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