What are the differences and similarities of Kepler's laws of planetary motion and Newton's law of universal gravitation?


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Rebecca Hunt answered
The similarities between Kepler's laws of planetary motion and Newton's law of universal gravitation state that the force which holds the planet within their orbits are continuously changing the velocity of the planet because they:

  • follow an elliptical path which is both directed towards the sun
  • is proportional to the total product of the Sun and earth's mass
  • is inversely proportional to the planet-sun separation square

In essence, both laws also state that the planets follow the same  motion of objects as those found in the surface of the earth. On the other hand, the differences are that Kepler's laws state:

  • Every planet's orbit is focused on the sun
  • A line joins every planet while the sun sweeps out equal areas during time intervals

While Newton's laws are:

  • Every force in the universe attracts all other objects with a force which is directly proportional to its mass while being inversely proportional to the calculated square of the distance
  • Every point attracts all other points through a force which points along the line which intersects them both. The said force is directly proportional to the product of two masses while being inversely proportional to the square of the distance between both bodies.

While studying both laws about universal gravitation, one seems to notice that Kepler's laws tend to put the sun at a pedestal. This is because Kepler did have mystical ideas about the sun and treated it as if it were some sort of a god. When Newton's laws came around, he demonstrated that the actual actions taking place were much more symmetrical than what Kepler had implied with his laws, and that the Sun does not occupy a special position in the universe. This is the reason why Newton modified Kepler's third law.

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