Cassini Spacecraft Crosses Saturn's Ring Plane When Saturn's "appendages" disappeared in 1612, Galileo did not understand why. Later that century, it became understood that Saturn's unusual protrusions were rings and that when the Earth crosses the ring plane, the edge-on rings will appear to disappear. This is because Saturn's rings are confined to a plane many times thinner, in proportion, than a razor bladeGalileo

Several out-of-class Activities have been posted on the class website. Homework #4 will be posted shortly.

Ptolemy’s Geocentric Model ● Earth is at center (Geocentric) ● Sun orbits Earth ●Planets orbit on small circles (epicycles) whose centers orbit the Earth on larger circles (this explains apparent retrograde motion) ●Planet orbits lie in approximately the same plane (this explains why the planets are always near the ecliptic) ●Inferior planet epicycles are fixed to the Earth- Sun line (this explained why Mercury & Venus never stray far from the Sun).

Copernicus’ Heliocentric Model ●Sun is at center of the Universe (heliocentric) ●Earth orbits the Sun like any other planet ●Earth rotates ●Circular orbits for all planets ●Inferior planet orbits are smaller ●Planets move at constant velocities in their orbits ●Retrograde motion occurs when we “lap” Mars & the other superior planets

Kepler's Laws 1.The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus. 2. The Law of Areas: Planets move faster in their orbit the closer they are to the Sun. 3. The Law of Periods: Planets on larger orbits take longer to complete an orbit than planets smaller orbits. a 3 / P 2 = constant

State of Affairs at beginning of 17 th Century -

GeocentricHeliocentric Two models of the Universe

Which model more accurately depicts nature?  Both make predictions for the apparent motions of planets and stars.  Heliocentric model, with modifications incorporating Kepler’s Laws, gives more accurate predictions  But, the Geocentric model might be made more accurate through appropriate modifications.  Need additional predictions that clearly differentiate between the two models.

The “Science” of Astronomy

In the broadest sense, Science refers to any system of knowledge which attempts to model objective reality.

a. Uninfluenced by emotions or personal prejudices. b. Based on observable phenomena; presented factually

Science attempts to systemized knowledge through:  observing  questioning  hypothesizing  testing

● Science seeks explanations for observed phenomena that rely solely on natural causes. ● Science progresses through the creation and testing of models of nature that explain the observations as simply as possible. ● A scientific model must make testable predictions that could force us to revise or abandon the model. The Nature of Science -- a model which survives repeated testing Theory

The word “Theory” has a very different meaning in science than in everyday parlance

A model is only referred to as a theory when it has successfully survived testing to such an extent that it is generally accepted as a valid representation of nature. Even then, testing continues…

Theories  Must be Testable  Must be continuously tested  Should be simple

“Testable” Separates science, nonscience & pseudoscience  Testing separates science from nonscience: e.g., religion is not accessible to experimental verification  Testing invalidates pseudosciences: e.g., astrology fails testing.

Testing of the “Two World” Models: Geocentric vs Heliocentric

Contemporary with Kepler was Galileo Galilei ( ), the “founder of experimental science” ● First person known to point a telescope at the sky ● He wanted to connect the physics understood on earth with objects in the heaven His work got him in trouble with the Church and led to his house arrest for many years.

 Galileo saw craters and shadows cast by the mountains on the Moon (Moon had a landscape; it was a “place”, not a perfect heavenly body) (Some of) Galileo’s Observations

 Galileo saw craters and shadows cast by the mountains on the Moon (Moon had a landscape; it was a “place”, not a perfect heavenly body)  Sunspots (sun not “perfect”) (Some of) Galileo’s Observations

 Galileo saw craters and shadows cast by the mountains on the Moon (Moon had a landscape; it was a “place”, not a perfect heavenly body)  Sunspots (sun not “perfect”)  Rotation of sun (Some of) Galileo’s Observations

 Galileo saw craters and shadows cast by the mountains on the Moon (Moon had a landscape; it was a “place”, not a perfect heavenly body)  Sunspots (sun not “perfect”)  Rotation of sun  Moons of Jupiter (Heavenly bodies existed which did not orbit the earth) (Some of) Galileo’s Observations

 Galileo saw craters and shadows cast by the mountains on the Moon (Moon had a landscape; it was a “place”, not a perfect heavenly body)  Sunspots (sun not “perfect”)  Rotation of sun  Moons of Jupiter (Heavenly bodies existed which did not orbit the earth)  Phases of Venus: the two models of the Universe made two very different predictions. (Some of) Galileo’s Observations

Phases of Venus

Galileo’s observation of the phases of Venus was the final evidence that buried the geocentric model. Geocentric Heliocentric No gibbous or full phases!All phases are seen! Galileo observed all phases!

