Kepler’s Laws of Orbital Motion
Concepts of Physics
Mr. Kuffer
Orbital Theories: Ptolemy
• Second Century A.D.
• Reinforced geocentric view of the Universe
(everything else revolved around the Earth)
Orbital Theories: Copernicus (1473-1543)
• Polish astronomer who surmised that the
Earth rotated about its own axis, and that it
revolved around a stationary Sun.
FYI: Died about 20 yrs before galileo’s birth
Orbital Theories: Tycho Brahe (1546-1601)
• Danish astronomer who spent years measuring
the position of astronomical objects, including Mars
• His goal: Understand the motion of the planets.
• Did not possess mathematical skills needed to
analyze his data.
Orbital Theories: Johannes Kepler (1571-1630)
• Mathematician hired by Brahe to analyze planetary
observations.
• Worked for ten years, realizing that Mars’ orbit did
not quite fit a circular orbit, or that of multiple circles.
• Finally, he fit the data into an ellipse – and it worked!
Let’s Put This Into Perspective…
Nicolas Copernicus
De Revolutionibus by Copernicus
Tycho Brahe
Galileo Galilei
Johannes Kepler
Telescope invented by Johann Lipperhey
Isaac Newton
1473 to 1543
1543
1546 to 1601
1564 to 1642
1571 to 1630
1608
1642 to 1727
The Ellipse
Definitions:
• F1 and F2 are foci (pronounced “Foh-sigh”)
• Lines from both foci to the same point along the ellipse
always add up to the same constant value
(we will do a lab with this!)
The Ellipse, Washington, D.C.
Kepler’s First Law
All planets move in elliptical orbits
with the Sun at one focus.
Important Vocabulary
Perihelion: Point of the orbit closest to the Sun.
Aphelion: Point of the orbit furthest from the Sun.
(Memory Trick: “Aphelion” = “Away”)
Kepler’s Second Law
“The Law of Equal Areas”
A line drawn from the Sun to the planet
sweeps out equal areas in equal time.
Kepler’s Second Law is the result of
the Conservation of Angular Momentum
A familiar example of the
Conservation of Angular
Momentum is an ice skater.
With her arms out, she turns
slowly. If she brings her arms
in close to her body, she will
speed up due to the Conservation
of Angular Momentum.
Remember, the force of gravity is inversely
proportional to the square of the distance between
the two objects.
Fg = G m1 m2 / r2
Intuitively,
As the planet gets closer to the Sun, the force of gravity
increases, accel increases, and the planet speeds up.
As the planet gets further from the Sun, the force of
gravity decreases, accel decreases, and the planet
slows down.
“It’s not magic, it’s Physics!”
Kepler’s Third Law
Planets distant from the Sun have longer orbital periods
than planets that are closer to the Sun.
R3 / T2 = Constant
Where T is the time (or period) for one orbit,
and R is the average orbital radius.
The Kepler Space Probe
• NASA’s first mission capable of finding Earth-size and
smaller planets around other stars.
• Will survey our region of the Milky Way to detect planets
in the “habitable zone,” which are distances from stars in
which liquid water can exist on the surface.
• Launched into space on March 6, 2009.
How will Kepler detect other Earth-like planets?
Kepler will use something called the “Transit Method”
Planetary transits can cause a 1/10,000th reduction in a star’s brightness
Once detected, the planet’s orbital size is calculated with Kepler’s Third
Law using the period of orbit and the mass of the star.
The size of the planet is calculated using the size of the star, along with
how much the brightness of the star dropped during the transit.