Quiz #2 Review Giants of Science (Ch. 2), Gravity and Motion (Ch. 3) Light and Atoms (Ch. 4)

1. Quiz #2 ReviewGiants of Science (Ch. 2), Gravity and Motion (Ch. 3)Light and Atoms (Ch. 4) Thursday 29 September 2011 Also study the Quiz 1 recap notes

2. What to Know from Chapter 2 • The accomplishments of the different astronomers from the ancient Greeks to Copernicus, Brahe, Kepler, and Galileo • What they knew and how they knew it. • What technological advances led to what discoveries • The difference between the geocentric and heliocentric models of the solar system • Arguments for and against the two models • Final arguments in favor of the heliocentric model • Kepler’s laws

3. What the Giants of Science Accomplished • Measured quantities of the solar system • Earth shape and size • Moon and Sun sizes and distances • Planet-Sun distances determined relative to Earth-Sun distances • Technological advances led-to and required changes in solar system model • Move from Earth-centered (geocentric) model to Sun-centered (heliocentric) model

4. Shape of the Earth is Spherical Aristotle • Earth shadow is always circular, never oval or linear, during a lunar eclipse • Observers at different latitudes see different stars and constellations at the same time.

5. Size of Moon – Distances to Moon and Sun -- Aristarchus • During lunar eclipse, found that apparent moon size was 1/3 of Earth shadow. • Distance to Sun is greater than distance to moon. • Size of Sun is greater than Earth or Moon • Proposed heliocentric model, but his contemporaries rejected that model since stellar parallax was not observed.

6. Size of EarthErastothenes • Derived angle of incidence for Sun’s rays based on shadow length in Alexandria—no shadows in Syene at time of observation. • Angle between cities is same as Sunlight angle (from geometry) • Know distance between cities • Derive Earth circumference (and radius) from geometry

7. Derive Planet-Sun Distances Copernicus • Inner-Planet-Sun distances can be derived relative to Earth-Sun distance using geometry when planet is at greatest elongation. • Outer-Planet-Sun distance: start at opposition, • (1) mark time that elapses until Sun-Earth-planet angle is at 90°, • (2) derive fraction of orbits traversed, • (3) used geometry to find Planet-Sun distance relative to Earth-Sun distance

8. Geocentric vs. Heliocentric Models • Arguments for the Geocentric model • Can not observe stellar parallax • It does not feel like we (on the Earth) are moving • Idea that the heavens are fixed and unchanging

9. Geocentric (Earth-centered) ModelEudoxus • Model: Earth at the center, then Moon, Venus, Mercury, Sun, Mars, Jupiter, Saturn • Problem: Can not explain apparent retrograde motion of planets • Lower figure shows actual heliocentric model

10. Geocentric (Earth-centered) ModelPtolemy • Model: Earth at the center, then Moon, Venus, Mercury, Sun, Mars, Jupiter, Saturn • Solution(?): Invoke epicycles to explain apparent retrograde motion of planets • Lower figure shows actual heliocentric model

11. Heliocentric ModelCopernicus • Moon orbits Earth; Mercury, Venus, Earth, Mars, Jupiter and Saturn orbit the Sun • Planetary orbits are circular; a planet moves at a uniform speed throughout its orbit (?) • Good: Derived good distances between planets and Sun • Good: Explains apparent retrograde motion of planets • Bad: Poor predictions of where planets will be in the future, still need epicycles.

12. Heliocentric Model Kepler • Major technological advance: high precision instruments for measuring angles, data set of full-time professional astronomer Tycho Brahe • Orbits are elliptical with Sun at a focus • A line between the Sun and a planet sweeps out equal areas in equal times • Or, a planet moves faster when is closer to the Sun, and slower when it is further from the Sun • When comparing different planets: the square of a planet’s orbital period is proportional to the cube of its semi-major axis (P2 = a3) • Planets with smaller orbits (closer to the sun) complete their orbits faster than planets with larger orbits.

13. Kepler’s Laws A planet sweeps out equal areas in equal time periods throughout its orbit. This occurs because a planet moves slower when it is far from the Sun, and faster when it is near the Sun A planet’s orbital period depends on it’s distance from the Sun. A planet closer to the Sun has a shorter orbital period than a planet far from the Sun. Planets orbit the sun in elliptical orbits with the Sun at one of the two focus points.

14. Heliocentric Model Galileo • Major technological advance: the telescope (at this time, a spyglass) • Observed mountains on Moon • concluded Moon was rocky like Earth • Venus shows gibbous phases, must orbit the Sun • Jupiter has moons like Earth • Not everything revolves around Earth

15. Geocentric vs. Heliocentric Models

16. What to Know About Gravity and Motion • Difference between • Mass (an intrinsic property of an object), and • Weight (the force one object exerts on another) • Newton’s Universal Law of Gravitation • Underlying force responsible for Kepler’s Laws • Newton’s modified version of Kepler’s third law is an extremely powerful tool • Can find mass of the Sun from the orbital periods of the planets • Can find masses of binary stars from their orbital period or orbital velocities • Can find the mass of a galaxy from the orbital velocities of the stars, gas, and dust within it

17. What to Know About Gravity and Motion • Surface Gravity • The acceleration a mass undergoes at the surface of a celestial object (e.g., an asteroid, planet, or star) • Escape Velocity • The speed required for an object to overcome a celetial object and escape into space

18. The Universal Law of Gravitation • Every particle in the Universe attracts every other particle. • The force of attraction increases as their separation decreases • Likewise the force decreases as their separation increases • The force of gravity follows an inverse square form: • If the separation increases by a factor of 2, the force decreases by a factor of 4 • If the separation increases by a factor of 3, the force decreases by a factor of 9 • If the separation increases by a factor of 4, the force decreases by a factor of 16 • Etc.

19. Gravity Holds the Planets in Their Orbits • Gravity is the force that is responsible for Kepler’s Laws

20. Surface Gravity • Surface gravity is the acceleration a mass undergoes at the surface of a celestial object (e.g., an asteroid, planet, or star) • Depends on mass and radius of celestial body • Surface gravity: • Determines the weight of a mass at a celestial object’s surface • i.e., explains why you would weigh less on the Moon than on the Earth. • Influences the shape of celestial objects • Influences whether or not a celestial object has an atmosphere

21. Escape Velocity:Depends on Radius and Mass of Celestial Body