Astronomy Picture of the Day

Astronomy Picture of the Day

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

Geocentric model fails to account for phases of the inner planets

Heliocentric model easily accounts for phases of the inner planets

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

The Scientific Method

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

• Occam's razor

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?

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 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

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.

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 (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.

Question

A circular orbit has an eccentricity of _____.

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

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- air track)

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.

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.

(DEMO – Air Track, Jet Cart)

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 1/7 what it is on Earth.

Gravitational Force

• The gravitational force is always attractive

• The strength of the attraction decreases with increasing distance

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