1 Unit 1 How Big is Big? How far away is the Moon? 240,000 miles = 384,000 km = 1 light second What does this really mean? How many McDonald’s hamburgers would it take to get from here to the Moon? How long would it take to drive there? How Big is Big? It would take 19 billion or 19000000000 or 19x10 9 hamburgers to reach the Moon. This is about 20% of the hamburgers that McDonalds has ever sold! Driving 80 miles per hour, it would take 3000 hours or about 4 months of non-stop driving! How Big is Really Big? • The solar system - our nearest planetary neighborhood – Size of Earth: 8,000 mile diameter – Size of Jupiter: 88,000 mile diameter – Size of the Sun : 800,000 mile diameter Relative Sizes of the Sun and Planets See also http://www.troybrophy.com/projects/solarsystem/index.html How Big is Really Big? • The solar system - our nearest planetary neighborhood – Size of Earth: 8,000 mile diameter – Size of Jupiter: 88,000 mile diameter – Size of the Sun : 800,000 mile diameter – Distance from Sun to Mercury: 36,000,000 miles – Distance from Sun to Earth: 93,000,000 miles – Distance from Sun to Jupiter: 500,000,000 miles
Transcript
1
Unit 1How Big is Big?
How far away is the Moon?240,000 miles = 384,000 km = 1 light second
What does this really mean?How many McDonald’s hamburgers would it take to get
from here to the Moon?How long would it take to drive there?
How Big is Big?It would take 19 billion or 19000000000 or19x109 hamburgers to reach the Moon.
This is about 20% of the hamburgers thatMcDonalds has ever sold!
Driving 80 miles per hour, it would take3000 hours or about 4 months of non-stopdriving!
How Big is Really Big?• The solar system - our nearest planetary
neighborhood– Size of Earth: 8,000 mile diameter– Size of Jupiter: 88,000 mile diameter– Size of the Sun : 800,000 mile diameter
Relative Sizes of the Sun and Planets
See also http://www.troybrophy.com/projects/solarsystem/index.html
How Big is Really Big?
• The solar system - our nearest planetaryneighborhood– Size of Earth: 8,000 mile diameter– Size of Jupiter: 88,000 mile diameter– Size of the Sun : 800,000 mile diameter– Distance from Sun to Mercury: 36,000,000 miles– Distance from Sun to Earth: 93,000,000 miles– Distance from Sun to Jupiter: 500,000,000 miles
2
How Big is Big?• Distance to the nearest star:
20000000000000 miles• Diameter of Our Galaxy:
200000000000000000 miles• Distance to Andromeda Galaxy
20000000000000000000 miles• Distance to most distant Galaxy:
100000000000000000000000miles
• Size of helium atom:0.0000000000001 miles
Scientific Notation• Distance to the nearest star: 20000000000000 miles
= 2x1013
• Diameter of Our Galaxy: 200000000000000000 miles= 2x1017
• Distance to Andromeda Galaxy20000000000000000000 miles = 2x1019
• Distance to most distant Galaxy:100000000000000000000000 miles = 1x1023
• Size of helium atom: 0.0000000000001miles = 1x10-13
Scientific Notation
• Multiplication– 2x1010 X 4x105 = (2X4)x10(10+5) =8x1015
Question• The distance between stars in our galaxy is
very large compared to the size of the stars.Thus, the galaxy is mostly empty space.
• Why do galaxies get damaged when onegalaxy hits another?
Question
• The atoms in your body are even moreempty than the space within our solarsystem.
• Why is it that when you clap your handsthey do not just pass through eachother?
Question
What daily motions do you observe ofdifferent celestial objects?
3
Daily MotionsSun
Daily MotionsStars
Solar and Sidereal DaysWhy is the Solar Day longer than the Sidereal Day? Coordinate system on Earth
Gainesville: 29.6510N, 82.3250W
Celestial Sphere
4
Annual Motions of the Sun
Annual Motion of Sun Annual Motionof the Stars
Annual Motions of the Stars Where are we?
• The position of acelestial pole nearthe horizon, tells uswe must be nearthe Equator. Alsoconsider the anglesthe star trails makewith the horizon: 90degrees.
