1. Chapter 3 Scales and Motion in the Universe
Investigating Astronomy, Slater & Freedman

2. In this chapter you will discover…
What makes a theory scientific
The scientific revolution that changed the idea of an unmoving Earth and allowed the Earth to move
Copernicus’s argument that the planets orbit the Sun
Why the direction of motion of the planets on the celestial sphere sometimes appears to change
That Kepler’s determination of the shapes of planetary orbits depended on the careful observations of his mentor Tycho Brahe
How Isaac Newton formulated an equation to describe the force of gravity and how he thereby explained why the planets and moons remain in orbit

3. The Ancient Mystery of the Planets
Our goals for learning:
What was once so mysterious about the movement of planets in our sky?
Why did the ancient Greeks reject the real explanation for planetary motion?

4. Planets Known in Ancient Times
Mercury
difficult to see; always close to Sun in sky
Venus
very bright when visible — morning or evening “star”
Mars
noticeably red
Jupiter
very bright
Saturn
moderately bright
This slide explains what students can see of planets in the sky. 4

5. Eratosthenes and Aristarchus (310-~230 BC)
Using simple tools and basic geometry to measure:
1. the size of the Earth, Moon, and Sun
220? – 143? BC
2. the distances to the Moon and Sun
He was the first person to use the word "geography" and invented the discipline of geography as we understand it.[3] He invented a system of latitude and longitude.
He was the first person to calculate the circumference of the earth by using a measuring system using stades, or the length of stadiums during that time period (with remarkable accuracy). He was the first to calculate the tilt of the Earth's axis (also with remarkable accuracy). He may also have accurately calculated the distance from the earth to the sun and invented the leap day.[4] He also created a map of the world based on the available geographical knowledge of the era. In addition, Eratosthenes was the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy.
However, if we assume that Eratosthenes used the "Egyptian stadion" of about m, his measurement turns out to be 39,690 km, an error of less than 2%
1st heliocentric theory
Sun 18 to 20 x Moon distance
Size of sun ~ 7x earth

6. What was once so mysterious about planetary motion in our sky?
Planets usually move eastward from night to night relative to the stars.
You cannot see this motion on a single night; rather, planets rise in the east and set in the west.
The diagram at left shows Jupiter’s path with apparent retrograde motion in The photo composite shows Mars at 5-8 day intervals during the latter half of 2003.
But sometimes they go westward for a few weeks or months: retrograde motion 6

7. Time-lapse images of Mars during retrograde
Early models of the universe attempted to explain the motion of the five visible planets against the background of “fixed” stars. The main problem was that the planets do not move uniformly against the background of stars, but at times appear to stop, move backward, then move forward again. This backward motion is referred to as retrograde motion.
Time-lapse images of Mars during retrograde
Jupiter retrograde motion

8. The retrograde motion of Mars as shown in a series of images taken on the same photographic plate.

9. Explaining Apparent Retrograde Motion
Easy for us to explain: occurs when we “lap” another planet (or when Mercury or Venus lap us)
But very difficult to explain if you think the solar system is geocentric and the Earth is unmoving
In fact, ancients considered but rejected the correct explanation… 9

10. We see apparent retrograde motion when we pass by a planet in its orbit.
We also recommend that you encourage students to try the apparent retrograde motion demonstration shown in the book in Figure 2.28a, since seeing it for themselves really helps remove the mystery… 10

11. Why did the ancient Greeks reject the real explanation for planetary motion?
Their inability to observe stellar parallax was a major factor.
The Greeks new that stellar parallax should occur if Earth orbits the Sun.
You should have students witness parallax for themselves by having them hold up one finger and alternately open and close one eye.
(Note: since the Greeks thought all stars lied at the same distance on the celestial sphere, they expected to see a shift in the angular separations of stars as they viewed them from different distances, rather than parallax as shown in this diagram. But we prefer not to bother students with this subtlety unless they ask about it.) 11

