Epicycles

• Ptolemy (100-170 C.E.) improved the geocentric models by including epicycles– Planets were attached to small circles

(epicycles) that rotated.

– These epicycles were attached to a larger circle, centered on Earth

• This can be visualized as a planet attached to a Frisbee, attached to a bicycle wheel with the Earth at the center.

• Did a fair job of reproducing retrograde motion.

Heliocentric Models

• Nicolas Copernicus devised a heliocentric (Sun-centered) model in which everything, including the Earth, revolves around the Sun

• Retrograde motion is a natural result of these models!

• Copernicus was also able to measure the relative distances between the Sun and the planets

Mercury and Venus

• It was found that Mercury and Venus were closer to the Sun than the Earth, as they were never found very far from the Sun in the sky

• Mercury’s greatest elongation, or angular separation from the Sun, is never more than 28 degrees

• Venus’s greatest elongation is never more than 47 degrees

• Mercury is therefore closer to the Sun than Venus

Tycho Brahe (1546-1601 C.E.)

• Built instruments to measure the positions of planets very accurately (~1 arc minute)

• Found that comets moved outside of the Earth’s atmosphere

• Witnessed a supernova and concluded that it was much farther away than any celestial sphere

• As he could detect no parallax motion in the stars, he held that the planets go around the Sun, but the Sun, in turn, orbits around the Earth

Johannes Kepler (1571-1630

• Using Tycho Brahe’s data, discovered that planets do not move in circles around the Sun, rather, they follow ellipses with the Sun located at one of the two foci!

Kepler’s First Law

• Planets move in elliptical orbits with the Sun at one focus of the ellipse– Developed a heliocentric

(Sun-centered) model– Did not agree with the

ancients (or Brahe!)– The shape of the ellipse

is described by its semi-major and semi-minor axes.

Kepler’s Second Law

• The orbital speed of a planet varies so that a line joining the Sun and the planet will sweep out equal areas in equal time intervals

• That is, planets move faster when near the Sun, and slower when farther from the Sun

• Explained the non-circular behavior of the planets!

Kepler’s Third Law

• The amount of time a planet takes to orbit the Sun (its period) P is related to its orbit’s size, a, by

P2 = a3

• Kepler’s Laws describe the shape of a planet’s orbit, its orbital period, and how far from the Sun the planet is positioned.

• These were empirical relationships, found from observation rather than the logic of the ancients.

Galileo Galilei (1564-1642)

• Using a Dutch-designed telescope that he built himself, he made several startling observations that disproved ancient thinking about the Universe– Found sunspots, showing that the Sun was not a

perfect sphere– Found craters on the Moon, showing that the Moon

was not a perfect sphere– Discovered four moons of Jupiter, showing that not

everything revolved around the Sun– Observed the rings of Saturn– Observed that Venus passed through all phases, just

as the Moon does. In a geocentric model, the phases of Venus were limited to crescents.

• One of the principal founders of the experimental method for studying scientific problems.

Isaac Newton (1642-1727)

• Isaac Newton described the fundamental laws covering the motion of bodies

• Had to invent his own mathematics (Calculus) to do it!

• His work is used even today in calculating everything from how fast a car stops when you apply the brakes, to how much rocket fuel to use to get to Saturn!

• And he did most of it before his 24th birthday…

Sun is approximately ...... than Earth

• a. 100x wider and 300 000x as massive as;

• b. 10000x wider and 100x as massive as;

• c. 10x wider and 300x as massive as;

• d. 100000000x wider and 10x as massive as.

When the Northern Hemisphere experiences summer the Southern Hemisphere

experiences

• a. spring;

• b. summer;

• c. fall;

• d. winter.

The size of the galaxy is about ....... times the size of the Solar System.

• a. 10

• b. 100

• c. 1000

• d. 100 000 000

If an event were to take place on the Sun, how long would it take to reach us?

• a. 8 minutes

• b. 11 hours

• c. 1 second

• d. 10 days

Mass and Inertia

• Mass is described by the amount of matter an object contains.

• This is different from weight – weight requires gravity or some other force to exist!

• Ex: while swimming, your weight may feel less because the body floats a little. Your mass, however, stays the same!

• Inertia is simply the tendency of mass to stay in motion

The Law of Inertia

• Newton’s First Law is sometimes called the Law of Inertia:

– A body continues in a state of rest, or in uniform motion in a straight line at a constant speed, unless made to change that state by forces acting on it

– Or, more simply, a body maintains the same velocity unless forces act on it

• A ball rolling along a flat, frictionless surface will keep going in the same direction at the same speed, unless something pushes or pulls on it

– Gravity!

Another View of Newton’s First Law

• If an object’s velocity is changing, there must be forces present!– Dropping a ball– Applying the brakes in a

car

• If an object’s velocity is not changing, either there are no forces acting on it, or the forces are balanced and cancel each other out– Hold a ball out in your

hand, and note that it is not moving

– Force of gravity (downward) is balanced by the force your hand applies (upward)!

Circular Motion

• Tie a string to a ball and swing it around your head

– Law of inertia says that the ball should go in a straight line

– Ball goes in a circle – there must be forces!

• Where’s the force?– It’s the tension in the string

that is changing the ball’s velocity

– If the string breaks, the ball will move off in a straight line (while falling to the ground)