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De motu corporum in gyrum - Quiz
  • 1. According to Theorem 2, what is the centripetal force proportional to in a uniform circular orbit?
A) Square of the arc-length divided by the radius
B) The square of the orbital period
C) The cube of the radius
D) Velocity divided by the radius squared
  • 2. In Corollary 1 of Theorem 2, what is the centripetal force proportional to in terms of orbital speed V and radius R?
A) V²R
B) V/R
C) V/R²
D) V²/R
  • 3. According to Corollary 2 of Theorem 2, centripetal force is proportional to which expression?
A) (1/P) * R²
B) P² * R
C) (1/P²) * R
D) P² / R
  • 4. What does Corollary 3 of Theorem 2 state about centripetal force if P² is proportional to R?
A) It is independent of R
B) It is proportional to the square of P
C) It is proportional to R²
D) It is inversely proportional to R
  • 5. What happens to the centripetal force if P² is proportional to R² as stated in Corollary 4 of Theorem 2?
A) It is proportional to R
B) It remains constant
C) It is proportional to 1/R²
D) It is proportional to 1/R
  • 6. According to Corollary 5 of Theorem 2, what is the relationship of centripetal force if P² is proportional to R³?
A) It is proportional to R²
B) It is proportional to R³
C) It is proportional to 1/R
D) It is proportional to 1/R²
  • 7. Which celestial bodies are mentioned in the scholium as obeying the Corollary 5 relation?
A) Planets orbiting the Sun and Galilean satellites orbiting Jupiter
B) Comets and the Sun
C) The Moon and the Earth
D) Mars and the Moon
  • 8. What method does Theorem 3 use to evaluate centripetal force in non-circular orbits?
A) The law of universal gravitation
B) A geometrical limit argument involving ratios of vanishingly small line-segments
C) Experimental measurements of speed
D) Algebraic equations of motion
  • 9. In Problem 1, what happens if an orbiting body reaches a center of attraction located on the circumference of its circular orbit?
A) It departs along the tangent
B) It stops moving
C) It accelerates towards the center
D) It spirals into the center
  • 10. What is the result for the centripetal force in Problem 2 where the center of attraction is at the center of an ellipse?
A) Inversely proportional to the radius vector
B) Inversely proportional to the square of the radius vector
C) Directly proportional to the radius vector
D) Independent of the radius vector
  • 11. In Problem 3, where is the center of attraction located for the ellipse?
A) At an infinite distance
B) On the circumference
C) At the geometric center
D) At one of its foci
  • 12. According to Problem 3, the centripetal force in an elliptical orbit (with force to a focus) is what?
A) Inversely proportional to the distance
B) Inversely proportional to the square of the distance
C) Constant regardless of distance
D) Directly proportional to the distance
  • 13. Which principle does the scholium of Problem 3 attribute to Kepler regarding orbital areas?
A) The Sun is at the center of the orbit
B) Speed is constant in all orbits
C) Planets move in circles
D) Radii drawn to the Sun describe areas proportional to the times
  • 14. What is the full Latin title of the manuscript sent by Newton to Halley in 1684?
A) Opticks
B) Philosophiæ Naturalis Principia Mathematica
C) De mundi systemate
D) De motu corporum in gyrum
  • 15. In what month and year did Newton send the manuscript to Edmond Halley?
A) August 1684
B) November 1684
C) December 1684
D) January 1685
  • 16. Who visited Newton to prompt the writing of the manuscript?
A) The Royal Society
B) Robert Hooke
C) Edmond Halley
D) Christopher Wren
  • 17. How many propositions (theorems and problems) does De Motu contain?
A) 3
B) 4
C) 11
D) 2
  • 18. How many definitions are listed in the preliminaries of De Motu?
A) 3
B) 11
C) 4
D) 2
  • 19. How many hypotheses are listed in the preliminaries of De Motu?
A) 4
B) 2
C) 11
D) 3
  • 20. Which term did Newton originate in his first definition in De Motu?
A) Vector
B) Centripetal force
C) Inertia
D) Gravity
  • 21. What mathematical rule describes how forces combine according to Newton's third hypothesis?
A) Parallelogram rule
B) Dot product rule
C) Triangle rule
D) Quadrilateral rule
  • 22. How many lemmas are included in the preliminary section of De Motu?