12. The Greeks knew that the lack of observable parallax could mean one of two things:
Stars are so far away that stellar parallax is too small to notice with the naked eye
Earth does not orbit Sun; it is at the bottom of the universe
With rare exceptions such as Aristarchus, the Greeks rejected the correct explanation (1) because they did not think the stars could be that far away…
Thus setting the stage for the long, historical showdown between Earth-centered and Sun-centered systems.
In fact, the nearest stars have parallax angles less than 1 arcsecond, far below what the naked eye can see. Indeed, we CAN detect parallax today, offering direct proof that Earth really does go around the Sun… 12

13. The most sophisticated geocentric model was that of Ptolemy (A. D
The most sophisticated geocentric model was that of Ptolemy (A.D ) — the Ptolemaic model:
Sufficiently accurate to remain in use for 1,500 years.
Arabic translation of Ptolemy’s work named Almagest (“the greatest compilation”)
Greeks also tended to Believe that planets were living beings influencing man’s life..
Ptolemy’s book, Tetrabiblios, is the bible of astrology.
Ptolemy

14. An Earth-centered, or geocentric, model of the universe
The Ancient Greek Model
An Earth-centered, or geocentric, model of the universe

15. Ptolemy’s model used a geocentric (Earth-centered) model of the solar system in which the planets orbited the Earth indirectly by moving on epicycles which in turn orbited the earth.

16. The Ptolemaic system was an ingenious and complicated system of circular orbits centered on other circular orbits called epicycles. It remained the best model for over 1500 years (with many modifications).
Celestial sphere
Earth Centered

17. The
The assumptions for this model were commonly accepted:
1. the earth did not move
2. the earth was the center of the system
3. the stars were located at a fixed distance on a transparent celestial sphere that rotated from E to W
4. the celestial realm was unchanging, and celestial motion was perfect, i.e. circular!

19. The Marriage of Aristotle and Christianity
In the 13th century St. Thomas Aquinas blended the natural philosophy of Aristotle, which included the Ptolemaic model, with Christian beliefs.
A central, unmoving Earth fit perfectly with prevalent Christian thinking, and various scriptures where found, whose literal interpretation, seemed to agree with this model.
1 Chronicles 16:30: “He has fixed the earth firm, immovable.”
Psalm 96:10: “He has fixed the earth firm, immovable ...”
Psalm 104:5: “Thou didst fix the earth on its foundation so that it never can be shaken.”
Isaiah 45:18: “...who made the earth and fashioned it, and himself fixed it fast...”

20. Timeline of Ancient Astronomy

21. Ptolemy’s system worked well in general detail
Ptolemy’s system worked well in general detail. It was used to create tables predicting the occurrence of astronomical events....
eclipses
conjunctions
etc.
Over several hundred years, small errors in the tables accumulated to produce large error in the timing of events - as much as a month by 1200 AD

22. A major revision was done in 1250 by a group of scholars under King Alfonso of Spain. Ptolemaic system was modified to include deferents (off center circles).
They produced the Alfonsine Tables
By 1500 even these tables were in error by several hours and even days in some cases

23. Epicycle with deferent
center of epicycle

24. Copernicus, a contemporary of Columbus, worked 40 years on a heliocentric—sun-centered—model for two reasons:
Ptolemy’s predicted positions for celestial objects had become less accurate over time.
(2) The Ptolemaic model was not aesthetically pleasing enough. He wanted to restore perfect” or circular motion and get rid of off-center circles!
Nicolaus Copernicus (1473–1543)
Copernicus, the youngest of four children, was born in Torun, Poland. He pursued his higher education in Italy, where he received a doctorate in canon law and studied medicine. Copernicus developed a heliocentric theory of the known universe and just before his death in 1543 published this work under the title De Revolutionibus Orbium Coelestium

25. Because both models (Ptolemaic & Copernican) were based on the assumption that the planets move at constant speed, Copernicus was forced to add small epicycles of his own to improve accuracy.
Copernicus would not abandon the circle as the preferred planetary orbit because he thought circles are the best representation of the perfect motions of the heavens.

