Orbital Velocity

geology.wmich.edu

Orbital Velocity

Finding Our

Place in Space

Chapter 1

The Great Galaxy Andromeda


1.1 Watching the Sky: SUN, Moon, Stars

The Constellations

Patterns of Stars

Names from Myths, Legends, Historical Events

• Move from East to West

Suggests EARTH Fixed in Place

Constellations Rotate About It

• Change with the Seasons

• Star Positions within Each

Constellation Remain Fixed

Orion –Showing the Brightest Stars

and Giant Gas Cloud (Orion Nebula)

Where New Stars Are Forming Today


Apparent Motion of the SUN and Stars

Implies that EARTH is Fixed in the Center, and That the SUN,

Planets and Stars Revolve Around It


Apparent Motion of the SUN and Stars

Solstice (Sun-Stationary) Equinox (Day = Night)


Apparent Motion of the SUN and Stars - Zodiac

(From Same Greek Word That Gives Us “Zoo” and “Zoology”)

(Most Constellations are Named for Animals)


Phases of the Moon


Eclipses


Multiple Exposure Photograph of an Eclipse of the SUN

Totality (Central Image) Lasts Only a Few Minutes


1.2 Watching the Sky: The Planets

Planets of Our Solar System

Are All Very Different


Planets of Our Solar System

Are All Very Different

EXCEPT

• They All Orbit the SUN


Planets of Our Solar System

Are All Very Different

EXCEPT

• They All Orbit the SUN

• They Are All Bound Together by Its Gravity


MERCURY

• Mostly Iron and Rock

• Most Heavily Cratered

of All Planets

• Boling During Day

Freezing During Night

• Interior is Cold

Surface is Hot

• Considered to be

a Dead Planet


VENUS

• Thick, Sulfuric

Cloud Cover

• Atmospheric

Pressure - 92 Times

That on EARTH

•Atmosphere -

96% CO 2

(Greenhouse Gas)

• Surface - Very

Hot, ~ 884 o F


MARS

The Red

Planet

• Seasons

• Little CO 2

• Possibly Most

Like EARTH ?

• Best Candidate

for Extra-

Terrestrial

Life ?


JUPITER

• 1000 Time Larger

than EARTH

• Great Red Spot

(centuries old storm

the size of

the United States

- visible in

southern hemisphere)


SATURN

• Prominent Rings

• Winds at 1,000’s mph


MARS, JUPITER and SATURN

Show Retrograde Motion


Retrograde Motion (Epicycles)

• JUPITER Takes 12 Years to Move Through the Zodiac

It Exhibits a Small Retrograde Loop Each Year

• MARS Makes a Retrograde Loop Just Before It Is in Opposition

• SATURN Takes 30 Years to Travel Through the Zodiac

It Makes Numerous Retrograde Loops During That Time


Opposition

• MARS is Now in

Opposition

-That Is –

MARS Is Now on the

Opposite Side of the

EARTH Than the SUN

• As the Changing Seasons

Cause the Stars to Rise

Earlier, MARS Rises

Earlier with Them

• MARS Becomes Visible

Shortly After Sunset and

Rides High in the Sky in the

Middle of the Night


Ancient Interpretations of Planetary Motion

Geocentric Model


1.3 The Slow Growth of Reason

Nicholaus Copernicus and the Heliocentric System

(1473 – 1543)

• Polish Astronomer and Cleric

• Contemporary of Botticelli and

Michelangelo

• 19 Years Old When Columbus

Voyaged to the New World

• Thought Geocentric System Was Too

Complex – Heliocentric System Much

More Aesthetically Pleasing


1.3 The Slow Growth of Reason

Nicholaus Copernicus and the Heliocentric System

• Direct Affront to

Entrenched Religion

and Philosophies

• Made the Universe Big

– But the EARTH and

Humans Small

• Humanity Was

Demoted from Its

Central Position

• Copernicus Had

NO PROOF


Tyco Brahe

(1546 – 1601)

• Born in Denmark 3 Years After the

Death of Copernicus

• Measured the Position of Planets and

Stars with High Precision Using

Instruments with No Optical Parts

• Observed a “New Star” That

Appeared in 1572 Was Farther Away

Than the Moon

• Showed That the Heavens Were Not

Immutable

They Could Change

• Colorful Character - Very Vain

Wore a Silver Nose as a Result of a

Dueling Injury


• 9 Years Later, Kepler Published

the Mathematical Relationships That

Express the Apparent Harmony of

Planetary Motions

Johannes Kepler

(1571 – 1630)

(Contemporary with Shakespeare)

