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Gravity & Orbits

That’s the trouble with science. You’ve got a bunch of empiricists trying to describe things of unimaginable wonder. Gravity & Orbits. Solar System Astronomy Chapter 3. But first… history. Solar System Astronomy. Some History. Ancient cultures & astronomical knowledge

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Gravity & Orbits

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  1. That’s the trouble with science. You’ve got a bunch of empiricists trying to describe things of unimaginable wonder.

  2. Gravity & Orbits Solar System Astronomy Chapter 3

  3. But first… history Solar System Astronomy

  4. Some History • Ancient cultures & astronomical knowledge • Already in the stone and bronze ages, human cultures realized the cyclic nature of motions in the sky. • Monuments dating back to ~ 3000 B.C. show alignments with astronomical significance. • Those monuments were probably used as calendars or even to predict eclipses

  5. Some History • Ancient cultures & astronomical knowledge • Nebra sky disk • ~1600 BC • bronze disk ~30cm diameter • sun or full moon, a lunar crescent, and stars (including Pleiades) • two golden arcs along the sides • marking angle between the solstices • arc at the bottom perhaps Milky Way or Rainbow

  6. Some History

  7. Some History • Ancient cultures & astronomical knowledge • Often timekeeping methods • Some objects ‘wandered’ • Greek πλανήτης, derivative of the word πλάνης "moving” • 7 in the sky • Sun • Moon • Mars • Mercury • Jupiter • Venus • Saturn

  8. Some History • Ancient cultures & astronomical knowledge • Often timekeeping methods • Some objects ‘wandered’ • Greek πλανήτης, derivative of the word πλάνης "moving” • 7 in the sky • Sun Dimanche • Moon Lundi • Mars Mardi • Mercury Mercredi • Jupiter Jeudi • Venus Vendredi • Saturn Samedi

  9. Some History • Ancient cultures & astronomical knowledge • Often timekeeping methods • Lunar cycles gave rise to months

  10. Some History • Ancient cultures & astronomical knowledge • Often timekeeping methods • When is Easter? • observed on the Sunday after the first full moon on or after the day of the vernal equinox • full moon involved is not an astronomical full moon, but an ecclesiastical moon – though it coincides more or less with the astronomical full moon • Easter falls on the first Sunday following the first ecclesiastical full moon that occurs on or after March 21 (the day of the ecclesiastical vernal equinox)

  11. Some History • Ancient cultures & astronomical knowledge • Often timekeeping methods • Sirius, the Dog Star • seiros σείριος, “scorcher” • Rising just before Sun marks the beginning of summer

  12. Some History • Ancient Greece • Astronomy was a branch of mathematics • Astronomers sought to create geometrical (mathematical) models that could imitate the appearances of celestial motions • tradition began with Pythagoreans, who placed astronomy among the four mathematical arts (along with arithmetic, geometry, and music) • Our conception of astronomy (and many sciences) inherited from Ancient Greek

  13. Some History • Ancient Greece • Eudoxus • Aristotle • Eratosthenes • Hipparchus • Ptolemy • All sought to describe motion of heavenly bodies • Mathematical behavior of motion

  14. Some History • Ancient Greece • Eudoxus (4009 – 356 BC) • assigned to each planet a set of 27 concentric spheres • first to attempt a mathematical description of the motions of the planets

  15. Some History • Ancient Greece • Aristotle (384 – 322 B.C.) • major authority of philosophy until late Middle Ages • divided universe into two parts • imperfect, changeable Earth • perfect heavens (described by spheres) • expanded Eudoxus’ model to 55 spheres • Aristotle taught the Earth is round • Why would he think that?