5
Question• You are kidnapped, drugged and placed in a dark room
for an indefinite period of time!• You escape and find a radio to call for help but you don’t
know where you are!• Luckily, it’s a clear night. You watch the stars for while
and you see the stars rising at a 20 degree angle withrespect to your horizon.
• What can you tell your rescuers about your location?
Seasons• With the annual motion of the Earth around the
Sun, we notice a cyclic pattern in the weather,know as the seasons.
• Observations:Seasons are reversed in the Northern andSouthern Hemispheres
•For example, you’re at the beach at Cape Cod inJuly, they’re skiing in New Zealand!
The region near the equator is hottest; poles are the coldest
The Sun’s position in the sky changes
Reasons for the Seasons?
• What causes this pattern?• Two Possible Models:
– Distance of the Earth from the Sun?– Tilt of the Earth’s axis with respect to the
Earth’s orbital plane (ecliptic)
Reason for Seasons:Distance?
• Predictions:– Relation between Earth-Sun distance and
season• for example, the Earth should be closest to the
Sun in summer– Same season every where on Earth
• since the Earth is tiny compared to the Earth-Sun distance
Reason for Seasons:Distance?
• Observations:
Reason for Seasons:Distance?
• Predictions don’t match Observations:– Seasons are reversed in the Northern and
Southern Hemispheres• For example, you’re at the beach at Cape Cod
in July, they’re skiing in New Zealand!– The Earth is closest to the Sun during
northern winter
6
Reason for the Seasons: Tilt?The Earth’s axis of rotation is tilted by 23.5
degrees with respect to the ecliptic pole
Reason for the Seasons: Tilt?• Predictions:
– Summer occurs in hemisphere pointedtoward the Sun
– Winter occurs in the hemisphere pointedaway from the Sun
– Therefore: Seasons are reversed innorthern and southern hemisphere
Reason for the Seasons: Tilt Reason for the Seasons: Tilt
Reason for the Seasons
• Demonstration
Reason for the Seasons: Tilt
• Predictions match observations:– The northern hemisphere and southern
hemisphere seasons are reversed– The region near the equator is hottest;
poles are coldest
7
Question• When is the hottest time of year in Quito Ecuador?• If the Earth’s rotation axis was perpendicular to it’s
orbital plane (ecliptic), what would you expect theseasons to be like?
• If the Earth’s rotation axis was parallel to it’s orbitalplane (ecliptic), what daily and annual effects wouldthis have?
Example of the ScientificMethod
Motion of the MoonEast to west in arc across sky
Eastward w.r.t. stars - half degreeper hour
Sidereal Period - 27.3 days
Moon rises ~ 50 minutes later each day
Phases of theMoonWhy does the Moon Shine?
Reflected sunlight
Half of the Moon isalways lit up
Fraction of lit surface wesee from Earth - phase
How much of the Moon is litup by Sun?
Synodic Period - 29.5 days
Sidereal & Synodic Periods
Sidereal Period: 27.3 days
Synodic Period: 29.5 days
8
Phases of theMoon
• The changes in the Moon’s phaseare due to changes in the anglebetween the Sun, Moon and theEarth
– 0 degrees : New Moon
– 90 degrees: Quarter Moon(First or Third)
– 180 degrees: Full
Question • If the Sun sets at 6pm, whendoes a first quarter Moon rise?
A First Quarter Moon rises at noonEclipses
• A solar eclipse occurs when the Moon movesbetween the Earth and the Sun
• A lunar eclipse occurs when the Earth movesbetween the Sun and the Moon and the Moon movesthrough the Earth’s shadow
• In ancient cultures eclipses were bad omens
The Moon Moves Over the Face of theSun
•
The Sun is Nearly Covered
•
9
The Diamond Ring Total Solar Eclipse
Angular Size of Sun and Moon
• The Sun and Moon have very differentphysical sizes– Radius of Sun is 7x105 km– Radius of Moon is 1.7x103 km– So the Sun is 400 times bigger than the
Moon!!• How can they appear to be nearly the
same size during an eclipse?