26. Advantages of Copernican System:
Simpler! [not more accurate!]
simple explanation of retrograde motion
explained the phases of Venus
explained why Mercury & Venus always close to the sun
Using trigonometry was able to calculate the relative distances to all visible planets

27. Timeline of Renaissance Astronomy

28. But What about the Scriptural Evidence for the Geocentric Model?
As more and more evidence began to build which indicated the correctness of Copernicus’ model, faithful Christians had to ask some fundamental questions about their interpretation of scripture.
By the end of the 17th century, most Christians had come to accept the heliocentric model.
These Christians had to make adjustments to their interpretation of certain scriptures: the Earth being “fixed” must be interpreted differently.
Make an ellipse on the board using two suction cups.
Describe the law of equal areas using this ellipse.
Write out the equation for the third law.

29. The basic scriptural re-interpretation typically involved asking the question, “What is the scripture talking about in the verses interpreted previously as a fixed Earth”?
The re-examination of scripture continues even today as we seek the message of scripture that God intended to deliver – which we have discovered is almost never scientific information.

30. Comparing The Two Models
There were strong argument against Copernican idea of a moving earth:
Inertia-if earth is moving, why don’t objects thrown upward fall behind as the earth rotates under the object?
Parallax-if earth moves, one should see stellar parallaxes (stars seem to move as viewed from different locations) 9

31. Parallax is the apparent shifting of nearby objects with respect to distant ones as the position of the observer changes.
Both the Copernican model and the Ptolemaic model held that all stars are at the same distance from the Earth.

32. Celestial Sphere 10

33. Stellar parallax is quite small- 0
Stellar parallax is quite small arcseconds for largest shift detected — because the stars are so far away from us.
Stellar parallax, the apparent annual shifting of nearby stars with respect to background stars, was not observed until 1838. 11

34. Stellar parallaxes prove the Earth moves, which supports the Copernican model and discredits the Ptolemaic model.
Had Copernicus known of stellar parallaxes his model could have accounted for them and even predicted their existence. 12 12

35. The Copernican Model had good Predictive Power
A good model (or theory) will make verifiable predictions that might allow the the theory to be disproved.
Using the Astronomical Unit (AU)—the average distance between Earth and Sun— Copernicus predicted with amazing accuracy the Sun-to-planet distances for the 5 planets visible from Earth in the 1500s. 13

36. Planetary Distances in AU
Copernicus Value Actual Value
Mercury
Venus
Earth
Mars
Jupiter
Saturn

37. The Copernican model was more aesthetic since it could explain the motions of Mercury and Venus without resorting to special rules needed by the Ptolemaic model.
Copernicus offered a simpler explanation for retrograde motion that required no use of epicycles. 16 16

39. Copernicus, who died in 1543 just as his book De Revolutionibus was published, started such an upheaval in people’s thinking that the word “revolution” took on a second meaning that is so familiar to us today.
Tycho Brahe
Tycho was born 3 years after Copernicus died. 17 17

40. Tycho Brahe
Tycho built the largest and most accurate naked-eye instruments yet constructed.
He could measure angles to within 0.1º, close to the limit the human eye can observe.
Tycho Brahe (1546–1601)
Tycho (depicted within the portrait of Kepler) was born to nobility in the Danish city of Knudstrup, which is now part of Sweden. At age 20 he lost part of his nose in a duel and wore a metal replacement thereafter. In 1576 the Danish king Frederick II built Tycho an astronomical observatory that Tycho
named Uraniborg (after Urania, Greek muse of astronomy). Tycho rejected both Copernicus’s heliocentric theory and the Ptolemaic geocentric system. He devised a halfway theory called the Tychonic system. According to Tycho’s theory, Earth is stationary, with the Sun and Moon revolving around it, while all the other planets revolve around the Sun. Tycho died in 1601 18 18

41. Tycho wanted to correct the tables
He not only made careful measurements, but he recorded the accuracy of each measurement.
1563 close conjunction of Jupiter & Saturn. Alfonsine tables were off by a month, while Copernican tables were off by several days.
Tycho wanted to correct the tables 19 19

42. Woodcut of Tycho
Silver nosepiece is visible in the picture
Tycho lost the tip of his nose in a duel at age 20 over a question in math.