  16. Some History • Ancient Greece • Aristotle (384 – 322 B.C.) • perhaps the philosopher most respected by European thinkers during and after the Renaissance • erroneous positions taken as a given, which held back science • analysis of procreation presupposes: • active, ensouling masculine element bringing life to • inert, passive, female element • assertion that objects of different mass fall at different speeds under gravity • refuted by Philoponus

  17. Some History • Ancient Greece • Aristotle (384 – 322 B.C.) • held back science for 2000 years • refuted Democritus's claim Milky Way was multitude of stars • refuted stars of night sky were just like Sun • calculated they would have to be millions of times farther away than Sun • thus dismissed for hundreds of years • theory of the natural slave was used to justify European domination of Native Americans • On Animals…

  18. Some History • Ancient Greece • Eratosthenes (276 BC - 194 BC) • Greek mathematician, geographer and astronomer • contemporaries nicknamed him Beta (2nd letter of alphabet) –supposedly proved himself to be the second in the Mediterranean world in many fields • first known to have calculated the size of the Earth

  19. Some History • Ancient Greece • Eratosthenes (276 BC - 194 BC) • Angular distance between Syene and Alexandria is ~ 7° • Linear distance ~ 5,000 stadia • Earth Radius ~ 40,000 stadia • probably ~ 14 % too large

  20. Some History • Ancient Greece • Hipparchus (2nd century BC) • access to Babylonian observations & predictions • used to create better geometrical models, constructed accurate models for movement of Sun & Moon • moved Earth from center of spheres • compiled star catalogue • recorded the position and brightness of the stars • Considered among most important Greek astronomers (& greatest astronomer of antiquity by some) • introduced the concept of exact prediction into astronomy • last innovative astronomer before Ptolemy

  21. Some History • Ancient Greece • Ptolemy (c. 90 – c. 168) • compiled and extended the astronomical knowledge and theories of the ancient Greek & Babylonian world • star catalog in Almagest lists forty-eight constellations • ancestral to the modern system of constellations • geocentric model widely accepted until Copernicus

  22. Some History • Ancient Greece • Ptolemy (c. 90 – c. 168) • Retrograde motion…

  23. Some History • Ancient Greece • Ptolemy (c. 90 – c. 168) • Epicycles…

  24. Some History • Ancient Greece • Ptolemy (c. 90 – c. 168) • Epicycles • Ptolemaic system was considered the “standard model” of the Universe until the Copernican Revolution

  25. Some History • Copernican Revolution & beyond • 99 years that changed our view of the Universe • Nicolaus Copernicus • Galileo Galilei • Tycho Brahe • Johannes Kepler • Isaac Newton

  26. Some History • Copernican Revolution • Copernicus (1473-1543) • one of the great Renaissance polymaths • mathematician, astronomer, jurist, physician, classical scholar, governor, administrator, diplomat, economist, and soldier

  27. Some History • Copernican Revolution • Copernican Model • No center to universe • Center of Solar System near sun • heliocentric • Distance to Sun imperceptible vs distance to stars • Earth’s motion accounts for apparent motion: • rotation accounts for daily rotation of stars • annual cycle of Sun’s movements caused by Earth’s orbit • apparent retrograde motion of planets is caused by orbit

  28. Some History • Copernican Revolution • Copernican Model • arrived at correct order of the known planets • Explained precession of the equinoxes correctly • slow change in the position of the Earth's rotational axis • gave a clear account of the cause of the seasons • Earth's axis not perpendicular to plane of orbit • added motion to Earth, keeping axis pointed throughout the year at the same place in the heavens

  29. Some History • Copernican Revolution • Copernican Model • not experimentally better than Ptolemy’s • from 1543 publication until about 1700, few astronomers were convinced by the Copernican system, though the book was relatively widely circulated • influenced Galileo & Kepler, others • ironically, this was at the behest of the Catholic Church as part of the Catholic Reformation efforts for a means of creating a more accurate calendar for its activities

  30. Some History • Copernican Revolution • Galileo (1564 – 1642) • Italian • physicist • astronomer • astrologer • philosopher • closely associated with the Scientific Revolution