Angular Size• Answer: the Moon and Sun,
coincidentally, have nearly the sameangular size
• Angular size of an object depends ontwo things– The physical size of the object– The distance to the object
Angular size (radians)= Physical Size
Distance
An Annular Solar Eclipse
10
Question
• Why does an annular eclipse lookdifferent?
Shadows & Eclipses
• A total solar eclipse can seen from only a small region onthe Earth– entire disk of the Sun covered– In umbra or inner shadow the Moon
• Partial solar eclipses are seen over a larger area– only part of the Sun is covered by the Moon– in the penumbraor Moon’s outer shadow
• The Moon’sshadow movesover the Earthduring a solareclipse
• Penumbral eclipse – the Moon passes through thepenumbra but does not come in contact with umbra
• Lunar eclipses are visible anywhere on the night-timeside of the Earth
A Lunar Eclipse
Question
• Why is the Moon’s surface still visibleduring a total lunar eclipse?
When & How Often?• Lunar eclipses occur at FULL
Moon PHASE• Lunar eclipses do not occur
every month because theMoon’s orbital plane is tiltedwith respect to the ecliptic– a total lunar eclipse occurs
when the Moon crosses theecliptic at full Moon
– since the Earth’s shadow ismuch bigger than the Moon,total lunar eclipses occurmore often than solareclipses
Lunar eclipses occur 2 to 5 times per year
Motion of the Planets• The planets are the brightest
objects in the night sky (with theexception of the Moon)
• Rise in the east and set in the west• Planet means “Wanderer”
– The planets move slowly amongthe stars staying near the ecliptic
– Different planets move at different speeds relative to thestars (of the visible planets,Mercury is the fastest, Saturn isthe slowest)
– They move in complex patternschanging their direction ofmotion
12
Motion of the Planets• Planets generally move eastward relative to the stars• Planets undergo retrograde motion
– motion relative to stars:• slows• reverses• moves westward relative to stars• slows again• reverses again• resumes its general eastward motion
• This motion is unique among all astronomical objects• This confused & perplexed people for centuries & led
people of many cultures to attribute superior powers tothe planets
Inferior Planets• Venus and Mercury• Stay near the Sun on
the sky• Are visible only near
sunrise and sunset(“morning & eveningstars”)
• Move away from theSun and then movetoward it
Mercury - (ca. 15th
century)
Mercury is holding abag for commerce andtwin snakes for healingpowers.
Reigns over Virgo &Gemini
Venus depicted in the AztecCodex: Aztec god, Xolotl(evening star) at thecrossroads of fate. Laterbecame twin of Quetzalcoatl(morning star & supreme god)
Superior Planets• The visible superior
planets are Mars,Jupiter and Saturn
• Can appear far fromthe Sun but remainnear the ecliptic
Mars & VenusFresco from Pompeii(ca. 1 A.D.)
Mars is the war-god& Venus, the god oflove.
Saturn (ca. 18th century) - Arabicillustration showing agriculturalactivities under direction of Saturn
Planets, Gods & Days ofWeek
• English names for mostof the days of the weekcome from Norse gods
• Tuesday : Tiwes - godof war
• Wednesday: Woden -god of day & night
• Thursday: Thor - god ofthunder - head god
• Friday: Frega - goddessof spring
15th centuryengraving ofdays of theweek andtheirastrologicalcounterparts
Ancient Astronomy• Since pre-historic times, ancient
people have observed andrecorded the regular & cyclicpatterns in the sky
• To explain these motions, a dualdevelopment in human thoughtbegan:– search for natural &
unchanging laws– creation of mythology
The Earliest Calendars• During the stone age (50,000 years ago) people first
began to leave a record in carvings and paintings.These included:– Pictures of constellations– The first calendars
25,000 year old Ishango bone (Congo, Africa)with possible lunar phase calendar
14 Phases of the moon seen in cave paintingsin Lascaux, France (18,000 BC)
13
Early Calendars-Alignments• Many archaeological sites reveal alignments with prominent celestial
events.• Archeoastronomy is the study and interpretation of such alignments.
