Amending Kepler's 3rd Law
Kepler's 3rd law of planetary motion was intended for planets. Even the name of these laws is explicit.
The description for its equation must be amended for an application to moons and exoplanets.
This post is a followup to my March 9 post: Redefining Kepler's 3rd Law.
I expect this might be just trivia to some and Kepler's laws are not affected by the Electric Universe theory.
Read further and open the attachment ONLY if you are interested in a law written in 1619 (400 years ago) which needs to be amended to apply to moons and exoplanets.
The 3rd law implies using AU and year units. It fails with other units. Nearly all moons have their orbits described in km and in days or hours. After converting km and hours into AU and years the equation still fails.
To confirm my amendment, I created 2 spreadsheets: 1) all the solar system objects including all the moons. 2) many of the exoplanets. Both spreadsheets use the proportional value as required for the unitless equation. As mentioned in that March 9 post, Europa can be used for all the main Jupiter moons. Janus can be used for all the main moons of Saturn. For Uranus, Miranda can be used; for Neptune, Naiad; for Pluto, Styx; for Mars its 2 are proportional to the other. All the giants and Pluto have groups of irregular moons. The irregular groups have a different proportion for their ellipses than the larger moons but the use of a basis for proportions in the equation still works for each group. The 3rd law is about proportions: an orbit's relationship of radius to duration. (2) is a challenge to present because clearly some of these exoplanets and their data are estimates. Sometimes Wikipedia describes 'unconfirmed' results or the suspicion of additional planets and one system even had 'excessive residual velocities' which implies to me this algorithm for extracting an exoplanet is not thoroughly verified. I am honestly surprised most exoplanets conform to this squaredcubed equation.
After the Excel exercise, the amended 3rd law applies to everything that rotates as part of a collection of bodies in orbit around a primary. The primary can be a star or a planet.
As the Electric Universe knows, stars do not move in a galaxy like planets move around the Sun. The 3rd law does not apply to the motion of stars; only the stuff in elliptical orbits around them. Kepler's laws are about ellipses.
Kepler's 3rd law is the mathematical expression of confirming all orbits of the bodies around the same primary are proportional. This is somewhat intuitive and is implied in the 2nd law: a longer radius needs more time.
This proportion of the ellipses in a system is demonstrated by this squaredcubed equation.
The document has links to the 2 spreadsheets.
this post is about only using the 3rd law equation. This is not about the actual data.
link
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