Kepler’s Laws of Planetary Motion

Kepler’s First Law: “LAW

OF ELLIPSES.” All objects

orbit the Sun in elliptical

paths.

Kepler’s Second Law:

“LAW OF EQUAL AREAS.” A

planet’s orbital velocity

changes as its position

changes.

Kepler’s Third Law: “LAW OF

PERIODS.” A planet’s period of

revolution is related to the distance

from its governing star.

Kepler’s Laws of Planetary Motion

In the 1500’s Nicolaus Copernicus challenged the

GEOCENTRIC (Earth-centered) model of the solar system.

Which solar system model is GEOCENTRIC?

Copernicus proposed a HELIOCENTRIC (Sun-centered)

model of the solar system, which placed Earth and the other

planets in circular orbits around the Sun.

Which solar system model is HELIOCENTRIC?

Copernicus proposed that all planets orbit in the same

direction, but each planet orbits at a different speed and

distance from the Sun.

According to Copernicus, which planet orbits the Sun at a

faster rate: MERCUCY or JUPITER ?

Later in the 1600’s Galileo made observations with

his telescope attempting to confirm or disprove the

Copernicus (Sun-centered) model. Assign the correct

symbol to “confirm” and “disprove”:

FASTER ORBIT =

CONFIRM DISPROVE

Galileo did NOT invent the telescope but was famous for

the observations he made using it.

Circle the telescope:

Tycho Brahe, a 16th Century astronomer, spent his life

making detailed, precise observations of the positions of

starts and planets. Johannes Kepler, his apprentice,

explained Brahe’s observations in mathematical terms and

developed the three laws of planetary motion. Based on

this background information, understanding the universe:

TAKES TIME HAPPENS FAST

KEPLER’S FIRST LAW:

“All objects that orbit the Sun, including planets,

asteroids, and comets, follow elliptical paths.”

Correctly label each figure as either an “ellipse” or “circle”:

According to the

image below, ellipses

have:

A CENTER POINT

or

2 FOCUS POINTS

Using the image above answer the following questions:

PLANETS ORBIT THE SUN or THE SUN ORBITS PLANETS

PLANETS are:

ALWAYS THE SAME DISTANCE FROM THE SUN

or

DIFFERENT DISTANCES FROM THE SUN DEPENDING ON

THEIR PLACE IN THEIR ORBIT

The image above shows which 2 orbits:

THE COMET AND THE EARTH AROUND THE SUN

or

THE EARTH AND SUN AROUND THE COMET

The orbits of the Earth and Comet:

CROSS or REMAIN APART

Lab Materials:

1. String

2. Cardboard or foam board

3. One sheet of blank paper or oversized white construction

paper

4. Wood screws, push pins, or thumb tacks

5. Pencil

6. Ruler

7. Calculator

Lab Procedure:

1. Tie as string into a loop about 6-7 cm across.

2. Fold your blank paper into thirds then flatten it out. The

folds divide the paper into 3 sections where you will draw

and compare 3 ellipses. Mark your sections: A, B, and C.

3. Measure and mark two dots 0.5cm apart in the center of

the top third, mark two dots 2.0cm apart in the middle

third, and in the bottom third, mark two dots 4.0cm apart.

4. Put the paper over the cardboard, and push the wood

screws or substitute material into one set of foci points.

These are the ellipse foci (F1 and F2). Put the string around

the foci and use a pencil to draw an ellipse around the foci

as seen below. Have a partner hold the foci steady if

needed.

5. Repeat step 4 for the other two sets of foci. It is OK if an

ellipse goes off the paper at the top and bottom, as long as

the major axis (across the screws) is on the paper.

6. Calculate Eccentricity (“out-of-roundness”)

ECCENTRICITY is the amount of flattening of an ellipse, or

how much the shape of an ellipse deviates from a perfect

circle.

a. Measure the foci distance between the screws for each

ellipse. Enter your data into the data table:

b. Draw a line across the foci to the edges of the ellipse.

This is the major axis. Measure the major axis. Enter your

data into the data table:

c. Calculate the eccentricity. Eccentricity = focal distance ÷

major axis difference. Enter your data into the data table.

Important: Eccentricity ranges between 0 and 1. Closer to

0 being circular; closer to 1 being highly elliptical (very

eccentric)

Eccentricity

(Closer to 0)

Eccentricity

(Closer to 0)

Complete Table Below:

Recommendation: Use dry erase crayons

Ellipse Focal

Distance

(a)

Major Axis

Difference

(b)

Eccentricity

a ÷b

SHOW WORK!

Most Circular?

Most Elliptical?

In the Middle?

