Kepler’s
Laws of
Planetary
Motion
Tycho Brahe’s Observations
Brahe’s observations
measured the
positions of stars
and planets with
phenomenal
accuracy. His data
supported the
heliocentric (sun
centered) model
Tycho Brahe (1546 – 1601)
How Tycho Observed the Sky
Parallax
:
apparent
difference in
position of
object viewed
from two
different
locations
Johannes Kepler
Johannes Kepler
(1571 – 1630)
Using data collected by Tycho
Brahe, Kepler derived three
laws of planetary motion.
These laws describe:
1. The shape of planetary
orbits
2. The speed of orbital
motion
3. The relation between
orbital size and orbital
period
ELLIPSE - an oval built around
two points, called foci
If you make a line from one focus, to any point on
ellipse, to the other focus, it will always be the
same length!
Ellipse animation
Kepler’s 1st Law:
“Planets orbit the
Sun in ellipses,
with the Sun at
one focus.”
The eccentricity of
the ellipse, “e”, tells
you how elongated it
is.
When e=0 the shape
is a circle, e<1 for
all other ellipses.
nd
2
Kepler’s
Law of
Planetary Motion:
Planets move fastest when closest to the Sun.
A.K.A. “Equal
areas in equal
times….”
sun
A.K.A. “The
Pizza Pie Law”
If it sweeps out equal areas in equal times,
does it travel faster or slower when it is
far from the Sun?
If it sweeps out equal areas in equal times,
does it travel faster or slower when far
from the Sun?
If is sweeps out equal areas in equal times,
does it travel faster or slower when far
from the Sun?
Same Areas
• Perihelion: point in orbit closest to the Sun
• Planet moves at its fastest velocity
• Aphelion: point in orbit farthest from the
Sun
• Planet moves at its slowest velocity
IN PLAIN ENGLISH:
A
planet moves faster in its
orbit when it is closer to the
Sun
 i.e. faster at perihelion &
slower at aphelion
A line joining a planet and the Sun sweeps
out equal areas in equal intervals of time.
•Perihelion: closest to Sun, fastest motion
•Aphelion: farthest from Sun, slowest
rd
3
Kepler’s
Law of
Planetary Motion:
A planet’s orbital period is
proportional to its average
distance from the Sun.
distance
period