43. 11/11/1572 Nova appeared in the sky and was closely observed by Brahe: he observed....
a. no apparent parallax, therefore the nova was not inside celestial sphere
b. thus an obvious change in the unchanging celestial sphere
Tycho writings about the Nova gained the attention/approval of Frederick, king of Denmark who built Tycho the world’s best observatory (Uraniborg) on island of Ven

44. Tycho’s supernova today
Woodcut of Tycho’s Stella Noveau

45. Woodcut of the inside of Brahe’s observatory
Blaeu ´s Atlas , 1663
Stjerneborg, 1584, partly underground

46. Aerial view of site of Uraniborg on the Island Ven

47. Sweden
Denmark
Tenant farmers had to do day jobs for the mansion they belonged to. In the 1500s, noblemen had increased their power, and the large estates had expanded. The day job system had increased continuously, and could be very demanding. Tenant farmers were not authorised to sell their own produce without first offering them to their masters. The master also had the right to punish his farmers. The island of Ven had never been under the reign of any nobleman. The Ven farmers had avoided the day job system. They saw themselves as freeholders and answered directly to the king. When Tycho Brahe was awardet the island of Ven (and everyone who lived there) in 1576, this was a major change for the peasants. The day job system was introduced, and Tycho's building projects demanded very large day jobs from the approximately 40 farmers that were living on the island. Many of the farmers therefore left Ven and went elsewhere. In a letter dated 1578, the king prohibited farmers from leaving the island without Tycho Brahe's consent. The work for those who stayed would be even harder. If anyone breached the prohibition, Tycho was allowed to punish him without mercy.
A few years later, the farmers went to the king, complaining that Tycho gave them too much work and other tasks they felt were not in accordance with the contents of the letter of endowment.
The king decided to check the circumstances, and as a result, an agreement was drawn up between Tycho Brahe and the Ven farmers, in Every half farm should carry out two day jobs per week, from sunrise to sunset. If you did not appear before 10am, 11am or 12 noon, only half a day was counted. The farmer then had to do the second half of the day job the following day, and also pay a disobedience fee to his master, unless he had good reason. Anyone picking hazelnuts, apples or chopped wood without permission was also punished. In the document, it is stated that the farmers on Ven did see themselves as freeholders, but there were no letters or privileges that proved this. Therefore, their farms would from now on be treated as other farms belonging to the Crown, and the farmers were not considered freeholders.
The farmers' goods should mainly be offered to Tycho Brahe, but to the same price they would be able to have in the nearest market town. Apparently, Tycho had forced the farmers to sell produce at too low prices. Thereby the relations between Tycho Brahe and the farmers were settled, but the problems with dissatisfied farmers continued. In 1597, the king finally arranged a royal commission to investigate the complaints from the farmers again. They argued that their situation had become one of great poverty and misery because of all the work they had to carry out for Tycho. But when the commission appeared in Ven, Tycho and his family had already left the island. This event was one of many reasons why he then left Denmark for good.
Poland

48. His commission was to revise Alfonsine tables
After Frederick’s death, Tycho fell out of favor and thus disassembled his observatory and moved it to Prague under HRE Rudolph II
Castle Benatky
His commission was to revise Alfonsine tables
Hired several mathematicians to handle the drudgery of the computations, one of whom was Johannes Kepler

49. Tycho’s model

50. Tycho Brahe died 24th October 1601 of a urinary bladder infection that he may have tried to cure himself, with a medicine containing mercury
Teyn Church in Prague where Tycho was buried
Body exhumed in 1901 to determine cause of death
1996 Particle Induced X-ray Emission (PIXE) showed recent high levels of Mercury in Brahe’s hair samples implying mercury poisoning.

