Download Kepler*s Laws of Planetary Motion

Kepler’s Laws of
Planetary Motion
Bormann
Honors 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)
Who is Johannes Kepler?
 Johannes Kepler came before Newton’s time. Between
the years (1571 and 1630) he developed
a quantitative description of the motions
of 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
Mercur
y
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
 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
Kepler’s 2nd Law
The 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 Law
 The 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 orbit
around another object.
Distance (d) – distance between planet
and the sun measured in Astronomical
Units.
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 km
or 93 million miles.
When we compare the orbits of the planets…
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
We find that T2 and R3 are essentially equal.
What does all of this have to do
with Isaac Newton?
 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
1642 (died in 1727)
mathematics
as a tool for understanding physics
 Newton built on Kepler’s Laws by using
 He provided the general explanation of the motions of planets
through Newton’s Laws of Motion
and The Universal Law of Gravitation
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?
A force constantly tugging at the planet (gravity) which would cause it to curve
inward.
 Because of gravity why don’t planets just get sucked into
the Sun?
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.
 Why do planets move faster when closer to the Sun?
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.