How Big is Big? Unit 1 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? How Big is Really Big? It would take 19 billion or 19000000000 or 19x109 hamburgers to reach the Moon. • The solar system - our nearest planetary This is about 20% of the hamburgers that neighborhood McDonalds has ever sold! – Size of Earth: 8,000 mile diameter – Size of Jupiter: 88,000 mile diameter Driving 80 miles per hour, it would take – Size of the Sun : 800,000 mile diameter 3000 hours or about 4 months of non-stop driving!
Relative Sizes of the Sun and Planets 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
See also http://www.troybrophy.com/projects/solarsystem/index.html
1 How Big is Big? Scientific Notation • Distance to the nearest star: 20000000000000 miles • Distance to the nearest star: 20000000000000 miles = 2x1013 • Diameter of Our Galaxy: • Diameter of Our Galaxy: 200000000000000000 miles 200000000000000000 miles = 2x1017 • Distance to Andromeda Galaxy • Distance to Andromeda Galaxy 20000000000000000000 miles = 2x1019 20000000000000000000 miles • Distance to most distant Galaxy: 100000000000000000000000 miles = 1x1023 • Distance to most distant Galaxy: • Size of helium atom: 0.0000000000001 100000000000000000000000 miles = 1x10-13 miles • Size of helium atom: 0.0000000000001 miles
Question Scientific Notation • The distance between stars in our galaxy is very large compared to the size of the stars. • Multiplication Thus, the galaxy is mostly empty space. – 2x1010 X 4x105 = (2X4)x10(10+5) =8x1015 • Why do galaxies get damaged when one • Division galaxy hits another? – 10x1010 / 5x1015 = (10/5)x10(10-15) = 2x10-5
Question Question
• The atoms in your body are even more empty than the space within our solar What daily motions do you observe of system. different celestial objects? • Why is it that when you clap your hands they do not just pass through each other?
2 Daily Motions Daily Motions Sun Stars
Solar and Sidereal Days Why is the Solar Day longer than the Sidereal Day? Coordinate system on Earth
Gainesville: 29.6510N, 82.3250W
Celestial Sphere
3 Annual Motions of the Sun
Annual Motion of Sun Annual Motion of the Stars
Annual Motions of the Stars Where are we?
• The position of a celestial pole near the horizon, tells us we must be near the Equator. Also consider the angles the star trails make with the horizon: 90 degrees.
4 Seasons Question • With the annual motion of the Earth around the • You are kidnapped, drugged and placed in a dark room Sun, we notice a cyclic pattern in the weather, for an indefinite period of time! know as the seasons. • You escape and find a radio to call for help but you don’t • Observations: know where you are! Seasons are reversed in the Northern and • Luckily, it’s a clear night. You watch the stars for while Southern Hemispheres and you see the stars rising at a 20 degree angle with •For example, you’re at the beach at Cape Cod in respect to your horizon. July, they’re skiing in New Zealand! • What can you tell your rescuers about your location? The region near the equator is hottest; poles are the coldest
The Sun’s position in the sky changes
Reason for Seasons: Reasons for the Seasons? Distance? • Predictions: • What causes this pattern? – Relation between Earth-Sun distance and • Two Possible Models: season – Distance of the Earth from the Sun? • for example, the Earth should be closest to the – Tilt of the Earth’s axis with respect to the Sun in summer Earth’s orbital plane (ecliptic) – Same season every where on Earth • since the Earth is tiny compared to the Earth- Sun distance
Reason for Seasons: Reason for Seasons: Distance? Distance? • Observations: • 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
5 Reason for the Seasons: Tilt? Reason for the Seasons: Tilt? • Predictions: The Earth’s axis of rotation is tilted by 23.5 – Summer occurs in hemisphere pointed degrees with respect to the ecliptic pole toward the Sun – Winter occurs in the hemisphere pointed away from the Sun – Therefore: Seasons are reversed in northern and southern hemisphere
Reason for the Seasons: Tilt Reason for the Seasons: Tilt
Reason for the Seasons Reason for the Seasons: Tilt
• Demonstration • Predictions match observations: – The northern hemisphere and southern hemisphere seasons are reversed – The region near the equator is hottest; poles are coldest
6 Example of the Scientific Question Method • 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 the seasons to be like? • If the Earth’s rotation axis was parallel to it’s orbital plane (ecliptic), what daily and annual effects would this have?