– The reality of such alignments can be scientifically verified– The cultural significance (e.g. purpose) has been lost to time– However, it is reasonable to assume that at least one purpose was to
predict the seasons, possibly for agriculture, hunting, migration…..
Hopi sunrisecalendar
•Observed by a“Sun priest” atPueblo
•Used to anticipateceremonials
Stonehenge c.a. 2800BC
• Constructed and reconstructed on SalisburyPlain in England over thousands of yearsbeginning about 2,800 BC
• Probably used as a calendar and almanac ofsolar and lunar motion
• Stones were brought from many miles awayshowing its importance
• There are many other similar Neolithic (newstone age) sites throughout Britain
STONEHENGE
The Great Pyramid c.a.2600BC
• Celestial bodies had greatsignificance in Egyptian cultureand was integrated into theirreligion
• Pyramids are the tombs ofEgyptian Pharaohs, who werebelieved to be divine gods whowere connected to the stars
• The side of the Pyramids were very accurately alignednorth-south
•The passages and shafts within the Pyramids may havebeen aligned with astronomical bodies (Orion and a PoleStar)
•The Pole star was called an “imperishable star” since itnever sets and the spirit of the Pharaoh would journey there
The Great Pyramids• The Great Pyramids of Gaza
may have been arranged in thepattern of the constellation ofOrion
• Orion had special significance inancient Egypt & represented thegod Osiris
• Osiris is the god of birth, death &resurrection
• By placing such a configurationon the ground, the god wasbrought to Earth
• The pyramids were placed alongthe Nile, which may haverepresented the Milky Way
Chichén Itzá c.a. 600-830AD• Chichén Itzá was an important Mayan & Toltec
ceremonial site on the Yucatan• Prominent alignments with Venus & Sun rise &
set were made through windows in the tower ofthe Caracol
Venus, as the morning star, was prominent in Mayan religion and representedtheir most important godQuetzaloatl
14
Chichén Itzá c.a. 600-830AD
• Widows in the top of pyramid arealigned with sunrises at the solstices
• There are also alignments (notshown) with the sunset points of theequinoxes
• Chaco Canyon was home to the Anasazi People from900 - 1300 A.D.
• Anasazi means “ancient ones” in Navajo• Atop of Fajada Butte, are 3 large stone slabs and a
petroglyph know as the Sun Dagger• The stones are aligned such that at noon on the
solstices & equinoxes, 1 or more daggers of the Sun’slight strike the petroglyph key locations.
Other North American Sites
• Casa Grande in Southern Arizona• A Hohokam pueblo built about 1000 A.D.• Hohokam means “those who have gone”• Windows are aligned with solar and lunar events
• Medicine Wheel in Wyoming• Built by Native Americans of the High Planes
• Rocks laid out in a 90 foot circle
• Radial spokes are aligned with the positions ofsunrise and sunset at the solstices and are alsoaligned with the rising & setting positions ofbright stars
Asian Alignment Sites
• Located in Gao ChengZhen, China, this giantgnomon was 1st built 2000years ago (Han Dynasty)
• Light passes through a 40 fthigh window - wall’s shadowis measured on a largehorizontal scale
• City of Vijayanagara in India - 14th century• Layout of city is aligned N-S & alignments withPole Star and other Astronomical objects
Constellations
PatternsOfStars
Constellations
StableOver Human History
15
ConstellationsReflect the cultures × of the peoplewho created them
The oldest constellations used by astronomers today originated ~ 3000 BC in Mesopotamia
Southern hemisphere constellations used by astronomers originated in the 17th century by sailors
Constellations
Orion the Hunter• Orion is a prominent winter
constellation• Located near the Celestial Equator so
it can been seen from eitherhemisphere
• Located near the Milky Way
Orion• Greek Mythology
– Orion, son of Poseidon and a great,fearless hunter
– His arrogance angered the goddess Herawho sent a scorpion to kill him
– The Moon god Artemis placed him in thesky far away from Scorpio
• Jewish - the Biblical Samson• Arab - Al Jabbar the giant• China - Hunter and warrior Tsan• Brazilian - A Cayman “cousin of the gator”• Egypt - The God Osiris
Ursa Major & Minor• Ursa Major is the most prominent northern
circumpolar constellation• Ursa Major contains the “Big Dipper” asterism• Ursa Minor contains the “Little Dipper”
asterism
Ursa Major
Ursa Minor Big Dipper
16
Ursa Major & Minor• Two stars in the front end of the Big
Dipper point to Polaris• Greco-Roman Mythology
– Callisto & Zeus were lovers & had ason, Arcas. Hera, Zeus’ wife, was angryand turned Callisto into a bear. Yearslater, Arcas was hunting & was about tokill his mother, so Zeus stepped in &threw them both into the sky. Hera stillwanted revenge so she made the paircontinually circle the sky, never beingable to refresh themselves in the River-Ocean that encircle the Earth.
