Kepler’s laws of planetary motion
(Extracted in pure ‘hullabaloo-headache-boosting-scientific-language’ from en.wikipedia, and gracefully ‘headache-disipate-translated’ to the average Joe’s language by me).
‘In astronomy, Kepler’s laws of planetary motion are three scientific laws describing the motion of planets around the Sun.
2. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
3. The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
Figure 1: Illustration of Kepler’s three laws with two planetary orbits.
(1) The orbits are ellipses, with focal pointsƒ1 and ƒ2 for the first planet and ƒ1 and ƒ3for the second planet. The Sun is placed in focal point ƒ1.
(2) The two shaded sectors A1 and A2have the same surface area and the time for planet 1 to cover segment A1 is equal to the time to cover segment A2.
(3) The total orbit times for planet 1 and planet 2 have a ratio [~= are proportional to] of
[semi-major axis for either of the planets to the third power]:
(a1/2)3 and (a2/2)3.’
‘Kepler’s laws improve the model of Copernicus. If the eccentricities of the planetary orbits are taken as zero, then Kepler basically agrees with Copernicus:
(These do not comply with real orbits, because they are elliptic).
The planetary orbit is a circle
The Sun at the center of the orbit
The speed of the planet in the orbit is constant
The eccentricities of the orbits of those planets known to Copernicus and Kepler are small, so the foregoing rules give good approximations of planetary motion; but Kepler’s laws fit the observations better than Copernicus’s.
Kepler’s corrections (<- these do comply) are not at all obvious:
The planetary orbit is not a circle, but an ellipse.
The Sun is not at the center but at a focal point of the elliptical orbit.
Neither the linear speed nor the angular speed of the planet in the orbit are constant, but the area speed is constant.’
I have already explained this, although not in these terms, instead I plunged into solving the problem, and explained only the basics. So if anybody is interested in an explanation more… technical about the eccentricity of the planets orbits or what I wrote in the post for which I have put the link above, feel free to comment and ask me, either here or through my email, which you can see by clicking on the ‘View full profile’ label hovering over my photograph.
‘A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.‘
For this I will upload an image of a lemniscata I provided in the ‘Meridiana… post‘
Image extracted from web.romascuola.net
This curve has this form due to the law #2 of Kepler for the planetary movements, which says the areas covered by the planets (considering they sweep the space between two points in their orbits with a line joining themselves and the astro around which they are revolving , just the way we can sweep an area on the sand if we put an astro-pencil, a thread-force, and a planet-pencil, and move the planet-pencil around the astro-pencil describing a sector of swept sand) all along their orbits are swept with the same velocity.
This is so, because when a planet is near the center of attraction has necessarily to move faster in order to counterpart the attraction force, be it magnetic, gravitational, electrostatic, weak or strong nuclear… because if they would not accelerate they would end up crashing against the astro-center for their orbits movements.
If you array the above image on a circumference, you make the same calculi you’ll end up concluding the same Kepler did some centuries ago.
I’ll go on writing about this in the ‘Kepler’s laws of planetary motions (II)’ post, that I’ll write soon (along with the previous series of posts I am writing about).