51. Johannes Kepler 1610 painting by unknown artist Born 1571
Died 1630 (58)
Johannes Kepler

52. Kepler was a sickly child of a protestant family living in predominantly catholic area.
Got scholarship to become Lutheran minister, but liked math better. Had influential teacher who was a Copernican.
Became Math teacher at Graz (not very good, only had 1 student last year)
1595 wrote almanac with astronomical & astrological weather predictions. They were correct and got reputation as astrologer
Kepler was educated in Germany, where he spent three years studying mathematics, philosophy, and theology. In 1596, Kepler published a booklet in which he attempted to mathematically predict the planetary orbits. Although his theory was altogether wrong, its boldness and originality attracted the attention of Tycho Brahe, whose staff Kepler joined in 1600

53. Tycho’s best data had been gathered for Mars.
In 1600, a year before Tycho died, Kepler accepted a position as Tycho’s assistant, working on calculations
Tycho’s best data had been gathered for Mars.
Based on circles and epicycles Kepler’s best Copernican model for Mars matched Tycho’s data to within 0.13º (8 arcminutes) [less than the accuracy of Tycho’s measurements]. 20

54. When Brahe died in 1601, Kepler got his job, and after a fight with Brahe’s widow, got possession of Brahe’s notebooks of data
The error in the position of Mars exceeded the error in Tycho’s measurements, which continued to bothered Kepler. Could get agreement within 8 arcmin, > Tycho data had a maximum error of 6 arcmin.
Kepler was lifelong mystic, enamored with numbers (we would say a numerologist)

55. In possession of Brahe’s data, Kepler spent more than 5 years pouring over the details, trying to reconcile the error.
Kepler’s persistence finally led him to abandon circles and try other shapes. The shape that worked for Mars and all other planets was the ellipse. 21

56. The Ellipse
The ellipse is a geometrical shape every point of which is the same total distance from two fixed points (the foci).
Eccentricity is the distance between the foci and its center divided by half the longest distance across (semi-major axis). 22

57. If the axes are equal, then e=0 and the ellipse becomes a circle.
The eccentricity of the ellipse measures the difference between the major and minor axes. e = c/a
sun
focus
If the axes are equal, then e=0 and the ellipse becomes a circle.
minor axis
All the planet orbits have e ~ 0.1 except Pluto (.248) and Mercury (.206)
major axis c
planet
focus
The center of force occupies one focus of the ellipse, while the other focus is usually empty a

60. Kepler also discovered what we call the Law of Equal Areas which showed that planets did NOT move at constant speeds in their orbits

61. Kepler’s 2nd Law – the law of equal areas
1 month
1 month

62. All of his discoveries are called Kepler’s 3 Laws of Motion
After more than 10 years further work, Kepler wrote a rather obscure and mystical book that showed a relationship between a planet’s orbit radius (a in AU) and its orbital period (P in years)
P2 = a3
All of his discoveries are called Kepler’s 3 Laws of Motion

64. In addition to the Laws of Motion, Kepler is also one of the 1st to try to give a physical reason for planets orbiting the sun. He thought that some type of magnetic force was responsible

65. Galileo Galilei
Born in Italy (1564), a contemporary of Copernicus. He was a Prof. at Padua in the Venetian Republic, & a Prof. at the University of Florence
Strong believer in experimentation
Strong, abrasive personality, popular writer who wrote in common Italian rather than Latin. He was very free to criticize and ridicule any who differed with him on any matter.

