Question

Both kepler's laws and newton's laws tell us something about the motion of the planets, but there are fundamental differences between them. What are the differences?

Answer 1

Answer: See description

Explanation:

Kepler's laws have three principal points:

1. planets orbit the sun in elliptical paths

2. the orbial period is related to the orbital distance by $T^{2} = d^3$

where T is the orbital period and d is the orbital distance, T is in years and d is measured in units of the earth sun distance.

3. planets closer to the sun move faster than planets far away from it.

Newton:

Newton discovered that there is a consequence to the gravity exerted by objects: mass, the heavier the planet, the more gravitational force it posseses ( thats why we orbit the sun)

with the gravitational force $F_{gravitational} =G \frac{Mm}{r^2}$ newton discovered the inverse-quadratic relationship between the distance of the planets and the acceleration exerted by the force one could exert on another.

Kepler's laws were mostly based on observed evidence with quantitative relationships between the mentioned variables. Newton's laws are based on calculus and symbolic equations. While Kepler's mode is basic, Newton took another step in and build a more general model for gravity (which was improved by general relativity later). In a nutshell Newton proved the scientific causes for Kepler's laws...