Page 23 - GALIET PHYSICS BLOSSOMS II+

moved by the greater force will accelerate more. The same applies to planetary orbits. By Newton’s Second Law, a force acts at every point on the orbit, which is not constant in magnitude given that the change in acceleration is larger when the planet is nearer the Sun on the elliptical orbit. For example, the greater the force that acts on the planet, or the smaller its mass, the greater is the planet’s acceleration. If two different planets are pulled with the same force, then it is up to mass: the more massive one will accelerate less, and the smaller one will accelerate more. If two identical planets are pulled with different forces, then the one that is acted on by the greater force will accelerate more, and the one that is acted on by a lesser force, will accelerate less. In our case, with the same masses for P1 and P2, acceleration and deceleration will be the same for both.
According to Newton’s Third Law for every force acting on a body, there is an equal and opposite reaction, acting somewhere. That is, if body A exerts a force on body B, then body B necessarily exerts a force on body A that is equal in magnitude, but of opposing direction. This scenario corroborates Newton’s Third Law. If P1 acts on P2, then P2 acts on P1, so there is an equal and opposite reaction.
Conclusion
Newton’s laws improve Kepler’s laws:
1. Because planets orbit elliptically (Kepler's 1st Law), they are continually accelerating implying that a force acts continuously on them.
2. Because the planet-Sun vector sweeps out equal areas in equal times (Kepler's 2nd Law), we can see that the force must be directed from the planet toward the Sun.
3. Newton’s Laws work best on this multiple planet system, while Kepler's laws seem to fail. Kepler’s Laws do not seem to consider the impact of gravitational effects by other additional orbiting planets such as the one had in the P1 and P2 scenario.
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