• Taught the Copernican System

While Studying to Become a

Lutheran Minister

• Instead Became a Mathematician

at the University of Graz,

Austria in 1594

• Invited by Tycho Brahe to Join

Him in Prague in 1600

• Tycho Died the Following Year, and

Kepler Took Over His Post


Kepler’s Laws of Planetary Motion

LAW 1

Each Planet

Moves in an

Elliptical Orbit

About the SUN,

with the SUN at

One Focus of

the Ellipse


Kepler’s Laws of Planetary Motion

LAW 2

An Imaginary Line Connecting the SUN with

a Planet Sweeps Out Equal Areas in Equal

Times as the Planet Moves About the SUN


Kepler’s Laws of Planetary Motion

LAW 3

The Cube of the

Distance from the

SUN divided by

the Square of the

Time Required to

Traverse the

Orbit Is a

Constant

The Same for

Every Planet


Galileo and the Foundation of Modern Science

(1564 – 1642)

• Son of a Musician, Studied

Medicine, Became Attracted to

Mathematics

• Recognized That Optical Lenses

Could Be Combined to Enhance

Sight

• Developed Telescopes and Began

Studying the Heavens

• Early Discovery - the 4 Large

Moons of JUPITER Proving the

Copernican System


Jupiter

Jupiter’s Four Largest Moons

(Galilean Moons – Discovered by Galileo)

These Moons of JUPITER, when first observed by Galileo, were

pointed to as proof that not all celestial bodies orbited around

EARTH, and that EARTH was not the center of the Universe

NASA/NGS Image Collection


Discovered VENUS

displayed Phases Like

Our Moon – Only

Explained by the

Copernican System


Galileo and the Foundation of Modern Science

(1564 – 1642)

• Catholic Church Did Not Accept

Proofs Because They Appeared to

Contradict Scripture

• Galileo Could Only Discuss His

Ideas as “Theories” and Not as Fact

• Unwilling – Arrested in 1633 and

Forced to Deny the Heliocentric

Theory (14 Years After Kepler’s

Publication)

• Held Under House Arrest for the

Last 8 Years of His Life

• Church Exonerated Him in 1992


1.4 Newton

and the

Law of

Gravitation

(1642 – 1727)

• Born Only Months After the Death of

Galileo

• Long Career – Died in 1727 at Age 84

• Newton Began Inventing Calculus as an

Undergraduate, While Also Formulating

Ideas About Optics and Mechanics

• One of the First Scientists to Use

Mathematical Arguments to Test

Scientific Ideas

• His Most Important Contributions to

Astronomy Are His Three Laws of

Motion


1.4 Newton and the Law of Gravitation

(1642 – 1727)

The Laws of Motion

LAW 1

Every Body Continues in Its State of Rest

or of Uniform Motion in a Straight Line

Unless It Is Compelled to Change That State

by the Action of Some Outside Force


Newton and the Law of Gravitation

The Laws of Motion

LAW 2

The Change of Motion (Acceleration)

Is Proportional to the Force That Acts on the

Body and Inversely Proportional to

the Mass of the Body

F = MA

F – Force, M – Mass, A - Acceleration


Newton and the Law of Gravitation

The Laws of Motion

LAW 3

To Every Action There Is

an Equal and Opposite Reaction


The Law of Gravitation

Newton’s Three Laws Provide the Framework

to Understanding Why the Planets Move

Around the SUN in the Way That

Kepler Explained


Law

of

Gravitation

Gravity Will Pull the Planet into the SUN

if the Planet Is NOT Moving


Law

of

Gravitation

Inertia of the Planet Will Keep It Moving in a

Straight Line if the Planet is Moving


Law

of

Gravitation

Earth – Moon – Sun System


Law

of

Gravitation

Gravity and Inertia Together Cause the Planet to Travel

a Fixed Path Around the Sun in a Stable Orbit


The Law of Gravitation

The Gravitational Force Between Two Objects is

Proportional to

the Product of Their Masses

and Inversely Proportional to

the Square of the Distance Between Them

F= GM 1 M 2 / R 2

F = Force

M = Mass

R = Distance

G = Gravitational Constant


Law of Gravitation

Earth – Moon – Sun System


1.5 Escaping From Earth

Rockets

Move by Expelling Gas Backwards

Newton’s Third Law

The Gas Goes One Way

The Rocket Goes the Other Way


1.5 Escaping From Earth

Rockets

• Large Brute-Force Applications

Solid-Fuel Rockets

(e.g. - Space Shuttle Boosters)

• More Easily Controlled Applications

Most Can Be Re-Started in Space

Liquid-Fuel Rockets

Most Efficient Liquid-Fueled Rockets

Hydrogen and Oxygen

(Must Be Extremely Cold to Be Used in Liquid Form)

Less Efficient Liquid-Fueled Rockets

Hydrazine (Nitrogen Compound)

(Remains Liquid at Moderate Temperatures)