Ursa Major• Aztec - Tezcatlipoca- Peg legged god
associated with death & the north• Hindu - the seven Rishi or primordial sages• Chinese - chariot carrying sages• Basques - 2 bullocks followed by 2 thieves,
watched by a herdsman & his 2 servants• Egyptian - ox pulling a man with a
hippopotamus and alligator on his back• Seen as a bear in many cultures despite its
long tail. Perhaps this is due to the notion thatit prowls around the sky like a bear.
Persian Representation
Arab Representation
Early Views of the Cosmos
• Ancient world pictures ofthe cosmo– geocentric - Earth
centered– finite - had boundary
• typically a shell ofstars closed offthe universe
• Ancient cosmologiespaid little attention tocelestial motions even ifcelestial cycles werecarefully observed
Nut,Egyptiangoddess ofsky, archedover Geb,god of Earth
– Earth is flat– Sky is like a flat plate support by 4 mountains– Sun is carried across the sky in a boat from
east to west. At night Sun is carried back tothe east through the Underworld
• India:– Earth is a circular disk surrounded by the
ocean– great mountain in center of world– Sun goes around mountain once a day
• China:– sky is a round dome, surrounding Earth– Earth is square– Sun travels in a big tilted circle
Egypt
India
China
Early Greeks• Ancient Greek astronomers were the first to attempt to
explain the workings of the heavens in a careful,systematic way using naked eye observations andmodels
• Greeks enjoyed philosophy which to them meant theattempt to understand all things in nature
• They used their highly developed mathematical skills(geometry & trigonometry) & logic to makeremarkable discoveries about their universe
17
Aristotle & A Spherical Earth• Aristotle (384-322 B.C.) showed by proof
that the Earth was spherical:1 He observed that the Earth’s shadow is
curved during a lunar eclipse– “The shapes that the Moon itself shows are
of every kind -straight, gibbous, and concave- but in eclipses the outline is always curved:and since it is the interposition of the Earththat makes the eclipse, the form of this linewill be caused by the form of the Earth’ssurface which is therefore spherical” -Aristotle’s treatise On the Heavens
Painting ofAristotle byRembrandt
Aristotle & A Spherical Earth
2 Aristotle learned from travelers that theheight of the Pole star above the horizonvaries as you travel from North to South• Going North: Polaris gets higher with
respect to the horizon• Going South: Polaris gets lower with
respect to the horizon• Go far enough south -- Polaris no longer
visible
⇒Earth must be spherical!
Flat Earth Spherical Earth
Question
• Aristotle also reasoned that the Earthwas spherical by watching ships leaveport and sail off towards the horizon. – What would you observed about a ship
sailing away from you if you lived on a:• Flat Earth ?• Spherical Earth ?
Aristarchus of Samos(310-230 B.C.)
• Estimated relative sizes of the Moon & Earth– timed duration of lunar eclipses– compared the time it takes the Moon to enter
the Earth’s shadow with the time it takes theMoon to cross the Earth’s shadow
• Estimated distance to Moon– measured angular size of Moon & compared
this to the estimate of the Moon’s size relativeto Earth’s diameter
• Estimated distance to Sun– assumed Moon’s orbit was circular & uniform– measured intervals between 1st and 3rd
quarter phases of the Moon & for 1 completephase cycle
– compared these intervals to determine theMoon-Earth - Sun angle
Aristarchus of Samos(310-230 B.C.)
