Toward a Universal Theory of Gravitation
We have shown that Kepler’s Laws follow from Newton’s 2nd Law if the force F on a planet is:
- Question: What more do we have to do to turn this into a “Universal” Law of Gravitation?
- Consider Newton’s 3rd Law:
- If this is the force on the planet due to the Sun, then the planet must also exert an equal force on the Sun, but in the opposite direction.
- There is no mention of the Sun in this equation, but there must be if this force describes the force on the Sun due to the planet.
- Therefore, Kepler’s constant k is not really a universal constant! It must depend on the mass of the Sun!!