LEARNING OBJECTIVES:

 

WORDS O' THE DAY:

• Centripetal ("towards the center")
• Centrifugal ("away from center")

WORK O' THE DAY:

Kepler's three laws of planetary motion can be described as follows:

• The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses)

• An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas)

• The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (The Law of Harmonies)

Mr W Addendums:

First Law: Regardless of the eccentricity of the orbit, the sun exists at one of the foci of each planet's orbit.

Second Law: Each arc of a planet's orbit sweeps out the same areas in the same amount of time.

 

Third Law: T² = A³    

Where T is the period of the planet around the sun and A is the average distance to the sun in Astronomical Units. 1 AU is equal to the average distance from the Earth to the sun and equal 93,000,000 miles which is about 150,000,000 km

═══════════════════════════

Let's digest:

How is it possible to use an equation like T² = A³?

After all, I've been hammering you all year long on the important of using appropriate units. If T (period) is years and A (average distance to the sun) is in AU then clearly (years)² does not equal (millions of kilometers)³.

Please discuss that inherent conundrum/riddle/enigma with your team and suggest an answer.

═══════════════════════════

How about this one?

We've all (?) been taught that the Earth's orbit around the sun is not a circle (True!). That is also very misleading, why is that?

Please take a few moments to look up the eccentricities of the planets. What stands out?

Now check out former planet which DOES have highly eccentric orbit. Does Kepler's Law of Periods work for Pluto?

═══════════════════════════

What is the significance of Kepler's Law of Equal Areas?

═══════════════════════════

Kepler's Law of Equal Areas

Let's try a couple of examples:

1) The average distance of the Earth is about 150,000,000 kilometers from the sun. How many years does it take for the Earth to orbit the Sun?

2) Venus has an average distance of about 2/3 of 1 AU from the Sun. How long does it take to orbit the sun?

3) The average distance of Saturn to the sun is precisely given as 1,433,449,370 km.

• Why do never, ever use such precision when applying Kepler's Law of Periods?
• How long does it take to go around the sun?

There is another version of this law that involves the mass of the sun. Go find it and discuss please with your team:

What is the significance of THAT version of the law?

═══════════════════════════

 

 

══════════════════════════