Download Kepler*s Laws of Planetary Motion

Kepler’s Laws of Planetary Motion
Tyco Brahe (1546-1601)
• Danish astronomer
• Had an island
observatory and the
best measurements of
the positions for all
know planets and the
moon
• Mercury, Venus, Mars,
Jupiter, Saturn
Johannes Kepler (1571-1630)
• Austrian mathematician
• Interested in how the
planets move around
the sun
• When to Tyco’s island to
get these accurate
measurements
• At that time, many astronomers believed that
planets orbited around the sun in perfect
circles
• Tyco’s accurate measurements for Mars didn’t
fit a circle
• Kepler found that the orbit of Mars fit an
ellipse the best
First Law of Planetary Motion: A planet’s
orbit is an ellipse with the sun at one
focus and nothing at the other focus
What is an ellipse?
2 foci
• An ellipse is a geometric
shape with 2 foci
• A circle has 1 central
focus
An ellipse also has…
…a major axis
Perihelion
…and a minor axis
Aphelion
Semi-major axis
• Perihelion: When Mars or any other planet is
closest to the sun
• Aphelion: When Mars or any other planet is
farthest from the sun
Second Law of Planetary Motion: the line joining
the planets to the Sun sweeps out “equal areas in
equal times” as the planet travels around the
ellipse
• Kepler also found that Mars changed speed as it
orbited around the sun
– Faster when closer to the sun
– Slower when farther from the sun
• Areas A and B swept out by
a line from the sun to
A
B
Mars, were equal over
the same amount of
time
• Kepler found a
relationship between
the time it took a planet
to go completely
around the sun (T, year)
and the average
distance from the sun
(R, semi-major axis)
T1 2
T2 2
=
T1
R1
T2
R1 3
R2 3
R2
Third Law of Planetary Motion: the ratio of the
square of the revolution time for two planets is
equal to the ratio of the cubes of their semi-major
axes
T2
R2
• Earth’s year (T) is 1 year
• Earth’s semi-major axis
(R), the distance from
the Earth to the Sun, is 1
astronomical unit (AU)
T1 2
R1 3 or T1 2 = R1 3 or T 2 = R 3
=
1
1
2
3
1
1
T2
R2
WHAT DOES THIS MEAN?!?
• If you know the distance from the sun and
year of planet A, and you know the distance
from the sun for planet B you can find the
year of planet B.
OR
• If you know the distance from the sun and
year of planet A, and you know the year of
planet B you can find the distance from the
sun for planet B
When we compare the orbits of the planets…
Planet T(yrs) R(au) T2
R3
Venus 0.62
0.72
Earth
1.00
1.00 1.00 1.00
Mars
1.88
1.52 3.53 3.51
Jupiter 11.86
0.38 0.37
5.20 141 141
We find that T2 and R3 are essentially equal.
Kepler’s Laws apply to any celestial
body orbiting any other celestial body
•
•
•
•
•
Any planet around a sun
The moon around the Earth
Any satellite around the Earth
The International Space Station
Any rings around any planet
Earth’s Movement
Barycenter
• The point between two objects where they
balance each other
– The center of mass where two or more celestial bodies
orbit each other.
– When a moon orbits a planet, or a planet orbits a star,
both bodies are actually orbiting around a point that lies
outside the center of the larger body. (1,710 km)
• The Sun is not stationary in our solar system.
• It actually moves as the planets tug on it,
causing it to orbit the solar system’s
barycenter.
• The sun never strays too far from the solar
system barycenter.
• http://www.youtube.com/watch?v=1iSR3Yw6
FXo
Precession
• Change in the direction of
the axis of the Earth, but
without any change in tilt
• This changes the stars
near (or not near) the
Pole, but does not affect
the seasons
• The Earth’s axis currently
points at Polaris as the
“Northern Star”, but it
wont always be..
Each gyration around the cone
takes 26,000 years
Nutation
• Wobbling around the
precessional axis
• Change in the angle: ½
degree one way or the
other
• Occurs over an 18 year
period and is due to the
Moon
• Very slightly increases or
decreases seasonal effects