Kepler’s Laws of

Planetary Motion

BormannHonors Science - 8

Lets make some connections…

Aristotle – (384-322 BC)

Nicolaus Copernicus (1473-1543)

Tycho Brahe (1546-1601)

Johannes Kepler (1571-1630)

Galileo Galilei (1564-1642)

Isaac Newton (1642-1727)

Johannes Kepler came before Newton’s time. Between the years (1571 and 1630) he developed

Who is Johannes Kepler?

a quantitative description of the motionsof the planets in our solar system

We classify these descriptions as the laws of planetary motion

Kepler’s 1st Law

Orbits of planets are ellipses with the Sun at one focus.

**Aphelion is the point on the orbit furthest to the Sun**Perihelion is the point on the orbit closest to the Sun

What is an ellipse?

Circle – has same diameter whether you measure across or up an down.

Ellipse – has diameters of different length Major axis – longest

length Minor axis – shortest

length The ratio of the axis

lengths determines the eccentricity of the ellipse.

Eccentricity (e) – measure of how elliptical a planet is

Circle e=0 Very stretched out

ellipse e=1

Mercury

0.206 Saturn 0.054

Venus 0.007 Uranus 0.048

Earth 0.017 Neptune 0.007

Mars 0.094 Pluto 0.253

Jupiter 0.048

Kepler’s 2nd LawThe Speed of Planets

A line from a planet to the Sun sweeps out equal areas in equal times.

More simple way to say it: planets move faster when closer to the Sun.

2nd Law Animation

Kepler’s 3rd LawThe square of a planet’s period equals the

cube of the semi-major axis (average distance between the planet and its Sun. .

Kepler's Laws Animation

Period (P) – The time it takes for one objet to make one complete orbitaround another object.Distance (d) – distance between planet and the sun measured in AstronomicalUnits.Astronomical Unit (AU) – convenient way to measure distances in the solar system. 1 AU is the distance from Earth to the Sun (also equals to 150 million kmor 93 million miles.

Planet T(yrs) R(au) T2 R3

Venus 0.62 0.72 0.38 0.37

Earth 1.00 1.00 1.00 1.00

Mars 1.88 1.52 3.53 3.51

Jupiter 11.86 5.20 141 141

When we compare the orbits of the planets…

We find that T2 and R3 are essentially equal.

Kepler was able to describe the motion of the planets, however he didn’t provide an explanation as to WHY the planets move this way.

Isaac Newton came along in

Newton built on Kepler’s Laws by using as a tool for understanding

He provided the general explanation of the motions of planets through

and

What does all of this have to do with Isaac Newton?

1642 (died in 1727)

Newton’s Laws of MotionThe Universal Law of Gravitation

mathematicsphysics

Kepler and Newton

Kepler’s Laws define the motion of the planets, but Newton’s Laws define motion.

Newton realized that all motion, regardless if it is occurring on a small scale in front of you or a large scale in space, follows the same basic principles.

Discuss with a partner – How do you think Newton used his laws of motion

to expand on Kepler’s Laws of Planetary Motion? – Be ready to share!

1 - An object in motion will stay in motion and an object at rest will stay at rest until acted upon by an unbalanced force.

2 - Acceleration of an object is dependent on the net force acting upon the object and the mass of the object.

3 – For every action there is an equal and opposite reaction.

Universal Law of Gravitation – Any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of distance between them.

Putting it all together…

A planet would move in a straight path at a constant speed forever unless an unbalanced force acted on it. So why do planets move in an ellipse around the Sun?

Because of gravity why don’t planets just get sucked into the Sun?

Why do planets move faster when closer to the Sun?

A force constantly tugging at the planet (gravity) which would cause it to curve inward.

An orbit is the balance between inertia and gravitational force. The planets in our solar system continually fall toward the Sun, but inertia also wants them to keep moving in a straight line, when these two balance out it results in a stable orbit.The closer the planet is to the Sun the stronger the gravitational force between them, increasing the acceleration of the object. The more distance, the slower they will move which enables the sun to still have a gravitational effect curving the planet toward the sun keeping it in its orbit.