A

B

C

Note: Alternative to Drawing Your Own Ellipses

Ellipse A (measurements in cm)

Focal Distance =

Major Axis Distance =

Eccentricity = Focal Distance ÷Major Axis Distance

FOCAL

DISTANCE

=

÷

Ellipse B (measurements in cm)

Focal Distance =

Major Axis Distance =

Eccentricity = Focal Distance ÷Major Axis Distance

FOCAL

DISTANCE

=

÷

Ellipse C (measurements in cm)

Focal Distance =

Major Axis Distance =

Eccentricity = Focal Distance ÷Major Axis Distance

FOCAL

DISTANCE

=

÷

Ellipse Eccentricity

Value

Description

A

B

C

Which solar system body in the image above has an orbit

that does NOT match the others?

Among the remaining bodies, which has the MOST elliptical

orbit?

Among the remaining bodies, which has the MOST circular

orbit?

Aphelion

Perihelion

Orbital

Position

Distance

from Sun

Date Season

(N.H.)

KEPLER’S SECOND LAW:

The Law of Equal Areas states “a line drawn from

the Sun to a planet sweeps equal areas in equal

time. A planet’s orbital velocity (the speed at

which it travels around the Sun) changes as its

position in its orbit changes. Its velocity is fastest

when it is closest to the Sun and slowest when it

is farthest from the Sun.

Areas and are:

THE SAME DIFFERENT

A B

B A

According to Kepler’s Second Law, during which month is

Earth revolving the fastest?

Isaac Newtonb later discovered that the force of

GRAVITY holds the planets in orbit around the Sun.

When a planet is closer to the Sun, the force of the Sun’s

gravitational attraction on the planet is:

When the planet is farther from the Sun, the gravitational

force is:

KEPLER’S THIRD LAW:

The Law of Periods states: “a planet’s period of

revolution (the time it takes to complete one orbit

of the Sun) to its average distance from the Sun.

Kepler determined the mathematical relationship

between period and distance. T2 = R3

T = The Planet’s Period in Earth Years

R = The Planet’s Mean Distance from the Sun in

Astronomical Units.

Distance to

the Sun

Millions of Miles Period of Revolution

in Earth Years

Planet X has an average distance from the Sun of

1.76AU. Compared to Earth, is it closer to the Sun

or farther from the Sun?

1 Earth Year

93,000,000

Closer to the Sun Farther from the

Sun

Planet X has an average distance from the Sun of

1.76AU. What is the planet’s period of

revolution, in Earth years?

Planet Distance to

Sun (AU)

Period of Revolution

(Earth Years)

Mercury

Mars

Saturn

Haley’s

Comet

2.33 Earth Years

(856 Days)

0.3 Earth Years

(110 Days)

0.39

AU

1.52

AU

9.54

AU

17.9

AU

Below, match the appropriate planet or comet

with its astronomical distance (AU) value

9.54 AU

17.9 AU

1.52 AU

Below, match the image with each specific law

and description of planetary motion:

Kepler’s First Law Kepler’s Second

Law

Kepler’s Third Law

All objects that orbit

the Sun, including

planets, asteroids,

and comets, follow

elliptical paths. NOT

CIRCUTLAR PATHS!

There is a

mathematical

relationship

(equation) between

the period of

revolution (one

orbit) to the average

distance from the

Sun.

A line drawn from

the Sun to a planet

sweeps out equal

areas in equal time

meaning there is a

relationship between

the orbital speed of a

planet and its

distance from the

Sun.

Ellipse A

MERCURY

ELLIPSE CIRCLE

1.6cm

4.2cm

1.6cm

4.2cm 0.38

Ellipse B and C

2.6cm

6.3cm

2.6cm

6.3cm 0.41

4.7cm

9.6cm

4.7cm

9.6cm 0.49

0.38

0.49

0.41

Most

Elliptical

In the Middle

Most Circular

Mercury

Neptune

Pluto

Point in orbit where a planet is

farthest from its star (Sun)

Point in orbit where a planet is

closest to its star (Sun)

Aphelion

Perihelion

94.5 million

miles

91.5 million

miles

July 3

January 4

JANUARY

JULY

STRONGER

WEAKER

0.24 Earth Years

(89 Days)

1.87 Earth Years

(684 Days)

29.4 Earth Years

(10,755 Days)

75.7 Earth Years

(27,642 Days)

1 AU

Saturn

Mars

Halley’s

Comet

Extras

Answer Key

Geocentric = Earth Centered

Heliocentric = Sun Centered

Faster = Mercury

Confirm = Check Mark; Disprove = X Mark

Telescope = Left Image

Understanding Takes Time

Left Image = Circle; Right Image = Ellipse

Planets Orbit the Sun; Planets are Different

Distances from the Sun

Comet and Earth Around the Sun; The Orbits

Cross

See Attached Images

Most Elliptical = Neptune. Most Circular =

Mercury

Aphelion = Orbit Where a Planet Is Farthest

From It’s Star; Perihelion = Closest

Pluto Does Not Match the Others

Areas A and B are Different

January = Earth is Revolving the Fastest

Stronger; Weaker

1 AU = 93,000,000 miles. Planet X is Farther

From the Sun

Planet X has a Period of Revolution of 2.33 Earth

Years

See Attached Images