The Solar System

1. The Solar System The Scientific Revolution

2. How Galileo’s pioneering observations with a telescope supported a Sun-centered model. How Galileo’s experimental investigations of motion furthered the emergence of the scientific method. How Newton’s described the motion of all physical objects, including the planets, in the form of mathematical laws — the 3 Laws of Motion and the Law of Universal Gravitation. Why planets stay in their orbits and don’t fall into the Sun. The emergence of the scientific method as a way to describe the behavior of all natural phenomena. Coming up in this lecture

3. Galileo Galilei (1564 – 1642) • Discovered empirical mathematical rules that described the motion of objects from data derived from experimental investigations. • Used the telescope to observe the heavens, whose results strongly supported a heliocentric model of the solar system. The Father of Science

4. Investigation of Motion Which ball hits the ground first? All objects fall to the ground with the same acceleration (g = 9.8 m/s2) — regardless of their weight!

5. Galileo’s Inclined Plane • Rolled balls down inclined plane to investigate accelerated motion. • Measure distances and time to travel those distances. • Question: How did Galileo measure time — clearly an hourglass wouldn’t work!

6. Galileo’s Data s = ½ g t2 s = t2 Question: What happens if angle of inclined plane is increased … suppose it’s increased to 900? If (s, t) are measured in conventional SI units (m. s), then For free fall, s = 4.9 t2— Units of the constantare m / s2 Newton later shows that the constant 4.9 m / s2 is ½ g, where g is the ‘acceleration of gravity! Thus, g = 9.8 m / s2.

7. Parabolic Motion of Projectiles x y y = k x2

8. Invention of the Telescope By 1450, the ingredients for making a telescope were in place! The telescope was unveiled in 1608 in the Netherlands. Hans Lippershey applied for a patent. Deemed too easy to copy and therefore un-patentable! In 1609, Galileo heard of the invention and quickly built several. He presented an 8 power telescope to the Venetian Senate in August and trained a 20 power instrument on the heavens in October. Aleaiactaest!

9. Galileo’s Discoveries • Sunspots Galileo’s Telescope • Craters and mountains on the Moon • Saturn has ‘ears’ • Moons of Jupiter • Phases of Venus • Merit more discussion! • Planets are disks, not points Jupiter • Stars not confined to thin shell

10. Why Galileo ‘Held His Tongue’ • On the morning of February 19, 1600 an event that was a harbinger of things to come ushered in the new century. Several hooded members of a group known as the Company of Mercy and Pity took a young man from the Nona Tower, a secular prison in Rome, separate from the “holy” one of Castel Sant'Angelo, put him in a wooden wagon and hauled him over to the Campo deiFiori, the Square of Flowers. • Along the way, Jesuit and Dominican priests mumbled their imprecations to the young man in an attempt to elicit a last minute recantation of his beliefs, lest he forever be damned as a heretic. • It would have been difficult for him to respond, even if he desired to do so in the affirmative—which he did not—since his jaw had been clamped shut with an iron gag, one long spike that pierced his tongue and another that had been driven through his lower jaw and upper palate. • Perhaps the priests, afraid of the impotence of their supplications to get the young man to recant, were even more afraid that he would use his tongue to incite the crowd of onlookers along the way. • As the wagon passed, bystanders asked who the young man was. “A Lutheran”, the priests replied, in those days a synonym for anyone branded a heretic. The young man was no Lutheran; he was a Dominican himself, a member of the group that would soon execute him for his beliefs. He had been charged with eight offenses. Upon several he had wavered. • On one, he stood firm. He believed in the infinity of the cosmos and the plurality of habitable worlds. He believed that God was infinite and so was his handiwork. He believed that the Earth traveled around the Sun and that there were many systems like it that contained other living creations of God. • The young man was stripped naked and a crucifix pressed to his face. He turned away, in obvious disgust., sending shrieks through the crowd. Then, Giordano Bruno was burned, the priests chanting their litanies while the crowd looked on. Statue of Giordano Bruno in Campo Dei Fiori

11. In 1610, Galileo discovered 4 ‘stars’ that orbit Jupiter. They are now called the ‘Galilean Moons’. Galileo named them the ‘Medicean stars’. Can you guess why? Compare drawing #13 with the next figure!