  31. Some History • Copernican Revolution • Galileo (1564 – 1642) • improved (but did not invent) telescope • invented first known microscope • observed Galilean moons • motion indicated orbits about Jupiter • observed rings of Saturn • observed full set of phases with Venus

  32. Some History • Copernican Revolution • Galileo (1564 – 1642) • improved (but did not invent) telescope • invented first known microscope • observed Galilean moons • motion indicated orbits about Jupiter • observed rings of Saturn • observed full set of phases with Venus

  33. Some History • Copernican Revolution • Galileo (1564 – 1642) • one of first Europeans to observe sunspots • Existence contradicted unchanging perfection of the heavens (Aristotle) • First to report lunar mountains & craters • Concluded “rough and uneven, and just like the surface of the Earth • Not Aristotle’s perfect sphere • Observed the Milky Way • Found to be multitude of distant stars

  34. Some History • Copernican Revolution • Galileo (1564 – 1642) • Demonstrated equal acceleration of unequal masses • Contrary to Aristotle • Determined rate objects fell • Demonstrated velocity constant (not zero) without outside force • Contrary to Aristotle • Basic principle of relativity

  35. Some History • Copernican Revolution • Galileo (1564 – 1642) • Early example of science conflicting with Church/authority • 1633 Heresy • required to recant heliocentric ideas • idea that Sun is stationary condemned as “formally heretical” • heliocentrism was never formally or officially condemned • ordered imprisoned • sentence later commuted to house arrest • Dialogue Concerning the Two Chief World Systems banned • and all past & future books

  36. Some History • Copernican Revolution • Tycho Brahe (1546 – 1602) • preeminent observational astronomer of pre-telescopic period • said to own 1% of Denmark’s entire wealth at one • observations of stellar/planetary positions unparalleled accuracy • observations of nova contradicted immutable heavens • Lost nose in duel 1566 • Fair amount of drinking involved • Replacement of silver & gold • Kept a jester (Jepp) beneath the table during dinner • Believed to be clairvoyant • Tame elk (or moose)…

  37. Some History • Copernican Revolution • Kepler (1571 – 1630) • German • Mathematician, astronomer, astrologer, sci-fi writer

  38. Some History • Copernican Revolution • Kepler (1571 – 1630) • Used the precise observational tables of Tycho Brahe to study planetary motion mathematically • Consistent description by abandoning both • Circular motion • Uniform motion • Planets move around the sun on elliptical paths, with non-uniform velocities

  39. Some History • Copernican Revolution • Kepler (1571 – 1630) • Kepler’s Laws • The orbits of the planets are ellipses with the sun at one focus • A line from a planet to the sun sweeps over equal areas in equal intervals of time • A planet’s orbital period (P) squared is proportional to its average distance from the sun (a) cubed

  40. Some History • Copernican Revolution • Kepler’s Law #1 & #2

  41. Some History • Copernican Revolution • Kepler’s Law #3

  42. Kepler’s Laws

  43. Some History • 99 years changed our universe

  44. Some History • Copernican Revolution Where do Kepler’s Laws come from? Why are they true? We don’t know… Until Newton.

  45. Some History • Copernican Revolution Where do Kepler’s Laws come from? Why are they true? We don’t know… Until Newton.

  46. Sir Isaac Newton, FRS

  47. Newton’s Laws • Newton discovered laws applying to all objects • Universal • Describe forces that act on all objects • Like gravity

  48. Newton’s Laws of Motion • Stationary objects stay stationary, moving objects stay in constant motion • Unless a force acts upon it • “constant” refers to speed AND direction • Forces change motion • No change in motion means no forces OR balanced forces #1

  49. Newton’s Laws of Motion • Force = mass × acceleration • F = ma a = F/m • More mass » less acceleration • Larger force » larger acceleration #2

  50. Newton’s Laws of Motion • Forces always come in pairs • Same size • Opposite direction • Applies to ALL forces, including gravity #3

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