbit based on observations of the object's positions in a part of its orbit.

In the fourth topic, the orbit that is found in the third topic is tested for conformity with the first two of the conclusions of Kepler.

The topics of this chapter can be accessed by clicking their names.

Topic Name An Image from the Topic Brief Description
Three-Dimensional Modeling with Application to Long-Range Artillery, Satellite and Planet Orbits A Rotating Spherical Earth

Keplerian Orbital Elements

Sensed Acceleration
Three-Dimensional Modeling -The Spreadsheet Documentation


Input Parameters

Output Table

Integration Routine

Second Order Integration
Use  a Spreadsheet to Find a Complete Orbit from Few Observations Part A Reference Ellipse

Ellipse that Fits the Observations

The Ellipse as a Path of an Earth Satellite
Part B - Does The Found Orbit Exhibit the Keplerian Properties?
The Three Conclusions of Kepler

Newton (P/2π )2 =a3/(G(M+m))
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