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 Project Jupiter
VI. Kepler's Laws

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Abstract
I. Purpose
II. Background
III. Orbits
IV. Period  Determination
V. Methods
VI. Kepler's Laws
VII. Observing Suggestions
VIII. Data Gathering
IX. Data Processing
X. Observer's Data Results
XI. Other Quad-A Results
XII. Conclusions
XIII. Attachments


This Project Jupiter Report was prepared by
Mizar Consulting
Eugene A. Lanning
130 Hillside Terrace
Nebraska City, NE
68410-3740
ealanni@alltel.net
Member of AAAA


AAAA
The American Association of Amateur Astronomers
P.O. Box 7981
Dallas, TX
75209-0981
e-Mail:
aaaa@astromax.com

www.AstroMax.com


Project Jupiter

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VI. Kepler’s Third Law

Project Jupiter will be using an enhanced version of Kepler’s Third Law, an enhancement that considers Newton’s Law of Gravitation.

A. Who was Kepler?

Johannes Kepler was a German mathematician and astronomer who lived from 1571 to 1630. At the time Kepler was alive, Newton’s Law of Gravitation was not yet discovered ( 8 ) , so Kepler’s Third Law is expressed as a proportion rather than an equation.

B. The Laws of Kepler

Based on his observations, Kepler developed three revolutionary thoughts. Thoughts that have withstood the test of time and scientific scrutiny to rise to the classification of a "Law". His Laws, paraphrased, are:

  1. The shape of a planetary orbit is an ellipse. The same hold true for the orbital shape of a moon about a planet. For ellipses, there are two "centers" (called foci ) rather than just one center as for a circle. The more massive of the objects being orbited is located at one of the foci.
  2. A line connecting the planet and the sun sweeps over equal areas in equal time periods. Again, the same is Law applies for a moon orbiting a planet.
  3. The square of the sidereal period 9 of a planet is proportional to the cube of the semi-major axis distance the planet is from the sun. Again, this Law holds for any moon orbiting a planet.

In the exaggerated diagram above, the semi-major axis length is labeled as ‘a’. Because of the mass of the sun, the difference between distance a and distance Rp is actually small.

C. Examining Law #3

Law #3 is the Law that enables us to "weigh" Jupiter in Project Jupiter, when combined with the Law of Gravitation. For the mathematically inclined, the mathematics are presented  in Attachment D. Attachment D is the solution for a circular orbit, an approximation that does not contribute too much uncertainty for Project Jupiter.

Normally an observation series like Project Jupiter is done in a college-level astronomy course. One exciting strength of Quad-A is that its members share expertise freely. This writeup is one such example of shared expertise that is intended to allow all Quad-A members to participate in this project, as the member need not personally fuss with the attendant mathematics.


8 Newton’s laws were formulated around 1666, and published in 1687.

[Home]
[Abstract]
[I. Purpose]
[II. Background]
[III. Orbits]
[IV. Period  Determination]
[V. Methods]
[VI. Kepler's Laws]
[VII. Observing Suggestions]
[VIII. Data Gathering]
[IX. Data Processing]
[X. Observer's Data Results]
[XI. Other Quad-A Results]
[XII. Conclusions]
[XIII. Attachments]

 

The image of Jupiter on the Project Jupiter cover page is courtesy of AAAA member Charlie Warren of Texas. Used by permission. Jupiter and three of its moons - right to left are the moons Europa, Io and Ganymede. Callisto is not on the image. CCD Image taken February 2, 2002.

AAAA
The American Association of Amateur Astronomers
P.O. Box 7981
Dallas, TX 75209-0981
e-Mail: aaaa@astromax.com

www.AstroMax.com