66. Galileo Galilei and the Telescope
Galileo built his first telescope in 1609, shortly after hearing about telescopes being constructed in the Netherlands.
Galileo was perhaps the first person to use a telescope to systematically study the sky and record his observations. 1 1

67. Galileo made 5 important observations:
Mountains and valleys on the Moon
Sunspots
More stars than can be observed with the naked eye
Four moons orbiting Jupiter
Complete cycle of phases of Venus 2

68. Though Galileo’s first three observations do not disprove the geocentric theory, they cast doubt on the the assumption of perfection in the heavens.
The existence of stars too dim to be seen with the naked eye also cast doubt on the the fact that stars were all the same. 3

69. In 1610 Galileo discovered that Jupiter had four satellites of its own, now known as the Galilean moons of Jupiter.
Jupiter and its orbiting moons contradicted the Ptolemaic notions that the Earth is the center of all things and that if the Earth moved it would leave behind its Moon. 4

70. In 1610, Galileo discovered four “stars” that move back and forth across Jupiter. He concluded that they are four moons that orbit Jupiter just as our Moon orbits Earth. These observations made
by Jesuits in 1620 of Jupiter and its four visible moons.

71. Galileo observed that Venus goes through a full set of phases: full, gibbous, quarter, crescent.
Venus’s full set of phases can be explained by the heliocentric theory.
The Ptolemaic theory predicts that Venus will always appear in a crescent phase, which is not borne out by the observations. 5

72. Venus’ Phases in Ptolemy’s Model

73. Galileo is also the first person to do any systematic study of motion and was the first person to understand the concept of inertia
Galileo did a wide variety of experiments, even attempting to measure the speed of light by using lanterns on distant hilltops (concl. either infinite or too large to measure)

74. Isaac Newton
Galileo is credited with setting the standard for studying nature through reliance on observation and experimentation to test hypotheses.
The year Galileo died—1642—is the year Isaac Newton was born.
Newton took the work of Galileo and Kepler and created an expansive theory of motion. 6 6

75. Isaac Newton (1642–1727)
Isaac Newton was undeniably one of the greatest/most influential scientists that ever lived.
Very religious man who believed the order in the universe was representative of God
Newton delighted in constructing mechanical devices, such as sundials, model windmills, a water clock, and a mechanical carriage. He received a bachelor’s degree in 1665 from the University of Cambridge. While there, he
began developing the mathematics that later became calculus (developed independently by the German Gottfried Leibniz). While pursuing experiments in optics, Newton constructed a
reflecting telescope and also discovered that white light is actually a mixture of all colors. His major work on forces and gravitation was the tome Philosophiae Naturalis Principia Mathematica, which appeared in In 1704, Newton published his second great treatise,
Opticks, in which he described his experiments and theories about light and color. Upon his death in 1727, Newton was buried in Westminster Abbey, the first scientist to be so honored.

76. Very cautious person who had to be persuaded by his friends to publish ANY of his work
plague in London, Newton left the university and went to his country home for a year. While there he:
developed basic ideas of mechanics
basic concepts of gravity
beginning ideas on light and optics
Work during the plague years
When Newton received the bachelor’s degree in April 1665, the most remarkable undergraduate career in the history of university education had passed unrecognized. On his own, without formal guidance, he had sought out the new philosophy and the new mathematics and made them his own, but he had confined the progress of his studies to his notebooks. Then, in 1665, the plague closed the university, and for most of the following two years he was forced to stay at his home, contemplating at leisure what he had learned. During the plague years Newton laid the foundations of the calculus and extended an earlier insight into an essay, “Of Colours,” which contains most of the ideas elaborated in his Opticks. It was during this time that he examined the elements ofcircular motion and, applying his analysis to the Moon and the planets, derived the inverse square relation that the radially directed force acting on a planet decreases with the square of its distance from the Sun—which was later crucial to the law of universal gravitation. The world heard nothing of these discoveries.

77. 1687 published Principia ( perhaps the most influential scientific book ever published)
In it he explained the motion of the planets, comets using his law of gravity and his 3 Laws of Motion. He also derived Kepler’s Laws

78. Could not solve the problem of gravitational attraction on a planet so he invented Calculus to solve it
Published a book Optiks giving the basic ideas of geometrical optics, light, and color, including the fact that white light is made up of different colors

79. To understand the motion of objects under the influence of gravity, we use the ideas of Isaac Newton and his 3 Laws of motion.
The first concept needed is the idea of INERTIA. This was the concept not understood by ancient observers in their arguments against a moving earth “toss object in the air, if the earth is moving then the object will fall behind its launch point...”