Motion of the Moon Moon rises ~ 50 minutes later each day
East to west in arc across sky Eastward w.r.t. stars - half degree per hour Sidereal Period - 27.3 days
Phases of the Moon Sidereal & Synodic Periods
Why does the Moon Shine? Reflected sunlight Sidereal Period: How much of the Moon is lit 27.3 days up by Sun?
Half of the Moon is Synodic Period: always lit up 29.5 days Fraction of lit surface we see from Earth - phase Synodic Period - 29.5 days
7 Phases of the Question • If the Sun sets at 6pm, when Moon does a first quarter Moon rise? • The changes in the Moon’s phase are due to changes in the angle between the Sun, Moon and the Earth
– 0 degrees : New Moon
– 90 degrees: Quarter Moon (First or Third)
– 180 degrees: Full
Eclipses A First Quarter Moon rises at noon
• A solar eclipse occurs when the Moon moves between the Earth and the Sun • A lunar eclipse occurs when the Earth moves between the Sun and the Moon and the Moon moves through the Earth’s shadow • In ancient cultures eclipses were bad omens
The Moon Moves Over the Face of the Sun The Sun is Nearly Covered
• •
8 The Diamond Ring Total Solar Eclipse
Angular Size of Sun and Moon
• The Sun and Moon have very different physical 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 An Annular Solar Eclipse • Answer: the Moon and Sun, coincidentally, have nearly the same angular size • Angular size of an object depends on two things – The physical size of the object – The distance to the object
Angular size (radians) Physical Size = Distance
9 Shadows & Eclipses Question
• Why does an annular eclipse look different?
• A total solar eclipse can seen from only a small region on the 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’s shadow moves over the Earth during a solar Paths of Solar Eclipses eclipse
Next solar eclipse visible from USA When and How Often Are Eclipses Aug. 21st 2017 Solar eclipses occur at new moon
New moon crosses ecliptic
partial, total or annular eclipse - 3 to 5 times each year
total eclipse - 0 to 3 times a year
http://sunearth.gsfc.nasa.gov/eclipse/eclipse.html
10 The Lunar Eclipse A Lunar Eclipse
• total lunar eclipse - the Moon moves completely through the Earth’s umbra • partial lunar eclipse - the Moon moves partially through the Earth’s umbra • Penumbral eclipse – the Moon passes through the penumbra but does not come in contact with umbra • Lunar eclipses are visible anywhere on the night-time side of the Earth
When & How Often? Question • Lunar eclipses occur at FULL Moon PHASE • Lunar eclipses do not occur • Why is the Moon’s surface still visible every month because the Moon’s orbital plane is tilted during a total lunar eclipse? with respect to the ecliptic – a total lunar eclipse occurs when the Moon crosses the ecliptic at full Moon – since the Earth’s shadow is much bigger than the Moon, total lunar eclipses occur more often than solar eclipses
Lunar eclipses occur 2 to 5 times per year
Motion of the Planets
• The planets are the brightest objects in the night sky (with the exception of the Moon) • Rise in the east and set in the west • Planet means “Wanderer” – The planets move slowly among the stars staying near the ecliptic – Different planets move at different speeds relative to the stars (of the visible planets, Mercury is the fastest, Saturn is the slowest) – They move in complex patterns changing their direction of motion
11 Motion of the Planets Inferior Planets • Planets generally move eastward relative to the stars • Venus and Mercury th • Planets undergo retrograde motion • Stay near the Sun on Mercury - (ca. 15 – motion relative to stars: the sky century) • slows • Are visible only near Mercury is holding a • reverses sunrise and sunset bag for commerce and • moves westward relative to stars (“morning & evening twin snakes for healing • slows again stars”) powers. • reverses again • Move away from the • resumes its general eastward motion Reigns over Virgo & Sun and then move Gemini • This motion is unique among all astronomical objects toward it • This confused & perplexed people for centuries & led people of many cultures to attribute superior powers to the planets Venus depicted in the Aztec Codex: Aztec god, Xolotl (evening star) at the crossroads of fate. Later became twin of Quetzalcoatl (morning star & supreme god)
