1. The Organization of the Solar System and Planetary Motion

2. At first… The Egocentric Earth
Ancient Greece: planets, Sun, Moon, and stars orbit around the Earth
Pythagoras and followers used math to describe natural phenomena
Aristotle: the universe is governed by regular laws

3. Ptolomy’s Geocentric Model
Complex interactions of circles
Each planet orbits around a circle - the epicycle
The epicycle orbits on a bigger circle - the deferent - around the Earth
The center of the deferent
a point near the midpoint of the distance between Earth and the Equant
The equant
the point at which an epicycle’s center always seems to move at the same speed.
each planet has a different equant.

4. Problems with the Geocentric Model
Retrograde motion of planets
Planets move eastward (left) relative to background of stars in the northern hemisphere
Occasionally, the planets seem to stop and then back up ofor several weeks or months (westward movement)
The mechanical description of a geocentric model was complex
As observations improved, the model increasingly failed to fit the data
Aristarchus: all planets orbit the Sun (ignored for 1800 years)

6. Copernicus: The Heliocentric Model
Assumed that everything orbits the Sun (circular orbits)
Mercury and Venus are always observed fairly near the Sun, then they must be closer to the Sun
Mars, Jupiter, and Saturn are high in the sky in the middle of the night, when the Sun is far below the horizon - they are farther way

7. Kepler’s First Law
Based on planets’ positions against the background of distant stars, orbits must be elliptical
First Law:
The orbit of a planet about the Sun is an ellipse with the Sun at one focus
Orbital Eccentricity (e):
Roundest ellipse is a circle (e = 0)
Straight line (e = 1)

9. The longest diameter (passing through the 2 foci) is called the major axis.
1/2 major axis = semimajor axis (a) -
the avg distance between a planet and
the Sun

10. Kepler’s Second Law
A line joining a planet and the Sun sweeps out equal areas in equal intervals of time (Law of Equal Areas)

11. Kepler’s Third Law
The square of a planet’s sidereal period around the Sun is directly proportional to the cube of the length of its orbit’s semimajor axis
Sidereal period: orbital period of one object about another measured with respect to the stars
Rotation versus revolution
A solar day (defined as noon-to-noon) is different from a sideral day (defined as one Earth rotation).
Mean Solar day: 24hrs
Sidereal day: 23hrs, 56min
This means that a fixed star rises 4 mins earlier each successive night, or two hours earlier each month.
P2 = a3
A planet closer to the Sun has a shorter year than does a planet further from the sun

12. Galileo
Venus appears smallest at gibbous phase and largest at crescent phase
This observation supported the fact that Venus orbits the Sun

13. Galilean Moons
Orbit Jupiter because they move across from one side of the planet to the other
Jupiter’s four moons obey Kepler’s third law

14. Newton’s First Law Law of Inertia:
A body remains at rest or moves in a straight line at constant speed unless acted upon by a net outside force
There must be an outside force acting on the planets, otherwise they would move away from the Sun along straight-line paths at constant speeds
Some force confines the planets to their elliptical orbits
Due to momentum
(how much the object tends
to stay in motion):
Momentum = Mass x Velocity

15. Newton’s Second Law
The acceleration of an object is proportional to the force acting on it
The harder you push on an object, the greater the resulting acceleration
F = m x a
If an object revolves around the Sun in circular orbit at constant speed, then it is constantly accelerating in order to change the direction of its motion
Net force causes acceleration

16. Newton’s Third Law
Whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body
The Sun exerts a force on each planet to keep it in orbit, and each planet exerts an equal and opposite force on the Sun

17. Conservation of Angular Momentum
Sun is pulling the planets
Planets don’t fall onto the Sun due to conservation of angular momentum
Measure of how much energy is stored in an object due to its rotation and revolution
Depends on mass, rotation, revolution, and how spread out the mass is
As the orbiting planets fall Sunward, their angular momentum provides them with motion perpendicular to that infall thus continuously missing the Sun

19. Newton’s Law of Universal Gravitation
Two bodies attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Gravitational force decreases with distance
F = G (m1m2/r2)
G = x N m2 kg-2 (universal constant of gravitation)
M = masses
R = radius

20. Example mEarth = 6.0 x 1024 kg mSun = 2.0 x 1030 kg
rS-E = 1.5 x 1011 m
Then,
F = 3.6 x 1022 N
Since, F = m x a,
aEarth = 6.0 x 10-3 m/s2
aSun = 1.8 x 10-8m/s2
Earth pulls on the Sun, causing the Sun to move toward it, but due to the Sun’s greater mass, the Sum accelerates the Earth 300,000x more than the Earth accelerates the Sun