Astronomy Picture of the Day

Windows on the Universe Simulation: Comets and Retrograde Motion

Testing - the key to science

● Greeks– Rational thought was sufficient

– Inconsistencies blamed on faulty perception● Modern Science

– Models make predictions

– Verification provides support for model

– A “Theory” is a generally accepted model

Geocentric model fails to account for phases of the inner planets

The Scientific Method

• Geocentric model abandoned because of its failure, and to a lesser extent because of its complexity.

The scientific method is used to develop new scientific theories. The scientific method is used to develop new scientific theories. Scientific theories are accepted when they make testable Scientific theories are accepted when they make testable predictions that can be verified using new observations and predictions that can be verified using new observations and experiments.experiments.

Heliocentric model easily accounts for phases of the inner planets

Geocentric vs. HeliocentricPredicted Phases of Venus

– Geocentric: only crescent phases

– Heliocentric: both full and crescent phases

Observations show both!

Tycho Brahe

• Collected vast amounts of astronomical data (positions of different bodies at certain times)

• Had a gold nose and a moose that couldn’t hold his liquor.

Kepler (1571-1630)

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

• Deduced three laws of planetary motion.

• Took him the last 30 years of his life.

Kepler’s Laws

• What are the shapes and important properties of the planetary orbits?

• How does the speed of a planet vary as it orbits the sun?

• How does the period of a planet's orbit depend on its distance from the Sun?

Kepler’s First Law

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

• 'a' = semi-major axis: Avg. distance between sun and planet

• video

The amount of elongation in a planet’s orbit is defined as its The amount of elongation in a planet’s orbit is defined as its orbital eccentricity.orbital eccentricity. An orbital eccentricity of 0 is a perfect circle An orbital eccentricity of 0 is a perfect circle while an eccentricity close to 1.0 is nearly a straight line. while an eccentricity close to 1.0 is nearly a straight line.

In an elliptical orbit, the distance from a planet to the Sun In an elliptical orbit, the distance from a planet to the Sun varies. The point in a planet’s orbit closest to the Sun is varies. The point in a planet’s orbit closest to the Sun is called called perihelion, perihelion, and the point farthest from the Sun is called and the point farthest from the Sun is called aphelion.aphelion.

Kepler's Second Law

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

Translation: planets move faster when closer to the Sun.video

slower faster

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

P2 is proportional to a3

or

P2 (in Earth years) = a3 (in A.U.)

1 A.U. = 1.5 x 108 km

Translation: The further the planet is from the sun, the longer the period.

Summary video

CPS Question

● Which of the following is not a stage in the cyclical representation of the scientific method.

● A)Observation● B)Argumentation● C)Theory● D)Prediction

CPS Question

● A circular orbit has an eccentricity of _____.

● A)exactly 0● B)between 0 and 0.5● C)exactly 1● D)infinity

CPS Question

● In Ptolemy's geocentric model, the normal ● (non-retrograde) motion of the planets was

attributed to actual motion along what circle?

● A)deferent● B)epicycle● C)retrograde loop● D)equant

Galileo was the first to use a telescope to Galileo was the first to use a telescope to examine celestial objects. His discoveries examine celestial objects. His discoveries supported a heliocentric model of the solar supported a heliocentric model of the solar system.system.

Galileo discovered that Venus, like the Moon, undergoes a series of phases as seen from Earth. In the Ptolemaic (geocentric) model, Venus would be seen in only new or crescent phases. However, as Galileo observed, Venus is seen in all phases, which agrees with the Copernican model as shown.

Galileo also discovered moons in orbit around the planet Jupiter. This was further evidence that the Earth was not the center of the universe.

Newton (1642-1727)

Newton’s laws are fundamental principles that govern the motions of all astronomical bodies!

What is the natural state of motion of a body with no forces acting on it?

Newton's First Law of Motion

● Every object continues in a state of rest or a state of uniform motion in a straight line unless acted on by a force. ● Inertia - resistance to change in motion of object - is related to its mass.(Demo- coin/ egg)/$ video

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 = Fm

or F = ma

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

Newton’s laws classify objects as accelerating or non-accelerating, not as moving or stationary.video

Newton's Third Law of Motion

To every action there is an equal and opposite reaction.

Or, when one object exerts a force on a second object, the second exerts an equal and opposite force on first.

(Video1, video2)

What force governs the motions of astronomical objects, and what factors determine how strong the force is?

Newton's Law of Gravity

For two objects of mass m1 and m

2, separated by a

distance R, the force of their gravitational attraction is given by:

F =G m

1 m

2

R2

Your "weight" is just the gravitational force between the Earth and you. On the moon your “weight” would be about 1/6 what it is on Earth.

Isaac Newton formulated three laws to describe Isaac Newton formulated three laws to describe the fundamental properties of physical reality.the fundamental properties of physical reality.

NEWTON’S THREE LAWS OF MOTIONNEWTON’S THREE LAWS OF MOTION

LAW #1: A body remains at rest or moves in a LAW #1: A body remains at rest or moves in a straight line at constant speed unless acted upon straight line at constant speed unless acted upon by a net outside force.by a net outside force.

LAW #2: The acceleration of an object is LAW #2: The acceleration of an object is proportional to the force acting on it.proportional to the force acting on it.

LAW #3: Whenever one body exerts a force on LAW #3: Whenever one body exerts a force on a second body, the second body exerts an equal a second body, the second body exerts an equal and opposite force on the first body.and opposite force on the first body.

Newton also discovered that gravity, the force that causes Newton also discovered that gravity, the force that causes objects to fall to the ground on Earth, is the same force objects to fall to the ground on Earth, is the same force that keeps the Moon in its orbit around the Earth. that keeps the Moon in its orbit around the Earth.

NEWTON’S LAW OF UNIVERSAL GRAVITATIONNEWTON’S LAW OF UNIVERSAL GRAVITATION

Two objects attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

With his laws, Newton was able to derive Kepler’s three laws, as well as predict other possible orbits.

Gravitational Force• The gravitational force is

always attractive

• The strength of the attraction decreases with increasing distance

• F=Gm1m2 • r2

CPS Question

● The force that holds you to the Earth is the same force that keeps the Earth in orbit around the sun and the moon in orbit around the Earth.

● A) True● B) False

Orbit of Earth around Sun(Demo - Ball on String)

Gravity and Orbits

• Throwing an object fast enough will put the object into orbit! (Neglecting air resistance)

• Moon is continually “falling” towards the Earth in its orbit (Gravity vs. inertia)

Correction to Kepler’s Third Law

• Earth and sun actually rotate about their common center of mass

• Corresponds to a point inside sun

• Used to detect extrasolar planets