1. Chapter 13: The Law of Gravity
Reading assignment: Chapter 13.1 to 13.5
Homework (due Wednesday, Nov. 14): OQ1, OQ2, OQ5, OQ8, 2, 3, 6, 10, 13, 14, 18, 28, 33
Historically very interesting, heliocentric vs. geocentric universe
The main cast: Copernicus, Brahe, Galileo, Kepler, Newton
Satellite motion
Copernicus
1473 – 1543
Brahe
1546 – 1601
Galileo
1564 – 1642
Kepler
1571 – 1630
Newton
1643 –

2. Geocentric vs. heliocentric model of earth
Earth is round! Slowly accepted, starting in ancient Greece, Magellan + Elcano circumnavigation (1519 – 1522).
Ptolemy (100 –170 A.D.) geocentric model: Sun revolves around earth (Wrong!)
From astronomical observations:
Copernicus ( ) heliocentric model: Earth & planets revolve around sun
Brahe ( ) Accurate observation of planetary motion
Galileo ( ) (1610) supports the heliocentric model
Kepler ( ), 1609: Laws I, II of planetary motion,
Kepler 1619: Law III of planetary motion
About falling objects
Aristotle ( B.C.) Heavier objects fall faster than light objects (Wrong!)
Galileo ( ) Neglecting air resistance, all objects fall at same acceleration

3. Newton’s Law of Universal Gravitation
Every particle in the Universe attracts every other particle with a force of:
G… Gravitational constant G = 6.673·10-11 N·m2/kg2
m1, m2 …masses of particles 1 and 2
r… distance separating these particles
… unit vector in r direction
Experimentally confirmed.
Measuring the gravitational constant – Cavendish apparatus (1789)

4. q
Black board example 13.1
What is the attractive force you (m1 = 100 kg) experience from the two people (m2 = m3 = 70 kg) sitting in front of you. Assume a distance r = 0.5 m and an angle q = 30° for both?

5. Free-Fall Acceleration and the Gravitational Force
Thus:
g is not constant as we move up from the surface of the earth!
G is a universal constant (does not change at all).

6. Variation of g with altitude
Black board example 13.2
Variation of g with altitude
The ISS photographed from shuttle Discovery in 2006.
From
What is the value of g in the ISS space station that is at an altitude of 400 km. Assume ME = 5.960·1024 kg and RE = 6.370·106 m.
Why does it feel like g = 0?

7. U will get smaller (more negative) as r gets smaller.
Gravitational potential energy
(similar equation for charge-charge interaction)
Notice the – sign
U = 0 at infinity
U will get smaller (more negative) as r gets smaller.
“Falling down” means loosing gravit. potential energy.
Use only when far away from earth; otherwise use approximation U = mgh.

8. A) ~10,000 m/s B) ~11,000 m/s C) ~20,000 m/s D) ~22,000 m/s
Black board example 13.3
First Rocket Launch from Cape Canaveral (NASA); July 1950
What is the escape speed of a particle on earth (ignore air resistance)?
A) ~10,000 m/s B) ~11,000 m/s C) ~20,000 m/s D) ~22,000 m/s

9. Kepler’s laws about planetary motion
These laws hold true for any object in orbit around a central mass
Kepler’s first two laws (1609):
Planets move in elliptical paths around the sun. The sun is in one of the focal points (foci) of the ellipse.
The radius vector drawn from the sun to a planet sweeps out equal areas in equal time intervals (Law of equal areas).
Area S-A-B equals area S-D-C

10. Kepler’s laws about planetary motion
Kepler’s third law (1619):
III. The square of the orbital period, T, of any planet is proportional to the cube of the semimajor axis of the elliptical orbit, a.
G… Gravitational constant G = 6.673·10-11 N·m2/kg2
MS … central mass, (i.e. mass of sun for planet motion)
Thus, for any two planets:

11. All nine eight planets of the solar system

12. Inner solar system: Outer solar system: Mercury Venus Earth Mars
Jupiter
Saturn
Uranus
Neptune
(Pluto)
My Very Educated Mother Just Served Us Nine (Plums)