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Ancient History of Astronomy
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• Why is the summer longer than winter? Because of the precession of the Earth’s axis of rotation.

• Because of the moon’s 5o inclination with respect to the Ecliptic.

• Because the Earth is rotating around its axis more slowly in the summer (→ longer days!).

• Because the Earth is closest to the sun in January and most distant from the sun in July.

• Because the Earth is closest to the sun in July and most distant from the sun in January.

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Ancient History of Astronomy

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Kepler’s Third Law

Kepler’s Third Law

A planet’s orbital period (P) squared is proportional to its average distance from the sun (a) cubed:

(Py = period in years; aAU = distance in AU)

Orbital period P known → Calculate average distance to the sun, a:

aAU = Py2/3

Average distance to the sun, a, known → Calculate orbital period P.

Slide 26

It takes 29.46 years for Saturn to orbit once around the sun. What is its average distance from the sun?

It takes 29.46 years for Saturn to orbit once around the sun. What is its average distance from the sun?

Slide 27

Think critically about Kepler’s Laws: Would you categorize his achievements as physics or mathematics?

Think critically about Kepler’s Laws: Would you categorize his achievements as physics or mathematics?

Slide 28

Kepler’s Third Law

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Kepler’s Third Law

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Kepler’s Third Law

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Kepler’s Third Law

Slide 32

Velocity and Acceleration Acceleration (a) is the change of a body’s velocity (v) with time (t):

Velocity and Acceleration

Acceleration (a) is the change of a body’s velocity (v) with time (t):

Velocity and acceleration are directed quantities (vectors)!

Different cases of acceleration:

Acceleration in the conventional sense (i.e. increa sing speed) Deceleration (i.e. decreasing speed)

Change of the direction of motion (e.g., in circular motion)

Slide 33

A ball attached to a string is in a circular motion as shown. Which path will the ball follow if the string breaks at the marked point?

A ball attached to a string is in a circular motion as shown. Which path will the ball follow if the string breaks at the marked point?

Slide 34

Newton’s Laws of Motion (II) The acceleration aof a body is inversely proportional to its mass m, directly proportional to the net force F, and in the same direction as the net force.

Newton’s Laws of Motion (II)

The acceleration aof a body is inversely proportional to its mass m, directly proportional to the net force F, and in the same direction as the net force.

Slide 35

Newton’s Laws of Motion (III) To every action, there is an equal and opposite reaction. The same force that is accelerating the boy forward, is accelerating the skateboard backward.

Newton’s Laws of Motion (III)

To every action, there is an equal and opposite reaction. The same force that is accelerating the boy forward, is accelerating the skateboard backward.

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