Kepler and Newton?

Question

In Kepler's thinking, what was the direction of force on a planet? In Newton's thinking, what was the direction of force?

Answer 1

Kepler was so frustrated trying to describe the planetary motin of Mars that he literally slammed his head against a wall.
Kepler believed that the sun did not sit passively at the center of the solar system but that through some mysterious power or “virtue” actually compelled the planets to hold to their orbits. Because the planets moved slower when they were farther from the sun, this power must diminish with increasing distance. The idea that the planets were controlled by the sun was developed by Isaac Newton in his laws of motion and law of gravitation. Newton assumed that the sun continuously exerts a force on each planet that pulls the planet toward the sun. He calculated that elliptical orbits would result if the force varied inversely as the square of the distance from the sun (i.e., when the distance doubles, the force becomes four times weaker). His law of universal gravitation predicts that the planets exert small forces on each other although subject to the dominant force of the sun. These small additional forces explain most of the small departures from Kepler's laws revealed by later, more accurate observations.

Kepler's Laws
The first law states that the shape of each planet's orbit is an ellipse with the sun at one focus. The sun is thus off-center in the ellipse and the planet's distance from the sun varies as the planet moves through one orbit. The second law specifies quantitatively how the speed of a planet increases as its distance from the sun decreases. If an imaginary line is drawn from the sun to the planet, the line will sweep out areas in space that are shaped like pie slices. The second law states that the area swept out in equal periods of time is the same at all points in the orbit. When the planet is far from the sun and moving slowly, the pie slice will be long and narrow; when the planet is near the sun and moving fast, the pie slice will be short and fat. The third law establishes a relation between the average distance of the planet from the sun (the semimajor axis of the ellipse) and the time to complete one revolution around the sun (the period): the ratio of the cube of the semimajor axis to the square of the period is the same for all the planets including the earth.

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