Going Into Orbit

Orbital Velocity

The Surface of

EARTH Curves Away

as Fast as the Ball

Falls, Resulting in a

Low-Altitude Circular

Orbit

EARTH Orbital Speed

is About 8 km/s or

About 28,000 km/hr


Law of

Gravitation

Square of

Orbital Velocity

is Proportional

to the Mass of

the Planet

Smaller Planet with

Weaker Gravity

Requires Lower

Speed to Achieve

Orbit

The Higher the

Orbit, the Slower

Its Speed -

Moon = 1.3 km/s

Gravity and Inertia Together Cause the Planet to Travel

a Fixed Path Around the Sun in a Stable Orbit


Orbital Period

The Distance of One Orbit

Divided by the Orbital Speed

• At a Distance of 35,680 km, the Orbital

Period is 24 hours

(1 EARTH Day)

• EARTH’S Circumference = 40,000 km

A Satellite Orbiting About 200 km

Above the Atmosphere, Traveling at

28,000 km/hr (Orbital Velocity)

Will Have an Orbital Period of

1.4 Hours (90 Minutes)

• The Moon Takes 29 Days to Orbit

EARTH at a Distance of

384,000 km


Orbital Period

The Distance of One Orbit

Divided by the Orbital Speed

• EARTH’S Circumference = 40,000 km

A Satellite Orbiting About 200 km

Above the Atmosphere, Traveling at

28,000 km/hr (Orbital Velocity)

Will Have an Orbital Period of

1.4 Hours (90 Minutes)

A Spacecraft Put Into

Orbit at 35,680 km Will

Appear Stationary from

EARTH

Geostationary

Useful for

Communication and

Weather Satellites

• The Moon Takes 29 Days to Orbit

EARTH at a Distance of

384,000 km

• At a Distance of 35,680 km, the Orbital

Period is 24 hours

(1 EARTH Day)


Going Into Orbit

Escape Velocity

Shoot a Ball Into Orbit at

a Greater Speed

Elliptical Orbit Becomes

More and More Elongate

Eventually Ball Escapes

Completely

EARTH

Perigee

SUN

EARTH

Apogee

SUN


Going Into Orbit

Escape Velocity

• Escape Velocity, as

Described Here, Is the

Same Speed for a Ball

Shot Directly Straightup

from the Surface

• At This Speed, Gravity

Can Slow the Ball, But

It Can Not Stop the

Onward Motion

• Equal to Orbital

Velocity Multiplied by

the Square Root of 2

EARTH Orbital Velocity=28,000 km/hr

EARTH Escape Velocity =

28,000 x 1.4 = 40,000 km/hr (11 km/s)


Going Into Orbit

Escape Velocity

• Escape Velocity

Becomes Easier if the

Planet’s Mass Is Small

• For Example:

Escape Velocity from the

Asteroid Eros Is Only 40

km/hr

(You Could Throw a Ball Into

Orbit)


1.6 The System Revealed

Inclination

All Orbits of the Planets, Except Those of MERCURY (closest to the

SUN) and PLUTO (Most Distant), Lie Essentially in the Same Plane

Eccentricity

MERCURY and PLUTO Also Have the Greatest Eccentricity of

All the Planets


1.6 The System Revealed

Which Way Is Up

• The Convention on EARTH Is North

• North in the Sky Is the Direction in Space

Toward Which the EARTH’S North Pole Points

Satellite/Planets ROTATE About Their Axis

Satellites/Planets REVOLVE About Their Planet/SUN

• Most Satellites Revolve Around Their Planets in the Same

Counterclockwise Direction as The Planet Revolves Around Its SUN

(e.g. – EARTH/SUN)

• Those Satellites That Revolve in the Opposite Sense Are

Considered to Display RETROGRADE Motion

(e.g. - VENUS/SUN, Several of JUPITER and SATURN’S Moons)


OUR SOLAR SYSTEM

A Scale Model

(Reduce Every Dimension by a Factor of 200 Million)

• EARTH = Orange

• Moon = Grape

• SUN Would Be More Than 1 km Away

and Have a Diameter of 7 m (2 Story House)

• JUPITER = Large Pumpkin

• SATURN (Including Rings) Just Fits Between the

EARTH and the Moon

• PLUTO = Small Grape 30 km from the SUN

The Real System

• JUPITER IS 5 Times the Distance from the SUN

as Is EARTH (5 AU)

• SATURN is That Distance Again from JUPITER

(10 AU)

• URANUS Doubles the Size of the System (20 AU)


(AU = Astronomical Unit: The Distance from EARTH to the SUN)


PLANETARY RULES

1.) The “History of Earth” is recorded in the

rocks, and can be deciphered by geological

study. It is the same for the other planets.


PLANETARY RULES

1.) The “History of Earth” is recorded in the

rocks, and can be deciphered by geological

study. It is the same for the other planets

2.) The Jovian (Outer – Frozen Gas) Planets have

no solid surface. “Traditional” Geology does

not exist on these planets. They must be

studied by other (although similar) means.

Scientific techniques do not always work the

same way on every planetary body


PLANETARY RULES

3.) Earth is just one planet of a family of

active worlds


PLANETARY RULES

3.) Earth is just one planet of a family of

active worlds

4.) The “Grand Finale” is yet to come


Finding Our

Place in Space

Chapter 1

The Great Galaxy Andromeda

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