12. Amateur’s Image of Jupiter with Small Telescope • Implication: • Another object in Solar System that serves as the center about which other objects orbit. • Jupiter is moving. It does not leave its moons behind, refuting Aristotle’s argument that our Moon would get left behind if the Earth were in motion!

13. Position of Sun, Moon & Planets — Heliocentric Model What would the sky look like at sunset?

14. Ecliptic at Sunset Moon at 1st Quarter Jupiter Venus Mars Sun

15. Position of Sun, Moon & Planets — Geocentric Model What would the sky look like at sunset?

16. Ecliptic at Sunset Moon at 1st Quarter Jupiter Venus What’s wrong with this picture? Mars Sun

17. Phases of Venus — Heliocentric Model

18. Galileo’s Observation of Venus α = angular diameter of Venus in arcsec.

19. Ptolemaic Model

20. Ptolemaic Model

21. Ecliptic at Sunset Moon at 1st Quarter Jupiter Venus What’s wrong with this picture? Venus is in crescent phase at maximum elongation Mars Sun

22. Note: Venus can be on other side of Sun!

23. Heliocentric Orbit of Earth & Mars Copy vectors to Sun (→) and vectors to Mars (→) Center them on Earth and see what happens! Ptolemy’s geocentric model is ruled out by the observation of the phases of Venus. But not Tycho’s!

24. Motion of Sun as Seen from Earth Vectors pointing to Sun from a moving Earth! Center the vectors pointing to Sun on an Earth at rest! It appears that the Sun orbits the Earth!

25. Motion of Mars as Seen from Earth As seen from Earth, Mars (and the other planets) appear to travel in orbits with retrograde loops. The orbit of the Sun is the deferent and the Sun is the center of planet epicycles. How do you prove that this ‘complicated’ geocentric motion is not the actual motion?

26. Galileo’s Recantation 22-Jun-1633 “I, Galileo, son of the late Vincenzo Galilei, Florentine, aged seventy years, arraigned before this tribunal, and kneeling before you, Most Eminent and Reverend Lord Cardinals, Inquisitors-General against heretical depravity throughout the entire Christian commonwealth, having before my eyes and touching with my hands, the Holy Gospels, swear that I have always believed, do believe, and by God's help will in  the future believe, all that is held, preached, and taught by the Holy Catholic and Apostolic Church. But whereas -- after an injunction had been judicially intimated to me by this Holy Office, to the effect that I must altogether abandon the false opinion that the sun is the center of the world and immovable, and that the earth is not the center of the world, and moves, and that I must not hold, defend, or teach in any way whatsoever, verbally or in writing, the said false doctrine…

27. and after it had been notified to me that the said doctrine was contrary to Holy Scripture -- I wrote and printed a book in which I discuss this new doctrine already condemned, and adduce arguments of great cogency in its favor, without presenting any solution of these, and for this reason I have been pronounced by the Holy Office to be vehemently suspected of heresy, that is to say, of having held and believed that the Sun is the center of the world and immovable, and that the earth is not the center and moves. Therefore, desiring to remove from the minds of your Eminences, and of all faithful Christians, this vehement suspicion, justly conceived against me, with sincere heart and unfeigned faith I abjure, curse, and detest the aforesaid errors and heresies, and generally every other error, heresy,  and sect whatsoever contrary to the said Holy Church …”

28. Question What was the real reason that Galileo was brought before the inquisition and tried for heresy? Galileo dropped a ball off the Leaning Tower of Pisa which struck Pope Barberini on the head and killed him. His telescopic observations of Venus proved conclusively that the Earth orbited the Sun. Galileo demonstrated that science offered a better way to explain observations of nature than did church authority. Galileo’s demonstration that projectiles travelled in parabolic paths gave the Medicis of Florence unfair advantage in battles with the hierarchy in Rome.

29. Sir Isaac Newton (1642 – 1727) • 3 Laws of Motion • Law of Universal Gravitation • Invented Calculus • Optics and the Newtonian telescope • 1687- The Principia • Arguably- the greatest scientific book ever written! "Nature and nature's laws lay hid in the night God said “Let Newton be!”—and all was light.” Alexander Pope, Epitaph for Isaac Newton

30. Newton’s 3 Laws of Motion • Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it. • The change of motion is proportional to the motive force impressed; and is made in the direction of the line in which that force is impressed. • To every action there is always imposed an equal reaction; or the mutual actions of two bodies are each other always equal, and directed to contrary parts.

