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Gravitation and the Motions of the Planets

Gravitation and the Motions of the Planets. Nicolaus Copernicus (1473 - 1543) - Heliocentric Cosmology The Sun is the center of the planets’ motions The planets’ orbits are circles The planets orbit the Sun with the closer ones moving faster than the farther.

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Gravitation and the Motions of the Planets

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  1. Gravitation and the Motions of the Planets

  2. Nicolaus Copernicus (1473 - 1543) - Heliocentric Cosmology The Sun is the center of the planets’ motions The planets’ orbits are circles The planets orbit the Sun with the closer ones moving faster than the farther
  3. The order of the planets from closest to farthest from the Sun: Mercury, Venus, Earth, Mars, Jupiter, Saturn The stars are very far away compared to the planets.
  4. The real explanation for retrograde motion
  5. Johannes Kepler (1571 - 1630) Kepler’s Laws of Planetary Motion (1609 -1619)
  6. Kepler’s First Law: The planets’ orbits are ellipses with the Sun at one focus.
  7. The First Law Semi-major axis, a Foci
  8. Kepler’s Second Law: The planets in their orbits sweep out equal areas in equal time intervals
  9. The Second Law 1 4 3 2
  10. The Third Law: P2=a3Where P = orbital period in yearsand a= semi-major axis in AU’s
  11. The Third Law: P2=a3Where P = orbital period in yearsand a= semi-major axis in AU’sP (yrs) A (AU’s)Earth 1 1Jupiter 11.8 5.2Pluto 248 39.5
  12. Galileo Galilei (1564 - 1642) -First Astronomer to use a telescope (1610) - Discovered: the phases of Venus
  13. Galileo Galilei (1564 - 1642) -First Astronomer to use a telescope (1610) - Discovered: the phases of Venus the moons of Jupiter
  14. Isaac Newton (1642 - 1727) Newton’s Laws of Motion and Gravitation
  15. Newton’s First law: An object at rest or traveling in a straight line at a constant speed remains in that state unless acted upon by an outside force.
  16. Newton’s Second Law: F = ma
  17. Newton’s Second Law: F = ma Force acceleration mass
  18. Newton’s Second Law: F = ma Force acceleration mass change in velocity
  19. Newton’s Second Law: F = ma Force acceleration mass change in velocity speed & direction
  20. Newton’s Third Law: For every action (force) there is an equal and opposite reaction(force)
  21. Newton’s Law of Gravity
  22. F = GM1M2 R2 G = universal gravitational constant M1 M2 R
  23. Newton’s modification of Kepler’s Third Law: (M1+ M2)P2 = a3
  24. Newton’s modification of Kepler’s Third Law: (M1+ M2)P2 = a3 masses in Solar Masses
  25. Angular Momentum: m v Angular Momentum=mvr r
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