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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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.

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

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

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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)

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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?

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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.

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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.