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

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

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### 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

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

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

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.

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.

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

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

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

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

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

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.

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.

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.

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

Geocentric vs. Heliocentric Models

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

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

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.

Gravity Holds the Planets in Their Orbits

- Gravity is the force that is responsible for Kepler’s Laws

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.

- Determines the weight of a mass at a celestial object’s surface

- Influences the shape of celestial objects
- Influences whether or not a celestial object has an atmosphere

Escape Velocity:Depends on Radius and Mass of Celestial Body

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