Kepler's Three Laws

Thanks for reminding us SGT (Join to see) that March 8, 1618 Johannes Kepler discovers the third law of planetary motion which is "sometimes referred to as the law of harmonies - compares the orbital period and radius of orbit of a planet to those of other planets. The third law makes a comparison between the motion characteristics of different planets. The comparison being made is that the ratio of the squares of the periods to the cubes of their average distances from the sun is the same for every one of the planets.

Kepler discovered that the size of a planet's orbit (the semi-major axis of the ellipse) is simply related to sidereal period of the orbit. If the size of the orbit (a) is expressed in astronomical units (1 AU equals the average distance between the Earth and the Sun) and the period (P) is measured in years, then Kepler's Third Law says:

After applying Newton's Laws of Motion and Newton's Law of Gravity we find that Kepler's Third Law takes a more general form:

Image: Kepler's 3rd law equation - General Form
where M1 and M2 are the masses of the two orbiting objects in solar masses. Note that if the mass of one body, such as M1, is much larger than the other, then M1+M2 is nearly equal to M1. In our solar system M1 =1 solar mass, and this equation becomes identical to the first.

Summary
Kepler's 1st Law the law of ellipses - explains that planets are orbiting the sun in a path described as an ellipse. Kepler's first law is rather simple - all planets orbit the sun in a path that resembles an ellipse, with the sun being located at one of the foci of that ellipse.

Kepler's 2nd Law the law of equal areas - describes the speed at which any given planet will move while orbiting the sun. The speed at which any planet moves through space is constantly changing. A planet moves fastest when it is closest to the sun and slowest when it is furthest from the sun. Yet, if an imaginary line were drawn from the center of the planet to the center of the sun, that line would sweep out the same area in equal periods of time.

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Great science share.

Interestingly, the most thought provoking of those is the concept that the square of the mean period of orbit is proportional to the cube of the mean radius, I've actually seen the proof, however, it is by no means instantly apparent, and actually takes a fair level of thought to be able to understand why it's actually true...just thought I'd mention that, I didn't know if you'd seen or noticed that aspect...