Foundations-Copernican RevolutionLecture 3:

Newton: Gravity and the Laws of Motion

Ancient Observatories

Ancient Peoples around the world made places to mark dates from the celestial calendar and/or observe the sky

Chaco Canyon, New Mexicohttp://www.exploratorium.edu/ancientobs/

Chichen Itzahttp://www.exploratorium.edu/ancientobs/

Angor Wat, Cambodia Medicine Wheel, Saskatchewan, Canada Stonehenge, England Abu Simbel, Egypt

Science vs. Pseudo-science

What makes science different? What do we know? How do we know it? Why do we believe it?

Is what we know supported by the evidence? Kuhn Paradigm

Thomas Kuhn: Structure of Scientific Revolution Navigating the web of a 1000 lies

End of the world in 2012?December 21, 2012

See National Geographic and NASA websites on this Mayan Calendar – long count calendar enters a new cycle

Each cycle is 5,125.37 years The sun will cross in front of the center of the Milky Way

But this has happened many times beforeNo significant increase in gravitational interaction

Sun will be in solar maximum – more solar flares and stormsThis has happened may times before

A tenth planet known to the ancients that would hit us by end of the year would be visible to astronomers for past decade

Why the hype?

a) planets move on epicycles.

b) planets orbit the Sun in the same direction.

c) Earth moves faster in its orbit.

d) they are closer than Uranus.

e) they rotate quickly on their axes.

Mars, Jupiter, and Saturn show retrograde motion because

Question 1

a) planets move on epicycles.

b) planets orbit the Sun in the same direction.

c) Earth moves faster in its orbit.

d) they are closer than Uranus.

e) they rotate quickly on their axes.

Mars, Jupiter, and Saturn show retrograde motion because

Question 1

As Earth overtakes and “passes” the outer planets, they seem to slow down and then reverse

direction.

a) why planets moved in the sky.

b) why Earth was at the center.

c) why retrograde motion occurred.

d) why Earth wobbled on its axis.

e) why inner planets were always seen near the Sun.

Epicycles were used in Ptolemy’s model to explain

Question 2

a) why planets moved in the sky.

b) why Earth was at the center.

c) why retrograde motion occurred.

d) why Earth wobbled on its axis.

e) why inner planets were always seen near the Sun.

.

Epicycles were used in Ptolemy’s model to explain

Question 2

Planets were assumed to move uniformly on an epicycle, as it

moved uniformly around Earth.

a) craters on the Moon

b) sunspots

c) lunar maria

d) satellites of Jupiter

e) stars of the Milky Way

Which of Galileo’s initial observations was most challenging to established geocentric beliefs?

Question 3

a) craters on the Moon

b) sunspots

c) lunar maria

d) satellites of Jupiter

e) stars of the Milky Way

Which of Galileo’s initial observations was most challenging to established geocentric beliefs?

Question 3

Seeing four moons clearly move around Jupiter disproved that

everything orbited Earth

and

showed Earth could orbit the Sun and not lose its moon, too.

Galileo (1564-1642)

Built his own telescope.

Discovered four moons orbiting Jupiter => Earth is not center of all things!

Discovered sunspots. Deduced Sun rotated on its axis.

Discovered phases of Venus, inconsistent with geocentric model.

Phases of Venus

The phases of Venus are impossible to explain in the Earth-centered model of the solar system.

Timelines of the Big Names

Copernicus

Galileo

Brahe

Kepler

Newton

1473-1543 1546-16011473-1543

1564-1642

1571-1630

1642-1727

Kepler (1571-1630)

Used Tycho Brahe's precise data on apparent planet motions and relative distances.

Deduced three laws of planetary motion.

Question 4

Earth is closer to the Sun in January. From this fact, Kepler’s 2nd law tells us

a) Earth orbits slower in January.

b) Earth orbits faster in January.

c) Earth’s orbital speed doesn’t change.

Earth is closer to the Sun in January. From this fact, Kepler’s 2nd law tells us

a) Earth orbits slower in January.

b) Earth orbits faster in January.

c) Earth’s orbital speed doesn’t change.

Kepler’s 2nd law means that a planet moves faster when

closer to its star.

FasterSlower

Question 4

Kepler's First Law

The orbits of the planets are elliptical (not circular) with the Sun at one focus of the ellipse.

Ellipses

eccentricity =

(flatness of ellipse)

distance between foci major axis length

Kepler's Second Law

A line connecting the Sun and a planet sweeps out equal areas in equal times.

Translation: planets move fasterwhen closer to the Sun.

slower faster

Kepler's Third Law

The square of a planet's orbital period is proportional to the cube of its semi-major axis.

P2 is proportional to a3

or

P2 a3

(for circular orbits, a=b=radius).

Translation: the larger a planet's orbit,the longer the period.

ab

3. Square of period of planet’s orbital motion is proportional to cube of semimajor axis.

Kepler’s laws:

1.3 The Laws of Planetary Motion

At this time, actual distances of planets from Sun were unknown, but were later measured. One technique is "parallax"

"Earth-baseline parallax" uses telescopes on either side of Earth to measure planet distances.

Newton (1642-1727)

Kepler's laws were basically playing with mathematical shapes and equations and seeing what worked.

Newton's work based on experiments of how objects interact.

His three laws of motion and law of gravity described how all objects interact with each other.

Newton's First Law of Motion

Last time – Demo of objects at rest

Demo – nature of how objects move

Hover disk

Newton’s laws of motion explain how objects interact with the world and with each other.

Newton’s first law:

An object at rest will remain at rest, and an object will move in a straight line at constant speed if and only if the sum of forces that act on it are balanced.

1.4 Newton’s Laws

Newton's Second Law of Motion

When a force, F, acts on an object with a mass, m, it produces an acceleration, a, equal to the force divided by the mass.

a = Fnet

m

or Fnet = ma

acceleration is a change in velocity or a change in direction of velocity.

Newton's Second Law of Motion

Demo - Force and Acceleration

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