Contributed by:

Kepler's first law, Kepler's second law, Orbital period, Orbital eccentricity, Kepler's third law

1.
Unit 1

Earth’s Role as a Body in Space

Earth’s Role as a Body in Space

2.
Lesson 2

The Third Rock from the Sun!

The Third Rock from the Sun!

3.
Think About It…

How would Earth be different

if its orbit was more oval

than circular?

How would Earth be different

if its orbit was more oval

than circular?

4.
Earth’s Orbit and

Kepler’s Laws

How do Kepler’s laws describe

Earth’s orbit?

Kepler’s Laws

How do Kepler’s laws describe

Earth’s orbit?

5.
Johannes Kepler (1571-1630)

Kepler based his three laws of planetary

motion on the earlier foundations provided

by Copernicus

Kepler was the assistant to Tycho Brahe

Brahe afraid that Kepler would surpass

him assigned him the daunting task of

solving Mars orbit. This Martian data was

the key piece needed to solve the motion

of all the planets

Kepler based his three laws of planetary

motion on the earlier foundations provided

by Copernicus

Kepler was the assistant to Tycho Brahe

Brahe afraid that Kepler would surpass

him assigned him the daunting task of

solving Mars orbit. This Martian data was

the key piece needed to solve the motion

of all the planets

6.
Kepler’s Laws…

Johannes Kepler,

working with data

painstakingly

collected by Tycho

Brahe (from 1576-

1601) without the aid

of a telescope,

developed three laws

which described the

motion of the planets

across the sky. http://www.nmspacemuseum.org/halloffame/images.php?image_id=131

Unless otherwise noted, the info on the slides on Kepler’s laws was taken from the

following website: http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html

Johannes Kepler,

working with data

painstakingly

collected by Tycho

Brahe (from 1576-

1601) without the aid

of a telescope,

developed three laws

which described the

motion of the planets

across the sky. http://www.nmspacemuseum.org/halloffame/images.php?image_id=131

Unless otherwise noted, the info on the slides on Kepler’s laws was taken from the

following website: http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html

7.
II. A-1.Kepler’s First Law…

• The Law of Orbits or Law of Ellipses: All planets

move in elliptical orbits, with the sun at one

focus.

• An ellipse is an oval shape that is centered on

two points (called foci) instead of a single point.

• The Law of Orbits or Law of Ellipses: All planets

move in elliptical orbits, with the sun at one

focus.

• An ellipse is an oval shape that is centered on

two points (called foci) instead of a single point.

8.
What is an ellipse?

• An ellipse has two foci.

• An ellipse has two axes.

– The long one is called the major axis

• Half of it is called a semi-major axis

– The short one is called the minor axis.

• An ellipse has two foci.

• An ellipse has two axes.

– The long one is called the major axis

• Half of it is called a semi-major axis

– The short one is called the minor axis.

9.
HANDS-ON ACTIVITY!!

• Planetary Orbits:

• Planetary Orbits:

10.
Orbital Period

• The orbital period of a planet is the length

of time it takes for it to travel a complete

orbit around the sun. (a year!)

• The orbital period of a planet is the length

of time it takes for it to travel a complete

orbit around the sun. (a year!)

11.
Orbit Eccentricity…

The eccentricity of an ellipse can be defined as the ratio of the distance between the foci

to the major axis of the ellipse. The more eccentric an orbit, the more of an oval it is.

The eccentricity is zero for a circle.

Pluto (no longer considered a planet by astronomers) has a large eccentricity.

http://solarsystem.nasa.gov/multimedia/display.cfm?IM_ID=175

The eccentricity of an ellipse can be defined as the ratio of the distance between the foci

to the major axis of the ellipse. The more eccentric an orbit, the more of an oval it is.

The eccentricity is zero for a circle.