80. While not the first person to properly conceive of inertia, Galileo was the first to arrive at his views based on actual experiments he performed.
Galileo’s work provided the basis for Newton’s formulation of the Law of Inertia.

81. Inertia is the property of an object whereby it tends to maintain whatever velocity it has. The inertia of an object is determined by it MASS.
Newton’s First Law (Law of Inertia): Unless an object is acted upon by a net, outside force, the object will maintain a constant speed in a straight line. Note: a speed of zero (rest) is a constant speed. 7 7

82. Block continues to move when the cart suddenly stops due to the inertia of the block!

83. Newton’s Second Law says that the acceleration of an object depends on the force applied to it and on its mass!
Acceleration is inversely proportional to the mass being accelerated.
What does “inversely proportional” mean?
As the mass gets bigger, the acceleration gets smaller 10 10

84. An object at rest has a speed of zero.
If an objects speed or direction of motion changes (like the block) - we say that the object is accelerated!
Acceleration is a measure of how rapidly the speed or direction of motion of an object is changing.
An object at rest has a speed of zero.
Newton’s first law says that a force is needed to change the speed and/or direction of an object’s motion. 8 8

85. No force means no acceleration!
Car remains at rest (law of inertia)
V=0 F
If an unbalanced force is applied, the car accelerates and its speed increases >0
V>0
V>>0 F
The longer the force acts, the longer the car accelerates and the faster it goes F
V>>>0

86. An Important Digression — Mass & Weight
Mass is the quantity of inertia an object has. Produced by particles from which it is made
Mass is NOT volume or weight.
Weight is the force of gravity.
The international (SI) unit of mass is the kilogram.
A kilogram on Earth weighs about 2.2 pounds. 9 9

87. Acceleration = force divided by mass
In symbols A = F/m
Often as Force = mass X acceleration or F = mA
If the left side = 0 then right side is also = 0
Thus when the net force is zero, there is no acceleration.

88. A = F / m
if the force is large then Acceleration is large:
A = F m
if the mass is large then acceleration is small

89. Newton’s Third Law
Third Law: When object X exerts a force on object Y, then object Y exerts an equal and opposite force back on X. X Y
X pushes on Y
Y pushes on X X Y
The forces are equal in size and opposite in direction 11 11

90. The Third Law is sometimes stated as “For every action there is an opposite and equal reaction,” but the first statement is more precise in terms of physical forces.
REMEMBER: The two forces ALWAYS act on DIFFERENT objects.
Also there is no such thing as a single force!!

91. Motion in a Circle
Motion of an object in a circle at constant speed (uniform circular motion) is an example of acceleration by changing direction.
Centripetal (“center-seeking”) force is the force directed toward the center of the curve along which the object is moving. 13 13

92. The most common force to discuss while studying the motion of planets, comets, stars, galaxies, and other such objects (including balls, etc. on the Earth) is GRAVITY.

93. As the Earth orbits the sun, the force of gravitational attraction from the Sun pulls on the Earth
Velocity at a and velocity at b are NOT the same – have diff. directions a
velocity b
velocity
The Earth is accelerated continuously in its orbit!

94. The Law of Universal Gravitation
This law states that between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects. 14 14

95. In equation form:
G is a constant, m1 and m2 are the masses, and d is the distance between their centers.

96. Two objects that have mass are attracted to each other.F1 F2
F1 & F2 are equal except for direction!

97. Weight is the gravitational force between an object and the planetary body on which the object is located.
mass
Weight : pull of planet on object
W = mg
Earth
mass

98. Pull of gravity on a mass on Earth – known as weight
Points approx. toward the center of the Earth or what we call DOWN

99. According to Newton, gravity…. --- makes objects fall to Earth
According to Newton, gravity… makes objects fall to Earth keeps the Moon in orbit around the Earth keeps the planets in orbit around the Sun
He could therefore explain the planets’ motions and why Kepler’s laws worked.

