Kepler,

Kepler, Newton, and Their Laws of Motion By: Wondra Lawson and Jessica Toole Sir Isaac Newton and Johannes Kepler had corresponding views on the motion of celestial bodies in the universe. On this page, you will find a brief explanation of what those beliefs were and how they relate to one another.

Kepler's Laws of Motion Johannes Kepler determined three laws characterizing orbital motion, using Tycho Brahe’s planetary observation data. These laws can be proven mathematically using Newton’s law of gravitation. These laws are:

Kepler’s First Law:

Satellite orbits are elliptical Paths with the Earth at one focus of the ellipse.

Kepler’s Second Law:

A line between the center of the Earth and the satellite sweeps out equal areas in equal intervals of time.

Kepler’s Third Law:

The square of the orbital period is proportional to the cube of the the orbit's semi major axis.

Newton's Laws of Motion Sir Isaac Newton formulated laws to explain the relationship between force and motion. In addition, these laws modified and completed Kepler's Laws. These laws are:

Newton's First Law:

Every body continues in a state of rest or in a state of uniform motion in a straight line unless it is compelled to change that state by a force acting on it.

Newton's Second Law:

When a force (F) acts on a body of mass (M), it produces an acceleration (A) equal to the force divided by the mass. In other words, A=F/M or F=MA.

Newton's Third Law:

To every action, there is an equal and opposite reaction.

Newton's Law of Gravity:

Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. In other words, two bodies of masses (M¹ and M²), separated by a distance (R), attract each other with a force (F) that is proportional to (M¹ and M²)/R². Or, in mathematical terms: F=GM¹M²/R².

How They Relate: Kepler's Laws are implied by those of Newton, and use his laws to supply corrections to them. Here are a few examples of how Newton's Laws correct and modify Kepler's Laws:

Since the planets move on ellipses (Kepler's 1st Law), they are continually accelerating. This implies a force acting continuously on the planets.

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

From Kepler's 1st Law the orbit is an ellipse with the Sun at one focus; from Newton's 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.

Kepler's 3rd Law and Newton's 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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