Pluto (no longer considered a planet by astronomers) has a large eccentricity.

http://solarsystem.nasa.gov/multimedia/display.cfm?IM_ID=175

12.
Examples of Ellipse Eccentricity

Planetary orbit

eccentricities

Mercury .206

Venus .0068

Earth .0167

Mars .0934

Jupiter .0485

Saturn .0556

Uranus .0472

Neptune .0086

Pluto .25

Planetary orbit

eccentricities

Mercury .206

Venus .0068

Earth .0167

Mars .0934

Jupiter .0485

Saturn .0556

Uranus .0472

Neptune .0086

Pluto .25

13.
Kepler’s Second Law…

• The Law of Areas: A line that connects a planet to

the sun sweeps out equal areas in equal times.

http://www.mathacademy.com/pr/prime/articles/kepler/index.asp

• The Law of Areas: A line that connects a planet to

the sun sweeps out equal areas in equal times.

http://www.mathacademy.com/pr/prime/articles/kepler/index.asp

14.
• Planets move fastest when they are at

their closest point to the Sun (called

perihelion) and slowest when they are at

their farthest point from the Sun (called

aphelion).

their closest point to the Sun (called

perihelion) and slowest when they are at

their farthest point from the Sun (called

aphelion).

15.
Kepler’s Third Law…

• The Law of Periods: The square of the period of any planet

is proportional to the cube of the semimajor axis of its orbit.

• This law arises from the law of gravitation. Newton first

formulated the law of gravitation from Kepler's 3rd law.

• The Law of Periods: The square of the period of any planet

is proportional to the cube of the semimajor axis of its orbit.

• This law arises from the law of gravitation. Newton first

formulated the law of gravitation from Kepler's 3rd law.

16.
• What does this mean? This means that if

you know how much time a planet's orbit

around the Sun takes, you can easily

know it's average distance from the Sun,

or vice-versa!

• The closer a planet is to the Sun, the less

time it takes for the planet’s orbit.

you know how much time a planet's orbit

around the Sun takes, you can easily

know it's average distance from the Sun,

or vice-versa!

• The closer a planet is to the Sun, the less

time it takes for the planet’s orbit.

17.
• Kepler's Third Law is written like

this: P2=a3

• P=the orbital period in Earth years

• A= the length of the semimajor

axis (average distance from the

Sun) in Astronomical Units.

this: P2=a3

• P=the orbital period in Earth years

• A= the length of the semimajor

axis (average distance from the

Sun) in Astronomical Units.

18.
Barycenter and Earth’s Orbit…

• The law of universal

gravitation states…

– that every pair of

bodies in the universe

attract each other with

a force that is…

• proportional to the

product of their masses

and

• inversely proportional to

the square of the

distance between them.

• The law of universal

gravitation states…

– that every pair of

bodies in the universe

attract each other with

a force that is…

• proportional to the

product of their masses

and

• inversely proportional to

the square of the

distance between them.

19.
Barycenter and Earth’s Orbit…

• A planet, such as Earth, actually orbits…

– a point between it and the Sun called the

center of mass

– This center of mass is called the barycenter.

http://www.barewalls.com/pv-605547_Barycenter-Diagram.html

• A planet, such as Earth, actually orbits…

– a point between it and the Sun called the

center of mass

– This center of mass is called the barycenter.

http://www.barewalls.com/pv-605547_Barycenter-Diagram.html

20.
Barycenter

• This is the point • The sun although the

between 2 objects center of the universe

where they balance is not stationary, it

each other. moves as other

planet’s gravity “tug”

• It is the center mass on it. But it never

where two or more strays too far from the

celestial bodies orbit solar system’s

each other. barycenter.

• This is the point • The sun although the

between 2 objects center of the universe

where they balance is not stationary, it

each other. moves as other

planet’s gravity “tug”

• It is the center mass on it. But it never

where two or more strays too far from the

celestial bodies orbit solar system’s

each other. barycenter.

21.
• The Effect of the Moon

• The moon has a noticeable effect on the

earth in the form of tides, but it also affects

the motion and orbit of the earth. The

moon does not orbit the center of the

earth, rather, they both revolve around the

center of their masses called the

barycenter. This is illustrated in the

following animation.

• The moon has a noticeable effect on the

earth in the form of tides, but it also affects

the motion and orbit of the earth. The

moon does not orbit the center of the

earth, rather, they both revolve around the

center of their masses called the

barycenter. This is illustrated in the

following animation.

22.

23.
Barycenter and Earth’s Orbit…

– http://spaceplace.nasa.gov/barycenter/

– http://spaceplace.nasa.gov/barycenter/