Amending Celestial Mechanics
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. The implementation of this new description for theequation also reveals more about the proportions of radius to period among the elliptical orbits in each set of bodies around a primary. One consequence is some descriptions in celestial mechanics should be amended.
This post supersedes my March 13 post: Amending Kepler's 3rd Law because the attachment draws an additional conclusion from the same data.
Kepler's 3rd law has an equation which implies using AU and year units. This 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.
Exoplanet orbits are in AU and days; again, the unit conversion fails.
To confirm my amendment for applying orbits of moons and exoplanets to the equation, I created 2 spreadsheets: 1) all the solar system objects including all the planets, moons, asteroids, and several periodic comets. 2) many of the exoplanets (some have missing data). Both spreadsheets use the proportional value as required for the unitless 3rd law equation. This Excel exercise confirms 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.
Stars do not move in a galaxy like planets move around the Sun. The disk rotates by the galactic magnetic field and birkelund currents (with their magnetic field) in the spiral arms provides that structure. 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 where a longer radius needs more time. The equation defines a r^2 = p^3 relationship between orbit radius and period.
This proportion of the ellipses in a system is demonstrated by this equation for each.
The document has links to the 2 spreadsheets.
Celestial mechanics concentrates on details about individual orbits without noticing an overall pattern found with different primary bodies for their respective sets of smaller bodies in orbit.
Proportional obits are observed with the primary either a star or planet.
Perhaps my conclusion reaches too far but it results from the data.
My case is presented in an 11page pdf rather than a long FaceBook post. This document format has much space.
link
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