Superior Planets Planets, Gods & Days of • The visible superior Week planets are Mars, Mars & Venus • English names for most Jupiter and Saturn Fresco from Pompeii of the days of the week (ca. 1 A.D.) come from Norse gods • Can appear far from Mars is the war-god • Tuesday : Tiwes - god & Venus, the god of the Sun but remain love. of war near the ecliptic • Wednesday: Woden - god of day & night 15th century • Thursday: Thor - god of engraving of thunder - head god days of the Saturn (ca. 18th century) - Arabic week and • Friday: Frega - goddess illustration showing agricultural their of spring activities under direction of Saturn astrological counterparts
Ancient Astronomy The Earliest Calendars • During the stone age (50,000 years ago) people first • Since pre-historic times, ancient began to leave a record in carvings and paintings. people have observed and These included: recorded the regular & cyclic – Pictures of constellations patterns in the sky – The first calendars • To explain these motions, a dual development in human thought began: – search for natural & unchanging laws – creation of mythology
14 Phases of the moon seen in cave paintings in Lascaux, France (18,000 BC)
25,000 year old Ishango bone (Congo, Africa) with possible lunar phase calendar
12 Early Calendars-Alignments Stonehenge c.a. 2800BC
• Many archaeological sites reveal alignments with prominent celestial events. • Constructed and reconstructed on Salisbury Plain in England over thousands of years • Archeoastronomy is the study and interpretation of such alignments. beginning about 2,800 BC – The reality of such alignments can be scientifically verified • Probably used as a calendar and almanac of – The cultural significance (e.g. purpose) has been lost to time solar and lunar motion – However, it is reasonable to assume that at least one purpose was to • Stones were brought from many miles away predict the seasons, possibly for agriculture, hunting, migration….. showing its importance • There are many other similar Neolithic (new Hopi sunrise stone age) sites throughout Britain calendar •Observed by a “Sun priest” at Pueblo •Used to anticipate ceremonials
S The Great Pyramid c.a. T 2600BC • Celestial bodies had great O significance in Egyptian culture and was integrated into their N religion • Pyramids are the tombs of E Egyptian Pharaohs, who were believed to be divine gods who H were connected to the stars
E • The side of the Pyramids were very accurately aligned N north-south •The passages and shafts within the Pyramids may have G been aligned with astronomical bodies (Orion and a Pole Star) E •The Pole star was called an “imperishable star” since it never sets and the spirit of the Pharaoh would journey there
The Great Pyramids Chichén Itzá c.a. 600-830AD
• The Great Pyramids of Gaza • Chichén Itzá was an important Mayan & Toltec may have been arranged in the ceremonial site on the Yucatan pattern of the constellation of • Prominent alignments with Venus & Sun rise & Orion set were made through windows in the tower of • Orion had special significance in the Caracol ancient Egypt & represented the god Osiris • Osiris is the god of birth, death & resurrection • By placing such a configuration on the ground, the god was brought to Earth • The pyramids were placed along the Nile, which may have represented the Milky Way Venus, as the morning star, was prominent in Mayan religion and represented their most important god Quetzaloatl
13 Chichén Itzá c.a. 600-830AD North America - Chaco Canyon
El Castillo - a Mayan pyramid at Chichén Itzá
• Widows in the top of pyramid are aligned with sunrises at the solstices • Chaco Canyon was home to the Anasazi People from • There are also alignments (not 900 - 1300 A.D. shown) with the sunset points of the • Anasazi means “ancient ones” in Navajo equinoxes • Atop of Fajada Butte, are 3 large stone slabs and a – step shadow projects onto northern or petroglyph know as the Sun Dagger southern staircase • The stones are aligned such that at noon on the solstices & equinoxes, 1 or more daggers of the Sun’s light strike the petroglyph key locations.
