Download Review Lecture 5

Review Lecture 5
1) Calendar
46 B.C. Julius Caesar - 365days + leap year every 4 years
1582 A.D. Gregory XIII - subtracted 10 days from the calendar, cut
leap year in centuries not divisible by 400, this is close to a
synodic year = 265.2422 days
2) Some distances
3) History
Earth’s radius
Sun’s radius
Earth - Moon
Earth - Sun
Moon’s radius
rearth = 6.4 x 106 m
rsun = 6.95 x 108 m ~ 100 rearth
3.8 x 108 m
1 A.U. = 1.5 x 1011 m
rmoon = 1.7 x 106 m
Thales ~ 600 B.C., predicted eclipses from Saros cycle.
Pythagorus ~ 500 B.C., said Earth was spherical from observation of
lunar phases.
Aristotle ~ 350 B.C. proposed Earth at center of universe. This is the
geocentric world view of Solar System.
Aristarchus ~ 250 B.C. estimated all the distances above. He
claimed the Sun was the center of the universe. This is the
heliocentric world view.
Eratosthenes ~ 200 B.C., estimated rearth from shadows cast on the
Moon during a lunar eclipse.
Hipparchus ~ 130 B.C., discovered the precession of the north
celestial pole.
Ptolemy ~ 150 A.D., explained motion of the Sun, planets, and Moon
with Epicycle Theory. This is the Earth at center of universe
theory = geocentric world view.
Copernicus ( 1473-1543) published De Revolutionibus (1543) to
explain heliocentric world view.
Tycho Brahe (1546-1630) built first modern European observatory.
Johannes Kepler (1571-1630) Brahe’s assistant calculated planetary
positions using heliocentric assumption.
Isaac Newton (1642-1727) explained all by introducing the
Universal Law of Gravitation.
4)
Ptolemy thought each planet moved in a circular epicycle, whose center moved
in a circular orbit (deferent) around a point near the Earth. The Ptolemaic view
of the universe was believed between A.D. 100 and 1500.
4) Kepler’s Laws and Planetary Motion
(1) Law or Orbits - orbits are elliptical with sun at one focus
(2) Law of Areas - A line joining a planet to the Sun sweeps out equal areas in
equal times
(3) Law of Periods - (orbital radius)3 ~ (orbital period)2
(1) Law of Orbits - All planets move in elliptical orbits with the sun at one focus.
e = eccentricity
a = semi-major axis
b = semi-minor axis
for an ellipse:
r1 + r2 = 2a = constant
x2 y2
+
=1
a2 b2
b = a 1 − e2
A few values for comparison:
e = .093 or b = .996 a only a .15% difference from sphericity
Mars
e = .007
Venus
e = .017
Earth
Jupiter
e = .048
(2) Law of Areas - A line joining the planet to the Sun sweeps out
equal areas in equal times.
For the areas to be the same in the
same time implies that the velocities
V >> v.
This says that a comet with a very
elliptical orbit will spend most of its
time at the farthest point from the sun.
(3) Law of Periods - The square of the period of any planet is proportional to the cube
of the semimajor axis of its orbit.
Name of
Planet
Mean Distance from the Sun
Period
T2
Eccentricity
R3
m
A.U.
Sec
Earth Years
Mercury
5.79 x 1010
0.387
7.6 x 106
0.241
0.2056
1.01
Venus
1.08 x 1011
0.723
1.94 x 107
0.615
0.0068
1.02
Earth
1.50 x 1011
1.000
3.16 x 107
1.000
0.0167
1.00
Mars
2.28 x 1011
1.574
5.94 x 107
1.881
0.0934
1.01
Jupiter
7.78 x 1011
5.204
3.74 x 108
11.86
0.0485
1.02
Saturn
1.43 x 1012
9.58
9.35 x 108
29.6
0.055
1.01
Uranus
2.86 x 1012
19.14
2.64 x 109
83.7
0.047
1.01
Neptune
4.52 x 1012
30.2
5.22 x 109
165.4
0.008
1.01
Pluto
5.90 x 1012
39.4
7.82 x 109
248
0.249
1.01