newton law of gravitation from kepler's law

Dear Shubham,

Since this is a survey course, we shall not cover all the mathematics, but we now outline how Keplers Laws are implied by those of Newton, and use Newtons Laws to supply corrections to Kepler Laws.

1. Since the planets move on ellipses (Kepler
2. s 1st Law), they are continually accelerating, as we have noted above. As we have also noted above, this implies a force acting continuously on the planets.

3.  

4. Because the planet-Sun line sweeps out equal areas in equal times (Keplers 2nd Law), it is possible to show that the force must be directed toward the Sun from the planet.

    

5. From Keples 1st Law the orbit is an ellipse with the Sun at one focus; from Newtons laws it can be shown that this means that the magnitude of the force must vary as one over the square of the distance between the planet and the Sun.

    

6. Keplers 3rd Law and Newtons 3rd Law imply that the force must be proportional to the product of the masses for the planet and the Sun.

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