Models and laws: Planets 2006 part 5. The modelyou found

Chapter 10, Problem 22

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Models and laws: Planets 2006 part 5. The modelyou found in Exercise 18 is a relationship noted in the17th century by Kepler as his Third Law of PlanetaryMotion. It was subsequently explained as a conse-quence of Newtons Law of Gravitation. The models242 CHAPTER 10 Re-expressing Data: Get It Straight!PlanetPositionNumberDistance from Sun(million miles)Length of Year(Earth years)Mercury 1 36 0.24Venus 2 67 0.61Earth 3 93 1.00Mars 4 142 1.88Jupiter 5 484 11.86Saturn 6 887 29.46Uranus 7 1784 84.07Neptune 8 2796 164.82Pluto 9 3707 247.686 Eris is the Greek goddess of warfare and strife who caused aquarrel among the other goddesses that led to the Trojan war.In the astronomical world, Eris stirred up trouble when thequestion of its proper designation led to the raucous meetingof the IAU in Prague where IAU members voted to demotePluto and Eris to dwarf-planet statushttp://www.gps.caltech.edu/~mbrown/planetlila/#paper. for Exercises 1921 relate to what is sometimes called theTitius-Bode law, a pattern noticed in the 18th centurybut lacking any scientific explanation.Compare how well the re-expressed data are describedby their respective linear models. What aspect of themodel of Exercise 18 suggests that we have found a phys-ical law? In the future, we may learn enough about aplanetary system around another star to tell whether theTitius-Bode pattern applies there. If you discovered thatanother planetary system followed the same pattern, howwould it change your opinion about whether this is a realnatural law? What would you think if the next systemwe find does not follow this pattern?