The History of Astronomy

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Slide 18

Kepler’s Laws of Planetary Motion

The orbits of the planets are ellipses with the sun at one focus.

c

Eccentricity e = c/a

Slide 19

Eccentricities of Ellipses

e = .2

e = .1

e = .2

e = .4

e = .6

1)

2)

3)

4)

5)

Slide 2

Eccentricities of planetary orbits

Orbits of planets are virtually indistinguishable from circles:

Earth: e = .167

Most extreme example:

Pluto: e = .248

Slide 21

A line from a planet to the sun sweeps over equal areas in equal intervals of time.

Fast

Slow

Animation

Slide 22

Are all four seasons equally long?

Yes.

No, summer is the longest; winter is the shortest.

No, fall is the longest; spring is the shortest.

No, winter is the longest; summer is the shortest.

No, spring is the longest; fall is the shortest.

Slide 23

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.

Slide 24

Autumnal Equinox (beg. of fall)

Winter solstice (beg. of winter)

Summer solstice (beg. of summer)

Vernal equinox (beg. of spring)

January

July

Fall

Winter

Spring

Summer

Slide 25

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

Py2 = aAU3

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

Kepler’s Third Law

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.

Py = aAU3/2

Slide 26

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

9.54 AU

19.64 AU

29.46 AU

44.31 AU

16.55 AU

Slide 27