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ASTRONOMY 202 Spring 2007: Solar System Exploration
Instructor: Dr. David Alexander
Web-site: www.ruf.rice.edu/~dalex/ASTR202_S07
Class 8: The Science of Astronomy [1/31/07]
Announcements
The Watershed: Kepler
• The Music of the Spheres
• The solution to planetary motion
Discussion & Questions?
Chapter 3
Announcements
Homework 3 available online – due Mon Feb 5
The Watershed of Science
Johannes Kepler was conceived on 16
May 1571 at 4.37am and was born on 27
December at 2:30pm, after a pregnancy
lasting 224 days 9 hours and 53 minutes.
- recorded in a horoscope cast by Kepler himself
“[Astronomers are] the priests of God, called
to interpret the Book of Nature.”
- in Tertius Interveniens
Johannes Kepler [1571-1630]
“Mars is a star who defies observation”
- Kepler in dedication of Astronomia Nova, 1609
“… those eight minutes point the road to a
complete reformation of astronomy…”
- Ch. 19 Astronomia Nova, on the power of Tycho’s observations of Mars
“The accused appeared in court, accompanied,
alas, by her son Johannes Kepler, mathematician.”
Court scribe at witchcraft trial of Katherine Kepler, 1615
See Sleepwalkers by Arthur Koestler
Kepler’s Three Laws of Planetary Motion
Kepler’s First Law:
An elliptical orbit
The orbit of each planet
about the Sun is an
ellipse with the Sun at
one focus.
There is nothing at the other focus.
The difference between a circle and an ellipse
The elliptical orbit
Eccentricity of an ellipse:
2
b
e2 = 1 − 2
a
c
e=
a
c
b
e = eccentricity
a = semi-major axis
b = semi-minor axis
c = distance from center to focus
a
From Kepler’s 1st law, the Sun lies at one of the foci of the ellipse. This means
that the distance of the planet from the Sun varies during its orbit.
Its closest point is called perihelion.
Its farthest point is called aphelion.
Using the equations for an ellipse we can show that:
dp = a(1-e) at perihelion and da = a(1+e) at aphelion
Kepler’s Three Laws of Planetary Motion
Kepler’s Second Law:
As a planet moves
around its orbit, it
sweeps out equal areas
in equal times.
A major consequence of this law is that:
The velocity of the planet around the Sun
is not uniform
Planets travel fastest at perihelion and
slowest at aphelion.
Comparing orbits
The 2nd Law was actually discovered before the 1st.
Kepler’s Three Laws of Planetary Motion
Kepler’s Third Law:
More distant planets orbit
the Sun at slower average
speed, obeying the
following precise
mathematical relationship:
p2 = a3
p = planet’s orbital period in years
a = planet’s average distance from Sun in AU
A major consequence of this law is that:
The more distant a planet from the Sun,
the slower its average orbital velocity.
vavg =
2πa 2π
= 1/ 2
p
a