Kepler's Laws Quotes

Yet the widespread planetary theories, advanced by Ptolemy and most other astronomers, although consistent with the numerical data, seemed likewise to present no small difficulty. For these theories were not adequate unless they also conceived certain equalizing circles, which made the planet appear to move at all times with uniform velocity neither on its deferent sphere nor about its own epicycle's center.

Many a zero thinks it is the ellipse on which the Earth travels.

Bullialdus wrote that all force respecting ye Sun as its center & depending on matter must be reciprocally in a duplicate ratio of ye distance from ye center.

Either... the moving intelligences of the planets are weakest in those that are farthest from the sun, or... there is one moving intelligence in the sun, the common center, forcing them all round, but those most violently which are nearest, and that it languishes in some sort and grows weaker at the most distant, because of the remoteness and the attenuation of the virtue.

Planets move in ellipses with the Sun at one focus.

...from the same principles, I now demonstrate the frame of the System of the World.

Planets' orbits are elliptical. It's a very pleasing shape.

I shall now recall to mind that the motion of the heavenly bodies is circular, since the motion appropriate to a sphere is rotation in a circle.

So, Fabricius, I already have this: that the most true path of the planet [Mars] is an ellipse, which Dürer also calls an oval, or certainly so close to an ellipse that the difference is insensible.

The radius vector describes equal areas in equal times.

They have likewise discovered two lesser stars, or satellites, which revolve around Mars, whereof the innermost is distant from the center of the primary exactly three of his diameters, and the outermost five: the former revolves in the space of ten hours, and the latter in twenty-one and a half, so that the squares of their periodical times are very near in the same proportion with the cubes of their distances from the center of Mars; which evidently shows them to be governed by the same Law of Gravitation that influences the other heavenly bodies.

The moon is not kept in her orbit round the earth, nor the earth in her orbit round the sun, by a force that varies merely in the inverse ratio of the squares of the distances.

What's the orbital velocity of the moon?