Other North American Sites Asian Alignment Sites
• City of Vijayanagara in India - 14th century • Casa Grande in Southern Arizona • Layout of city is aligned N-S & alignments with • A Hohokam pueblo built about 1000 A.D. Pole Star and other Astronomical objects • Hohokam means “those who have gone” • Windows are aligned with solar and lunar events
• Medicine Wheel in Wyoming • Located in Gao Cheng Zhen, China, this giant • Built by Native Americans of the High Planes gnomon was 1st built 2000 years ago (Han Dynasty) • Rocks laid out in a 90 foot circle • Light passes through a 40 ft • Radial spokes are aligned with the positions of high window - wall’s shadow sunrise and sunset at the solstices and are also is measured on a large aligned with the rising & setting positions of horizontal scale bright stars
C C o o n n s s t t e e Patterns Stable l Of l Over l Stars l Human a a History t t i i o o n n s s
14 Reflect the cultures & Constellations times of the people Constellations who 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
Orion the Hunter • Orion is a prominent winter constellation • Located near the Celestial Equator so it can been seen from either hemisphere • Located near the Milky Way
Orion Ursa Major & Minor Ursa Major
• Greek Mythology • Ursa Major is the most prominent northern – Orion, son of Poseidon and a great, circumpolar constellation fearless hunter • Ursa Major contains the “Big Dipper” asterism – His arrogance angered the goddess Hera who sent a scorpion to kill him • Ursa Minor contains the “Little Dipper” – The Moon god Artemis placed him in the asterism sky 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 Minor Big Dipper
15 Ursa Major & Minor Ursa Major • Two stars in the front end of the Big • Aztec - Tezcatlipoca- Peg legged god Dipper point to Polaris associated with death & the north • Greco-Roman Mythology • Hindu - the seven Rishi or primordial sages – Callisto & Zeus were lovers & had a • Chinese - chariot carrying sages son, Arcas. Hera, Zeus’ wife, was angry • Basques - 2 bullocks followed by 2 thieves, and turned Callisto into a bear. Years watched by a herdsman & his 2 servants later, Arcas was hunting & was about to kill his mother, so Zeus stepped in & • Egyptian - ox pulling a man with a threw them both into the sky. Hera still hippopotamus and alligator on his back Arab Representation wanted revenge so she made the pair • Seen as a bear in many cultures despite its continually circle the sky, never being long tail. Perhaps this is due to the notion that able to refresh themselves in the River- it prowls around the sky like a bear. Ocean that encircle the Earth.
Persian Representation
Early Views of the Cosmos Babylonians
• Ancient world pictures of Colored the cosmo wood cut by • The Babylonians were among the first French – geocentric - Earth people known to have kept astronomer astronomical records centered Flammarion – careful observers – finite - had boundary circa 1880 – kept continuous written records of • typically a shell of observations on clay tablets stars closed off – observations used for making calendars the universe & predicting celestial motions • Ancient cosmologies • Babylonian Cosmos: paid little attention to Nut, – finite cosmos celestial motions even if Egyptian – no specific shape to Earth celestial cycles were goddess of – stars attached to a shell far beyond Earth carefully observed sky, arched – Sun entered through a gate at edge of over Geb, Universe Babylonian tablet recording god of Earth astronomical information circa 550 B.C.
Ancient Views of the Cosmos • Egyptian: Early Greeks – Earth is flat – Sky is like a flat plate support by 4 mountains – Sun is carried across the sky in a boat from • Ancient Greek astronomers were the first to attempt to east to west. At night Sun is carried back to explain the workings of the heavens in a careful, the east through the Underworld systematic way using naked eye observations and • India: Egypt models – Earth is a circular disk surrounded by the ocean • Greeks enjoyed philosophy which to them meant the – great mountain in center of world attempt to understand all things in nature – Sun goes around mountain once a day • They used their highly developed mathematical skills • China: India (geometry & trigonometry) & logic to make – sky is a round dome, surrounding Earth remarkable discoveries about their universe – Earth is square – Sun travels in a big tilted circle
China
16 Aristotle & A Spherical Earth 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 2 Aristotle learned from travelers that the curved during a lunar eclipse height of the Pole star above the horizon – “The shapes that the Moon itself shows are varies as you travel from North to South of every kind -straight, gibbous, and concave • Going North: Polaris gets higher with - but in eclipses the outline is always curved: respect to the horizon and since it is the interposition of the Earth • Going South: Polaris gets lower with that makes the eclipse, the form of this line respect to the horizon will be caused by the form of the Earth’s Painting of Go far enough south -- Polaris no longer surface which is therefore spherical” - • Aristotle by Aristotle’s treatise On the Heavens visible Rembrandt ⇒Earth must be spherical!