31. Newton’s 3 Laws of Motion Law of Inertia F = ma Action - Reaction No force … ball keeps moving at same speed Wall exerts force on ball and changes its motion. F Ball exerts equal and opposite force on wall. -F F

32. Newton at home in Woolsthorpe during the Great Plague, 1665-1667 — realizes that the force that causes apple to fall towards Earth also causes Moon to fall towards Earth! Eureka! Gravity!

33. A ‘Falling’ Projectile v = 50 ft/sec 16 ft 16 ft They both fall at the same rate g! A projectile is shot at a speed of v = 50 ft/sec at a target 50 ft away. Both projectile and target are 16 ft above the ground. At the moment the projectile is fired, the target is dropped and falls freely towards the ground. Will the projectile hit the target?

34. The Moon is ‘Falling’ Toward Earth! g a • The force that causes ‘apples to fall towards Earth’ also causes all other ‘nearby’ objects to fall towards Earth — with acceleration g. • Objects further away, such as the Moon, also fall towards Earth, but it’s so far away that the strength of the force and resultant acceleration a is much weaker!

35. Centripetal Force Bounces at 2 points

36. Centripetal Force Bounces at 4 points

37. Centripetal Force Bounces at 8 points

38. Centripetal Force A constant inward force, called a ‘centripetal force, continually re-directs the motion but does not change the speed. The inward centripetal force causes the ball to accelerate inward. This inward acceleration is called centripetal acceleration. Newton calculated its value — v2 / R where v is the speed of the ball and R is the radius of the circle. ‘Bounces’ at ∞ # of points

39. A High Speed Projectile A ball dropped from 16 ft, hits the ground 1 sec later. 16 ft Projectiles shot at increasingly greater speeds still hit the ground 1 sec later. What happens if projectile is shot at 5 miles/sec?

40. Ball falls 16 ft every 5 miles of travel … But so does the Earth! Ball is in orbit 16 ft above ground! There must be a centripetal force that causes the centripetal acceleration — g! There is … it’s called ‘Universal Gravitation’!

41. Orbits Depend on Speed of Projectile

42. Centripetal Acceleration of Moon • The centripetal acceleration of a falling ball or a ball in orbit near the surface of the Earth is g. The ball is 1 RE away from Earth’s center and it falls 16 ft in 1 sec. • What is the centripetal acceleration, a, of the Moon, which is 60REfrom Earth’s center? g a 60RE RE • Newton calculated that the Moon falls 16 ft in 1 minute!

43. Gravitational Force on the Moon • Galileo showed that the distance an object falls is given by the formula s = ½ g t2. 16 ft in 1 sec • Newton applied it to the Moon…s = ½ a t2. • The Moon and the ball fall the same distance, 16 ft, but in different times. • s = ½ g (1 sec)2 = ½ a (1 min)2. • 1 min = 60 sec. • ½ g (1 sec)2 = ½ a (60 sec)2 • a = g / 602 • The acceleration of the Moon is weaker by 602. It is 60 times further away from the center of Earth, so Newton hypothesized • … that the force of gravity weakens by the square of the distance! Falling ball 16 ft in 1 min Moon in orbit

44. The Law of Universal Gravitation A gravitational force of attraction exists between any two masses, m1 and m2, in the Universe. F = G m1 m2 / R2 The strength of the gravitational force between the two masses weakens with distance of separation R, according to 1/R2. F F/9 F/4 R 2R 3R Bigger masses exert bigger forces, so the strength of the force depends on the amount of each mass.

45. Question Suppose that sometime in the future the Moon is 3 x further away from Earth than it is now. What would be the strength of Earth’s gravitational force on the Moon? 3 x greater 3 x weaker 1/3 of its current strength 9 x weaker

46. Lunar Lander Eagle in Orbit Around Moon (1969) The Moon is much less massive than the Earth … but the Lunar Lander is a lot closer to the Moon !

47. All Circular Motion Requires an ‘Inward’ Centripetal Force

49. Centripetal Acceleration of Planets Centripetal acceleration of planets ‘weakens’ as the inverse-square of distance from the Sun!

50. Possible Orbits Are Conic Sections