• Estimated size of Sun– from total Solar Eclipse using
relationship between angulardiameter, size and distance
Aristarchus estimated all these quantities in terms of the Earth’s diameter
⇒ Aristarchus found that the Sun was much bigger & much farther awaythan the Moon⇒ He therefore concluded that the Sun, not the Earth was at the center ofthe Universe
7.20 5000 stadia=
Eratosthenes (c. 200 B.C.)Eratosthenes estimated the Earth’s diameter, and therebytook the relative measurements of Aristarchus and placedthem on an absolute scale
3600 Earth’s circumference7.20 5000 stadia
18
Hipparchus (c. 150 B.C.)• Erected an observatory on Rhodes & built instruments to
measure as accurately as possible the direction of objectsin sky
• compiled catalog of stellar coordinates - 850 entries• discovered precession - Earth’s axis of rotation (about the
• determined length of year to within 6 minutes• carefully observed motions of Moon, Sun & planets• predicted lunar eclipses to within 1 hour• 1st to deal with the problem of parallax for solar eclipses &
predicted the paths of totality for solar eclipses• Developed a geometrical, geocentric model of the
Universe
Scientific Models• Conception of a physical model to explain the workings of nature
is a creative act of science• Models apply known laws of nature to explain observations• Key aspects of a scientific model
⇒ models explain what is seen⇒ models predict observations accurately⇒ simplify your understanding of nature
• Validity of models is tested by checking how well predictions fit thebest & new observations
• Scientific models are not static but evolve when new & betterobservations become available
Modeling the Cosmos• Key Observations to Explain
– Motion of Sun• East to West in about 12 hours from
sunrise to sunset• West to East along ecliptic ~ 10 per day• variation in speed along the ecliptic• variation of length of day & height of Sun
with season– Motion of Moon
• East to West in about 12 hours 25 minutesfrom Moonrise to Moonset
• West to East within 50 of ecliptic• sidereal & synodic periods
Modeling the Cosmos• Key Observations to Explain
– Motion of Stars• East to West in ~ 12 hours
from star rise to star set• star rise is ~ 4 minutes
earlier each day• circumpolar stars• stars in fixed position
relative to one another• precession• yearly motion relative to
Sun
Modeling the Cosmos• Key Observations to Explain
– Motion of Planets• East to West in ~ 12 hours from rising
to setting; interval varies depending onrate of planet’s motion with respect tostars
• West to East, within 70 of ecliptic• Average speed varies along ecliptic
– fastest for Mercury– slowest for Saturn
• Variation in speed along ecliptic foreach planet
• Retrograde motion from West to Eastat a time specific for each planet
Newton 1642-1727• Only child, posthumous son of an illiterate
yeoman– born prematurely - sickly as child– raised by maternal grandmother– as a child he built clocks & sundials– practical joker
• Trinity College, Cambridge University at 19– studied mathematics & astrology– encouraged to study physics by Barrow
• University closed in 1665 due to plague– Invented calculus studied gravity, optics
• Barrow resigns & gives Newton his post atCambridge
19
Describing Motion
• Velocity– Rate of change of position– speed & direction
• Acceleration– Rate of change of velocity
Laws of Motion• Law I: Law of Inertia
– A body at rest or inmotion at a constantvelocity along a straightline remains in that stateof rest or motion unlessacted on by a net outsideforce
• Takes next logical stepbeyond Galileo’s definitionof inertia
• Uniform motion is asnatural a state for a bodyas rest
Force=Mass x Accel
F = m x a
Laws of Motion• Law II - Force Law
– The rate of change in an object’s velocitydue to an applied force is in the samedirection as & proportional to the force andinversely proportional to the object’s mass
• To have acceleration there must be a force• Force & acceleration always work in the same
direction• Given the same force, a more massive object
accelerates more slowly than a less massiveone
Examples of the Second Law
• Friction– Hockey puck on ice vs. on a street
• Impact of a bat on a baseball– The bat imparts a force to the ball and
sends it flying in the opposite direction
Question?
• A ball is attached to a string and I spin itabound my head in a circle– Is the ball accelerating?– If it is accelerating what is the force?– If the string were to break what path would
the ball follow?