Spherical Earth Flat Earth
Aristarchus of Samos Question (310-230 B.C.)
• Estimated relative sizes of the Moon & Earth • Aristotle also reasoned that the Earth – timed duration of lunar eclipses – compared the time it takes the Moon to enter was spherical by watching ships leave the Earth’s shadow with the time it takes the Moon to cross the Earth’s shadow port and sail off towards the horizon. • Estimated distance to Moon – What would you observed about a ship – measured angular size of Moon & compared this to the estimate of the Moon’s size relative sailing away from you if you lived on a: to Earth’s diameter • Estimated distance to Sun • Flat Earth ? – assumed Moon’s orbit was circular & uniform – measured intervals between 1st and 3rd • Spherical Earth ? quarter phases of the Moon & for 1 complete phase cycle – compared these intervals to determine the Moon-Earth - Sun angle
Aristarchus of Samos Eratosthenes (c. 200 B.C.) (310-230 B.C.) Eratosthenes estimated the Earth’s diameter, and thereby took the relative measurements of Aristarchus and placed them on an absolute scale • Estimated size of Sun – from total Solar Eclipse using relationship between angular diameter, 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 away than the Moon ⇒ He therefore concluded that the Sun, not the Earth was at the center of 77.2.200 5000 500 s0tadia stadia = the Universe 3600 Earth’s circumference
17 Hipparchus (c. 150 B.C.)
• Erected an observatory on Rhodes & built instruments to Scientific Models measure as accurately as possible the direction of objects in sky • Conception of a physical model to explain the workings of nature • compiled catalog of stellar coordinates - 850 entries is a creative act of science • discovered precession - Earth’s axis of rotation (about the • Models apply known laws of nature to explain observations celestial sphere) continually changes • Key aspects of a scientific model • refined Aristarchus’ technique to measure Moon’s size & ⇒ models explain what is seen distance ⇒ models predict observations accurately – 29.5 Earth diameters (actual distance = 30 Earth diameters) • determined length of year to within 6 minutes ⇒ simplify your understanding of nature • carefully observed motions of Moon, Sun & planets • Validity of models is tested by checking how well predictions fit the • predicted lunar eclipses to within 1 hour best & new observations • 1st to deal with the problem of parallax for solar eclipses & • Scientific models are not static but evolve when new & better predicted the paths of totality for solar eclipses observations become available • Developed a geometrical, geocentric model of the Universe
Modeling the Cosmos Modeling the Cosmos
• Key Observations to Explain • Key Observations to Explain – Motion of Sun – Motion of Stars • East to West in about 12 hours from • East to West in ~ 12 hours sunrise to sunset from star rise to star set • West to East along ecliptic ~ 10 per day • star rise is ~ 4 minutes • variation in speed along the ecliptic earlier each day • variation of length of day & height of Sun • circumpolar stars with season • stars in fixed position – Motion of Moon relative to one another • East to West in about 12 hours 25 minutes • precession from Moonrise to Moonset • yearly motion relative to • West to East within 50 of ecliptic Sun • sidereal & synodic periods
Modeling the Cosmos Newton 1642-1727 • Key Observations to Explain – Motion of Planets • Only child, posthumous son of an illiterate • East to West in ~ 12 hours from rising yeoman to setting; interval varies depending on – born prematurely - sickly as child rate of planet’s motion with respect to – raised by maternal grandmother stars – as a child he built clocks & sundials • West to East, within 70 of ecliptic – practical joker • Average speed varies along ecliptic • Trinity College, Cambridge University at 19 – fastest for Mercury – studied mathematics & astrology – slowest for Saturn – encouraged to study physics by Barrow • Variation in speed along ecliptic for • University closed in 1665 due to plague each planet – Invented calculus studied gravity, optics • Barrow resigns & gives Newton his post at • Retrograde motion from West to East Cambridge at a time specific for each planet
18 Describing Motion
• Velocity – Rate of change of position – speed & direction • Acceleration – Rate of change of velocity
Laws of Motion Laws of Motion • Law I: Law of Inertia • Law II - Force Law – A body at rest or in – The rate of change in an object’s velocity motion at a constant due to an applied force is in the same velocity along a straight direction as & proportional to the force and line remains in that state inversely proportional to the object’s mass of rest or motion unless • To have acceleration there must be a force acted on by a net outside • Force & acceleration always work in the same force direction • Takes next logical step • Given the same force, a more massive object beyond Galileo’s definition accelerates more slowly than a less massive of inertia one • Uniform motion is as natural a state for a body Force=Mass x Accel as rest F = m x a
Examples of the Second Law Question?
