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

Thursday 29 September 2011Also 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

Planets orbit the sun in elliptical orbits with the Sun at one of the two focus points.

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.

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

Geocentric Heliocentric

-Can not observe stellar parallax -Stars are too far awy, need powerful telescope

-It does not feel like we (on Earth are moving

-Earth’s rotation rate is relatively constant

-The heavens are fixed and unchanging -Brahe observed supernova, comets

-Explains retrograde motion of planets and phases of Venus

-Better predictor of planetary positions

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

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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

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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

Escape Velocity:Depends on Radius and Mass of

Celestial Body