20
Laws of Motion• Law III - Reaction Law• For every applied force, there is an
equal, but opposite force• Forces always occur in pairs• A force cannot be created in isolation• If gravity is a force it must act
between bodies
Examples
Question?
• You push a cart and it moves but youdo not appear to move.– Why don’t you move if there is an opposite
and equal force pushing on you?
Newton Figures Out Gravity
• He unified the force which makes an apple drop from atree and the force which makes the Moon orbit theEarth– Gravity causes all objects to attract one
another• He intuitively figured out that the force of gravity
between two objects depends on only three things:– The masses of each object: more massive objects
gives a stronger attractive force– The distance between the objects: moving objects
further apart weakens the force• This is true on size scales from a laboratory desk to
groups of stars and galaxies
Mass1 x Mass2Separation 2Force ∝
Newton’s Law of UniversalGravitation
•Force is proportional to themasses
–Smaller mass →smaller force
•Force is inversely proportional tothe distance between the objects
–Further apart→ weaker force
Mass1 Mass2Force Force
Separation
The Inverse Square Law• Force weakens like the
square of the distance
21
Question• The spaceship Enterprise is orbiting the
planet Vulcan. The crew increases theship’s orbital distance from the planetby a factor of 10. What happens to thegravitational force between the planetand the ship?
Orbits and Gravity
• Gravity is the force which keeps theplanets from flying off into space– Because the Sun is much more
massive then the planets the suncontrols the motion of the planets
• Gravity always pulls the planet towardthe Sun
• Inertia wants to keep the planetmoving in a straight line
• The balance between gravity andinertia leads to the stable orbit of aplanet
The Shapes of Orbits• The shape of an object’s orbit
depends on its velocityperpendicular to the force ofgravity– A body with a small
perpendicular velocity willfall nearly straight in
– A body with a largeperpendicular velocity willovercome the force ofgravity and move to a largerdistance
• For closed orbits the shapeswill be ellipses
Kepler’s 2nd Law• As a planet moves
toward the sun theforce of gravitycauses it toaccelerate alongits orbits and itmoves faster
• As a planet movesaway from the sunthe force of gravityacts along its orbitand slows it down
Kepler’s 3rd Law
• Planets with largeraverage distances fromthe sun have longerperiods– Since the gravitational
acceleration is less theymove more slowly alongthere orbits
– The orbits are larger
• Newton applied his laws of motion and gravity to derive amodified version of Kepler’s 3rd law
• In the solar system the mass of the sun is so large thatMsun+Mplanet is almost exactly equal to Msun
• This law allows the determination of masses for orbitingdistant objects
Newton’s Adaptation of Kepler’s 3rd Law
(Mass1+Mass2) Period2 = (average distance)3
22
Newton’s Cosmology• Gravity holds the solar system together
– The Sun is the most massive object so its gravitydominates the solar system
– The law of Universal Gravitation naturallyproduces elliptical orbits (Kepler’s 1st law)
– The law of Universal Gravitation naturallyproduces Kepler’s 2nd and 3rd laws
• The universe must be infinite or it wouldcollapse
Complexity to Simplicity
Complexity to Simplicity1- They were Gods that hadspecial power over our lives
2- They were mystical bodiesmoving in a complex clock workuniverse with orbits, epicycles,equants & deferents
•Not composed of the same materialas the Earth•Not covered by the same laws ofnature as the earth
Complexity to Simplicity3 - They were special places moving under the
control of three laws of planetary motion
Complexity to Simplicity
4 - Two universal laws of physicsdescribed the motion of the planets &much much more
Tides - Earth MoonConnection
• Tides - cyclic change in water depth– 2 high tides per day
• Primarily due to gravitational pull ofmoon– Due to inverse square law of gravity
• moon pulls hardest on the water nearestthe moon
• Moon pulls less hard at the center of theearth
• Moon pulls least on the water on the farside
23
The Inverse Square Law• Force weakens like the
square of the distance
Tides
• Sun has weaker effect on tides than moon– About half that of lunar tides
• The local ocean floor has a large effect on the size and timingof tides
