Lecture #5: Plan
•  The Beginnings of Modern Astronomy
•  Kepler’s Laws
•  Galileo
Heliocentric Universe
•  Nicolas Copernicus
(Poland, 1473 – 1543)
– Revived Sun-centered
model of the Heavens
(On the Revolutions of
Celestial Orbs)
– Explained retrograde
motion (circular orbits)
Distances to the Other Planets
•  Copernicus measured the
time it took a planet to
move from opposition to
quadrature, and calculated
the planet’s relative
distance from the Sun
•  Remarkably accurate!
Planet
Copernicus’s
Calculation (AU)
Actual Distance
(AU)
Mercury
0.38
0.39
Venus
0.72
0.72
Earth
1.00
1.00
Mars
1.52
1.52
Jupiter
5.22
5.20
Saturn
9.17
9.54
Heliocentric Universe
(Copernicus’ version)
•  Assumption: heavenly motion must occur in perfect circles
•  Problem: the predicted planet positions were off!
•  His Solution: added complexities to his model including
circles on circles much like the epicycles of Ptolemy!
Heliocentric Universe
(Copernicus’ version)
Heliocentric Universe
(Copernicus’ version)
•  Assumption: heavenly motion must occur in perfect circles
•  Problem: the predicted planet positions were off!
•  His Solution: added complexities to his model including
circles on circles much like the epicycles of Ptolemy!
→ his model gained relatively few converts
over the next 50 years
The Beginnings of Modern Astronomy
•  Tycho Brahe (Denmark, 1546-1601)
– Made detailed observations of
planetary positions (to within
~1/60th degree = 1 arc min)
– Found that comets moved outside
of the Earth’s atmosphere
– In 1572, he witnessed a supernova &
concluded that it was much farther
away than any celestial sphere
– Did not detect parallax
à seemingly measurable size of stars
implied gigantic objects >> Sun!
à planets go around the Sun, but
Sun orbits around the Earth
The Beginnings of Modern Astronomy
•  Tycho Brahe (Denmark, 1546-1601)
The Beginnings of Modern Astronomy
•  Johannes Kepler (Denmark,
1571 – 1630)
– Used data of Tycho (his mentor)
to derive the laws of planetary
motion
→ “Kepler’s Laws”
Kepler’s First Law (1609)
1. 
Planets move in elliptical
orbits with the Sun at one
focus of the ellipse
a
Kepler’s First Law (1609)
1. 
Planets move in elliptical
orbits with the Sun at one
focus of the ellipse
eccentricity = 0
for a circle
Kepler’s Second Law (1609)
2. 
Planets sweeps out equal
areas in equal times =
“Equal Area Law”
Kepler’s Third Law (1619)
3. 
Orbital period is related to
orbital size:
P2 = a3
P is the period (in years)
a is the semi-major axis (in A.U.)
Kepler’s Third Law (1619)
Example:
Jupiter is 5.2 A.U. from the Sun.
What is its Period?
P2 = a3
P2 = (5.2)3 = 5.2 x 5.2 x 5.2
= 140.6
P = sqrt(140.6) ~ sqrt(12 x 12)
~ 12 years (11.9 years)
Galileo Galilei (Italy, 1564-1642)
•  Applied telescope to study the Heavens
•  Discovered moons (satellites) orbiting
Jupiter
→ Earth is not at the center of all motions
•  Discovered phases of Venus
→ Venus orbits Sun, not the Earth
•  Observed craters on the Moon and
sunspots on the Sun
→ Moon & Sun are “imperfect” like Earth
•  Roman Inquisition found him
“vehemently suspect of heresy” !
→ Forced to recant + house arrest rest of his life
•  One of the principal founders of the
experimental method for studying
scientific problems.
Galileo Galilei (Italy, 1564-1642)
•  Inertia:
Tendency of an object at rest to remain at rest
& an object in motion to keep moving
mass = measure of an object’s inertia