With Galileo’s observations, the revolution begun by Copernicus was nearly complete…  The structure of the universe had been totally changed.  The motions of the planets were understood, at least from a geometrical perspective.  Earth was no longer a “special” place in the universe.  The crowning achievement was yet to come - discovering the laws of nature and that naturally led to the newly determined structure.

Sir Isaac Newton ( ) Invented calculus Invented the reflecting telescope Connected gravity and planetary forces

Universal Law of Gravitation Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects.

● Extending Kepler’s Law #1, Newton found that ellipses were not the only orbital paths. ● All orbits are “conic sections” – ellipse (bound) – parabola (unbound) – hyperbola (unbound) ● Orbital motion takes place around the center of mass Orbital Paths from Law of Gravitation

The Center of Mass In Kepler's Laws, the Sun is fixed at a point in space (a focus of an ellipse) and the planet revolves around it. Why is the Sun privileged? Kepler had mystical ideas about the Sun, endowing it with almost god-like qualities that justified its special place. Newton demonstrated that the the Sun does not occupy a privileged postion and in the process he modified Kepler's 3rd Law.

The center of mass is familiar to anyone who has ever played on a see-saw. The fulcrum point at which the see-saw will exactly balance two people sitting on either end is the center of mass for the two persons. m 1 d 1 = m 2 d 2

 Newton realized that in the planet-Sun system the planet does not orbit around a stationary Sun (a planet exerts as much gravitational force on the Sun as the Sun does on a planet).  Instead, Newton proposed that both the planet and the Sun orbited around the common center of mass for the planet-Sun system.  This led Newton to modify Kepler's 3rd Law. Recall Kepler’s 3rd law:P 2 / a 3 = constant F g = Gm 1 m 2 /d 2

P 2 = 4  2 a 3 / G (m 1 + m 2 ) G is known as the universal gravitational constant. Newton’s Version of Kepler’s Third Law If you can measure the orbital period of two objects (P) and the distance between them (a), then you can calculate the sum of the masses of both objects (m 1 + m 2 ).

We will return to Newton and discuss his “Laws of Motion” after we learn some simple background physics

A Universe of Matter and Energy What is matter? What is energy?

Matter – material such as rocks, water, air; “stuff” composed of atoms Energy – makes or has the potential to make matter move! The history of the universe, including biological organisms, is based upon the interplay between matter and energy.

Three Basic Types of Energy kinetic – energy of motion potential – stored energy; e.g., chemical, gravitational, electrical, etc. radiative – energy transported by light (electromagetic radiation)

Conservation of Energy  Fundamental law of nature  Energy can be neither created nor destroyed  It can change form or be exchanged between objects.  The total energy content of the Universe was determined in the Big Bang and remains the same today. K.E. P.E.R.E.

Kinetic Energy (K.E.): energy of motion K.E. = 1/2 mv 2 (m is mass, v is velocity)

On the microscopic level: temperature is a measure of the average kinetic energy of particles within a substance

Temperature Scales

Temperature vs. Heat ● Temperature is the average kinetic energy. ● Heat (thermal energy) is the total kinetic energy. lower Thigher T same T less heatmore heat

Sound waves are a form of kinetic energy on a microscopic level (organized vibration of molecules)

Potential Energy: Energy that is “stored” within an object and that has the potential of being released in a different form

Gravitational Potential Energy ● gravitational potential energy is the energy which an object stores due to its ability to fall ● It depends on: – the object’s mass (m) – the strength of gravity (g) – the distance which it can fall (d) m d g ● P.E. = mgd

● gravitational potential energy g ● P.E. = mgd

Mass-Energy Potential Energy ● mass-energy: energy is stored in matter itself ● this mass-energy is what would be released if an amount of mass, m, were converted into energy E = mc 2 [ c = 3 x 10 8 m/s is the speed of light]

Chemical Potential Energy ● Chemical potential energy: energy stored chemical bounds

There are many additional examples of potential energy. e.g., stretched springs, …

Energy, while conserved, can be transformed from one type of energy to another Potential Kinetic

Kinetic Potential

Orbits & Energy Maximum Kinetic Energy Maximum Potential Energy Downhill Uphill