100. The pull of the Earth’s gravity could be tied in with the orbit of satellites (such as the Moon) around the Earth.
Newton made an argument to show this that is now known as Newton’s Cannon!

101. Applet

102. Newton’s Laws and Kepler’s Laws
Kepler’s first law—the planets move in elliptical orbits—can be derived from Newton’s laws but requires calculus.
Kepler’s second law—planets sweep out equal areas in equal times—can also be derived from Newton’s laws. As planets orbit the Sun they show a change in both speed and direction. 20 20

103. Newton and Kepler’s 3rd Law
Newton showed mathematically that Kepler’s third law—the period-distance relationship—derives from the inverse square law for gravitation.
Newton modified Kepler’s third law, showing that mass is an important factor. a3
Where a is in meters and p is in seconds k is a constant and M is mass in kilograms
= k M p2 21 21

104. The Center of Mass Seesaw principle
Center of mass is the average location of the various masses in a system, weighted according to how far each is from that point. The CM is sometimes called the center of gravity.
Barycenter is the center of mass of two astronomical objects revolving around one another. 22 22

105. The barycenter for the Earth-Moon system is inside the Earth, 4641 km from its center and inside its 6378 km radius
The location of the center of mass of the Earth-Moon system was determined by observing parallax of nearby planets due to the Earth’s motion as the Moon went around. 23 23

106. Using Newton’s Laws of Motion allows us to understand the general features of satellite motion, such as the moon, or any other orbiting satellite.
Careful measurements of the orbits and periods of satellites (natural and man-made) allow one to accurately determine the mass of the body being orbited.

107. Concept checks!
If the 815-kg unmanned Voyager 2 interplanetary space probe was traveling at 60,000 km per hour without any rocket engines firing in 2006, how fast will it be moving in 2012, still without engines?
Why is the mass of Pluto the least accurately know planetary mass?
If a door on the International Space Station requires 100 newtons of force to be pushed open, and, according to Newton’s third law, the door pushes back on an astronaut with an equal but opposite force of 100 newtons, why is it that an astronaut can successfully open the door?

108. How much does the gravitational force of attraction change between two asteroids if the two asteroids drift three times closer together?
What keeps the International Space Station from crashing into Earth when it has no rocket engines constantly pushing it around Earth?

109. One of the crowning achievements of Newton’s gravitational law was the discovery of Neptune.
After it’s accidental discovery, the orbit of Uranus was analyzed using Newton’s Laws and the Law of Gravity.

110. Despite careful measurements, the observed orbit did not match the one predicted by Newton’s Laws.
Uranus & 3 moons

111. The discrepancies were attributed to another unknown mass orbiting outside Uranus’ orbit. Using these results, the mass and location of the unknown object was predicted.
Neptune & 1 moon
Assuming Newton was correct, the discrepancies could only be explained by another planet, about the same size, orbiting outside of the orbit of Uranus.

112. Gravity Works at All Scales
This figure shows a few of the effects of gravity here on Earth, in the solar system, in our Milky Way Galaxy, and beyond.

113. The Importance of Newton’s Laws
Kepler’s laws can be derived from them.
They explain tides and precession.
Their use predicted the existence of the planet Neptune.
They provide a way to measure things quantitatively and predict the motion of things.
Newton laid the foundation for our concept of the Universe. 32 32

114. Beyond Newton: How Science Progresses
Newton proposed that inertial mass was equivalent to gravitational mass, but he had no idea why. Subsequent measurements confirmed this coincidence.
Einstein in his General Theory of Relativity showed mathematically that the two types of masses are indeed equivalent. 33 33

115. This coincidence was one of the seeds leading Einstein to the development of the General Theory of Relativity

116. The End
Next, Chpt. 4
Exploring Our Evolving Solar System