Chapter 1 Kepler’s Laws Charles Hakes Fort Lewis College 2

Outline Logistics Review Kepler’s Laws Charles Hakes Fort Lewis College 3

Logistics http://faculty.fortlewis.edu/hakes_c/ Read about Newton (1.4). Charles Hakes Fort Lewis College 4

I read the section on Kepler’s laws. A) True B) False Charles Hakes Fort Lewis College 5

Planetary orbits are A) Circular. B) Parabolic. C) Elliptical. D) Hyperbolic. Charles Hakes Fort Lewis College 6

Planetary orbits are A) Circular. B) Parabolic. C) Elliptical. D) Hyperbolic. Charles Hakes Fort Lewis College 7

Two planets have orbits with the same periods. Which is true? A) Their velocities must be the same. B) They must have the same eccentricity. C) They must have the same semi-major axis. D) Their orbits must be identical. Charles Hakes Fort Lewis College 8

Two planets have orbits with the same periods. Which is true? A) Their velocities must be the same. B) They must have the same eccentricity. C) They must have the same semi-major axis. D) Their orbits must be identical. Charles Hakes Fort Lewis College 9

Figure 1.15 Johannes Kepler (1571-1630) Charles Hakes Fort Lewis College 10

Kepler Overview Theoretician Used observations of Tycho Brahe Wanted a unifying principle to explain the motions of the planets without epicycles. Took ~29 years, but he did it. Charles Hakes Fort Lewis College 11

Figure 1.16 Tycho Brahe Charles Hakes Fort Lewis College 12

Kepler’s “Laws” http://faculty.fortlewis.edu/hakes_c/ Allow pop-up windows! Charles Hakes Fort Lewis College 13

Kepler’s “Laws” That “shape” law Orbits are elliptical, with the Sun at one focus. Charles Hakes Fort Lewis College 14

Kepler’s “Laws” That “shape” law That “speed” law Orbits are elliptical, with the Sun at one focus. That “speed” law (A line between the Sun and a)Planet sweeps out (in the ellipse) equal areas in equal times. Charles Hakes Fort Lewis College 15

P2 (years) = a3 (astronomical units) Kepler’s “Laws” That “shape” law Orbits are elliptical, with the Sun at one focus. That “speed” law (A line between the Sun and a)Planet sweeps out equal areas (of the ellipse) in equal times. That “math” law P2 (years) = a3 (astronomical units) Charles Hakes Fort Lewis College 16

A planet orbit could be circular. A) True B) False Charles Hakes Fort Lewis College 17

A planet orbit could be circular. A) True B) False Charles Hakes Fort Lewis College 18

Two planets have orbits with the same sized semi-major axis Two planets have orbits with the same sized semi-major axis. Which is true? A) The planet with the most eccentric orbit moves faster all the time. B) The planet with the most eccentric orbit moves faster some of the time. C) The planet with the most eccentric orbit never moves faster. D) Not enough information to answer. Charles Hakes Fort Lewis College 19

Two planets have orbits with the same sized semi-major axis Two planets have orbits with the same sized semi-major axis. Which is true? A) The planet with the most eccentric orbit moves faster all the time. B) The planet with the most eccentric orbit moves faster some of the time. C) The planet with the most eccentric orbit never moves faster. D) Not enough information to answer. Charles Hakes Fort Lewis College 20

Assume a planet orbits exactly twice as far from the Sun as the Earth does. A) It’s period is 2 years exactly. B) It’s period is between 2 and 3 years C) It’s period is between 3 and 4 years D) It’s period is 4 years exactly. Charles Hakes Fort Lewis College 21

Assume a planet orbits exactly twice as far from the Sun as the Earth does. A) It’s period is 2 years exactly. B) It’s period is between 2 and 3 years C) It’s period is between 3 and 4 years D) It’s period is 4 years exactly. Charles Hakes Fort Lewis College 22

Three Minute Paper Write 1-3 sentences. What was the most important thing you learned today? What questions do you still have about today’s topics? Charles Hakes Fort Lewis College 23

Three Minute Paper Answer this question (without discussion): What is the air-speed velocity of an unladen swallow? Charles Hakes Fort Lewis College 24