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Lecture 5

Galileo, Brahe, and

Kepler

September 19, 2018

Galileo Galilei (1564-1642)

• Supported Copernican

model.

• Used telescope to observe

sky (1610).

– Mountains on the moon

– Rings of Saturn

– Sunspots

– Milky Way is made of

stars

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Geocentric Model of Venus3

Observations of Venus

• Venus has phases similar to the moon.

• The apparent size of Venus changes with

the phase.

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Phases of Venus

• If Venus was orbiting the Earth, its distance

would not change and its size would stay

the same.

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Basic Geocentric View

• Order of planets somewhat arbitrary.

• Mercury and Venus always orbit at velocity to

keep them near the Sun.

E

Sun

Moon

Mercury

SaturnCelestial Sphere

Jupiter

Mars

Venus

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Galileo’s observations of Jupiter

• Observed the 4 largest

moons of Jupiter

(Galilean Moons).

• The fact that bodies

could orbit other

planets supported

heliocentric view.

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What would you expect to see if Venus orbited the

Earth in the manner Ptolemy described?

A. You would not observe all of the

phases, but the size would change.

B. You would observe all of the

phases and the size would change.

C. You would observe all of the

phases but the size would not

change.

D. You would not observe all of the

phases and the size would not

change.

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Tycho Brahe

(1546-1601)

• Born 18 years before

Galileo

• Supported geocentric

model

• Died before invention of

telescope

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Tycho’s Observations

• Designed state of the art instruments to observe

sky (all naked eye observations).

• Made detailed observations of planetary and

stellar positions.

– Positions accurate up to 1 arcminute (1/60 of a

degree)

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Tycho’s observations

• Used many

instruments to confirm

results.

• Same method used by

modern astronomers.

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Tycho’s Supernova (1592)

• Believed stars unchanging

– “New” star must be near Earth

• Tried to measure distance to

object using parallax.

• No parallax observed

– Object much more distant that

originally thought.

– Heavens are not unchanging

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A key contribution that Tycho Brahe made to

astronomy is

A. his theoretical predictions of

planetary positions

B. his observation that a

supernova was very distant.

C. his observations of the

phases of Venus.

D. his invention of the

telescope.

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Johannes Kepler (1571-1630)

• Assistant to Brahe (1600-01)

• Believed in heliocentric

model (Copernicus).

• Wanted mathematical model

of orbits

• Used observations by Brahe

• Used trial and error to test

models

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Kepler’s First Law17

• The orbit of a planet about the Sun is an

ellipse with the Sun at one focus.

• Animation

of how to draw

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Focus

Focus

Semi-major axis

There is nothing physically at the

second focus of the ellipse.

For the Sun and the planets the orbits are are almost circular.

Perihelion: closest

distance to the Sun

Aphelion: furthest

distance from the Sun

Elliptical Orbit

Animation

appleta

b

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Eccentricity = Shape of Orbit

• Values range from 0 to 1

▪ ε = 0 = circle

▪ ε = 0.5 = ellipse

▪ ε = 1 = straight line

2

2for the curious: 1

b

a = −

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Kepler’s Second Law

• “The Law of Equal Areas” -- A line joining

a planet and the Sun always sweeps out

equal areas in equal intervals of time.

Animation

applet

What does Kepler’s Second Law imply

about the speed of the planet?

A. It moves fastest when it is

midway between the nearest and

farthest points from the Sun.

B. It moves faster when it is far

from the Sun.

C. It moves faster when it is near

the Sun.

D. Its speed is constant.

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Planet moves

fastest at

perihelion

Planet moves

slowest at aphelion

Speed of planets in elliptical

orbits

Animation

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Kepler’s Third Law

• P2 = a3

– P = sidereal period in years

– a = semi-major axis in AU

– The closer a planet is to the Sun, the less time it takes to

go around the Sun.

( )22 3

3

Example: If 8.0 years then

8.0 y 64

64 4.0 AU

P

P a

a

=

= = =

= =

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What is the semi-major axis of an asteroid

that orbits the Sun with a period of 11 years?

A. 3 AU

B. 5 AU

C. 7 AU

D. 11 AU

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What is the semi-major axis of an asteroid

that orbits the Sun with a period of 11 years?

A. 3 AU

B. 5 AU

C. 7 AU

D. 11 AU

3 2

3 2 311 121

4.95 AU 5 AU

a P

a

=

= =

=

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If this asteroid has a perihelion distance

of 1.5 AU, what is its aphelion distance?

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A. 1.5 AU

B. 3.5 AU

C. 5.0 AU

D. 8.5 AU

If this asteroid has a perihelion distance

of 1.5 AU, what is its aphelion distance?

A. 1.5 AU

B. 3.5 AU

C. 5.0 AU

D. 8.5 AU

( )

2

2

2 5 AU 1.5 AU

8.5 AU

PD AD a

AD a PD

AD

+ =

= −

= −

=

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General Comments on Kepler’s

Laws

• Can apply to all orbiting bodies (moons, planets,

stars, galaxies..) in slightly modified form.

• Best model that fit data -- not derived from

physical principles

• Simpler than Copernican model

• Fits data more accurately