Astronomy Lecture Notes Week 06
1. Updates to
a. Daily Schedule
b. Study Guide for Exam #2
2. Review HW #3 Handout
a. Planetary Configurations
b. Lunar Sidereal Period vs. Lunar Synodic Period.
3. Finish Copernicus
a. Retrograde Motion explained
i. See McConnell’s web page
ii. Retrograde motion is an illusion caused by passing a planet.
iii. Retrograde at opposition and brightening at opposition are a natural consequence of the geometry
of the orbits. No more mysterious communications between the planets and the Sun.
b. New Phenomena: See handout
i. True Orbital Periods
ii. Relative Distances to the Planets
c. Problems with the original Copernican Model
i. No Proof the Earth moved
ii. It didn’t work well (circles at constant speeds were the problem)
iii. No mechanism to hold the Earth in orbit around the Sun.
4. Galileo Galilei 1564 –1642
a. His telescopic observations of the
i. Moon – had terrestrial features, not the perfect celestial object Aristotle postulated it was.
ii. Sun – had “blemishes” we now know as sunspots (cooler spots), not the perfect celestial object
Aristotle postulated it was.
iii. Jupiter – had moons orbiting it, so not all motion was around the Earth as Aristotle postulated
iv. Venus – had phases like the Moon but were correlated with different configurations than the
Moon’s phases definitively proving that Venus orbited the Sun, so not all motion was around the
Earth as Aristotle postulated
b. Observations did not prove the Earth moved but they completely undermined the foundational principles
of Aristotle.
5. Johannes Kepler (1571 – 1630)
a. Three Laws of Planetary Motion
i. 1st Law: Law of non-circular orbits
1. Planets orbit on ellipses not circles
a. The structure of an ellipse
i. One formula to compare to a circle.
ii. Major axis, a
iii. Semi-major axis, b
iv. Eccentricity, e
1. Discuss the eccentricities of the planets
2. Calculating perihelion and aphelion from the semimajor axis and
eccentricity.
2  a  rP  rA see it in the figure.
r
b. e  1  P by definition
a
c.  rP  a1  e and rA  a1  e
a.
2  a  a1  e   rA
d.
2a  a  ae  rA
rA  a1  e 
v. Example problems
1. Find the perihelion distance of asteroid 2101 Adonis.
2. Find the greatest distance of asteroid 2101 Adonis from the Sun.
nd
ii. 2 Law: Law of non-constant speeds
1. Planets travel faster when closer to the Sun and slower when farther from the Sun?
2. “Equal Areas in Equal Times”
3. How far is asteroid 2101 Adonis from the Sun when is it moving the fastest?
iii. 3rd Law: Grand Design Law
1.
2
3
PYears
 aAU
2. Example:
3. What is the orbital period of asteroid 2101 Adonis in days?
Planets: Orbital Properties
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Distance
(A.U.)
0.387
0.723
1.000
1.524
5.203
9.537
19.191
30.069
39.482
Revolution Revolution
Eccentricity
Period
Period
days
years
87.969 d
0.2408
0.2056
224.701 d
0.6152
0.0068
365.256 d
1.000
0.0167
686.98 d
1.881
0.0934
11.862 y
0.0484
29.457 y
0.0542
84.011 y
0.0472
164.79 y
0.0086
247.68 y
0.2488
Asteroid 2101 Adonis
Aphelion
3.307 AU
Perihelion
0.441 AU
Semi-major axis
1.874 AU
Eccentricity
0.765
Inclination
(deg)
7.005
3.3947
0.0000
1.851
1.305
2.484
0.770
1.769
17.142