• Friction • A ball is attached to a string and I spin it – Hockey puck on ice vs. on a street abound my head in a circle • Impact of a bat on a baseball – Is the ball accelerating? – The bat imparts a force to the ball and – If it is accelerating what is the force? sends it flying in the opposite direction – If the string were to break what path would the ball follow?
19 Laws of Motion • Law III - Reaction Law Examples • 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
Newton Figures Out Gravity Question?
• He unified the force which makes an apple drop from a tree and the force which makes the Moon orbit the • You push a cart and it moves but you Earth – Gravity causes all objects to attract one do not appear to move. another • He intuitively figured out that the force of gravity – Why don’t you move if there is an opposite between two objects depends on only three things: and equal force pushing on you? – 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
Newton’s Law of Universal Gravitation The Inverse Square Law •Force is proportional to the masses • Force weakens like the square of the distance –Smaller mass →smaller force Mass1 x Mass2 Force ∝ Separation 2 •Force is inversely proportional to the distance between the objects –Further apart→ weaker force
Force Force Mass1 Mass2 Separation
20 Question Orbits and Gravity
• The spaceship Enterprise is orbiting the • Gravity is the force which keeps the planet Vulcan. The crew increases the planets from flying off into space – Because the Sun is much more ship’s orbital distance from the planet massive then the planets the sun controls the motion of the planets by a factor of 10. What happens to the • Gravity always pulls the planet toward gravitational force between the planet the Sun • Inertia wants to keep the planet and the ship? moving in a straight line • The balance between gravity and inertia leads to the stable orbit of a planet
The Shapes of Orbits Kepler’s 2nd Law • As a planet moves • The shape of an object’s orbit depends on its velocity toward the sun the perpendicular to the force of force of gravity gravity causes it to – A body with a small accelerate along perpendicular velocity will its orbits and it fall nearly straight in moves faster – A body with a large • As a planet moves perpendicular velocity will overcome the force of away from the sun gravity and move to a larger the force of gravity distance acts along its orbit • For closed orbits the shapes and slows it down will be ellipses
Kepler’s 3rd Law Newton’s Adaptation of Kepler’s 3rd Law • Planets with larger • Newton applied his laws of motion and gravity to derive a average distances from modified version of Kepler’s 3rd law the sun have longer periods (Mass1+Mass2) Period2 = (average distance)3 • In the solar system the mass of the sun is so large that – Since the gravitational Msun+Mplanet is almost exactly equal to Msun acceleration is less they • This law allows the determination of masses for orbiting distant objects move more slowly along there orbits – The orbits are larger
21 Newton’s Cosmology Complexity to Simplicity
• Gravity holds the solar system together – The Sun is the most massive object so its gravity dominates the solar system – The law of Universal Gravitation naturally produces elliptical orbits (Kepler’s 1st law) – The law of Universal Gravitation naturally produces Kepler’s 2nd and 3rd laws • The universe must be infinite or it would collapse
Complexity to Simplicity Complexity to Simplicity 1- They were Gods that had special power over our lives 3 - They were special places moving under the control of three laws of planetary motion 2- They were mystical bodies moving in a complex clock work universe with orbits, epicycles, equants & deferents •Not composed of the same material as the Earth •Not covered by the same laws of nature as the earth
Complexity to Simplicity Tides - Earth Moon Connection • Tides - cyclic change in water depth – 2 high tides per day • Primarily due to gravitational pull of moon – Due to inverse square law of gravity • moon pulls hardest on the water nearest the moon • Moon pulls less hard at the center of the earth 4 - Two universal laws of physics • Moon pulls least on the water on the far side described the motion of the planets & much much more
22 Tides Spring The Inverse Square Law Tides • Force weakens like the square of the distance Neap 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 timing of tides
23