A) 11
B) 4
C) 2
D) 3
  • 23. Which book did Newton develop from the ideas outlined in De Motu?
A) Philosophiæ Naturalis Principia Mathematica
B) Arithmetica Universalis
C) Opticks
D) The System of the World
  • 24. To which society did Halley report Newton's communication on 10 December 1684?
A) The London Scientific Circle
B) The French Academy of Sciences
C) The Royal Observatory
D) The Royal Society
  • 25. How does Newton divide the area swept out by the radius vector in his derivation?
A) Into concentric circles.
B) Into non-overlapping parallelograms.
C) Into squares of equal size.
D) Into triangle-sectors.
  • 26. In the derivation of Theorem 1, what happens to the size of the triangle-sectors as the limit is approached?
A) They become negative.
B) They remain constant.
C) They increase towards infinity.
D) They tend towards zero.
  • 27. According to Theorem 4, the time of revolution in an elliptical orbit is the same as a circular orbit with what property?
A) The same area as the ellipse
B) The same circumference as the ellipse
C) The same radius as the minor axis
D) The same diameter as the major axis
  • 28. Which proposition in the Principia corresponds to Theorem 4?
A) Proposition 32
B) Proposition 15
C) Proposition 3
D) Proposition 17
  • 29. In Problem 4, what happens if the speed of an orbiting body is high enough?
A) The orbit collapses into the center
B) The orbit becomes a perfect circle
C) The orbit becomes a parabola or hyperbola
D) The orbit becomes a straight line
  • 30. Which proposition in the Principia corresponds to the content of Problem 4?
A) Proposition 32
B) Proposition 15
C) Proposition 2
D) Proposition 17
  • 31. According to the text, what allows for the definition of the orbits of comets?
A) A bonus demonstration from the scholium
B) The invention of the telescope
C) The measurement of solar flares
D) The discovery of gravity
  • 32. What is discussed in Problem 5 regarding a degenerate elliptical orbit?
A) A straight-line fall or ejection
B) A highly eccentric hyperbola
C) A parabolic path
D) An orbit oscillating between two centers
  • 33. Which proposition in the Principia corresponds to Problem 5?
A) Proposition 2
B) Proposition 32
C) Proposition 3
D) Proposition 15
  • 34. How are Problems 6 and 7 addressed geometrically?
A) Using elliptical integrals
B) Using parabolic tangents
C) Using hyperbolic constructions
D) Using circular projections
  • 35. What kind of proof did Newton often treat as already demonstrated based on the original proof in 'De Motu'?
A) The converse
B) The mass of the Sun
C) The initial velocity
D) The orbital period
  • 36. How did critics characterize Newton's style of demonstration in his writings?
A) Entirely mathematical
B) Rather brief
C) Overly verbose
D) Purely experimental
  • 37. What did Newton assume his readers would find in his proofs?
A) Extensive bibliographies
B) Self-evident steps
C) Confusing logic
D) Contradictory evidence
  • 38. When did Newton acknowledge that correspondence with Robert Hooke stimulated his investigations?
A) 1686
B) 1727
C) 1679
D) 1690
  • 39. In what year did Robert Hooke begin his correspondence with Newton?
A) 1680
B) 1686
C) 1679
D) 1727
  • 40. What position had Robert Hooke been appointed to at the Royal Society?
A) Head of national surveys
B) President of the society
C) Chief mathematician
D) Managing the society's correspondence
  • 41. What did Newton suggest using to determine the Earth's motion in his reply to Hooke?
A) A falling body
B) The trajectory of a comet
C) The orbit of the moon
D) A swinging pendulum
  • 42. What law of attraction did Hooke claim Newton owed to him?
A) Law of universal gravitation
B) Linear attraction law
C) Law of planetary inertia
D) Inverse-square law
  • 43. Which astronomer did Newton acknowledge as having suggested an inverse-square attractive force without demonstration?
A) Ismaël Bullialdus
B) Giovanni Alfonso Borelli
C) Robert Hooke
D) Alexis Clairaut
  • 44. Who wrote that there is a distance between a glimpsed truth and a demonstrated truth?
A) Alexis Clairaut
B) Isaac Newton
C) Robert Hooke
D) Edmond Halley
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