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Kepler's Laws

Sections involving Kepler's Laws in "From Stargazers to Starships"

    The following 9 sections discuss Kepler's laws and develop some applications. Includes equations and properties of conic sections, the derivation of the scale of the solar system (absolute distances, not relative ones), the energy equation for Keplerian motion and the reason why spring and fall equinox are not exactly half a year apart. Much of this is optional material for individual exploration.

    Section 12b goes into some details of interest to those who wish to study more of celestial mechanics, , e.g how the "mean anomaly" (briefly defined in sect. 12) is actually derived, and how the orbit is defined in three dimensions.

    This discussion continues in section #20 on Newton's "Universal Gravitation" and the two that follow, in which Kepler's 3rd law is derived for circular orbits.

    In section #21b Kepler's 3rd law is used to calculate (approximately) the time needed for a spaceship to fly from Earth to Mars.

    Later section #S-4A-4 discusses deviations from Kepler's 3rd law in the rotation of galaxies, part of the evidence for the existence of "dark matter".

    Lesson plans for teachers exist for most of these sections, starting with and continuing in sections 11, 12, 11a, 12, 20 and 21 of

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Author and Curator:   Dr. David P. Stern
     Mail to Dr.Stern:   stargaze("at" symbol) .

Updated: 18 September 2004, last updates 3 April 2014