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By Benjamin Crowell

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6 millimeters over a distance of 1,100 meters! ” His notebooks, however, show that although he did the calculation on that date, the result didn’t quite come out quite right, and he became uncertain about whether his theory of gravity was correct as it stood or needed to be modified. Not until 1675 did he learn of more accurate astronomical data, which convinced him that his theory didn’t need to be tinkered with. It appears that he rewrote his own life story a little bit in order to make it appear that his work was more advanced at an earlier date, which would have helped him in his dispute with Leibniz over priority in the invention of calculus.

Q / As the Earth and Mars revolve around the sun at different rates, the combined effect of their motions makes Mars appear to trace a strange, looped path across the background of the distant stars. a surprisingly simple set of mathematical and geometrical rules for describing the planets’ motion using the sun-centered assumption. After 900 pages of calculations and many false starts and dead-end ideas, Kepler finally synthesized the data into the following three laws: Kepler’s elliptical orbit law The planets orbit the sun in elliptical orbits with the sun at one focus.

5 The ice skaters of figure d on page 46 make forces on each other, and their forces are equal in strength and opposite in direction. That doesn’t mean they won’t move. They’ll both move — in opposite directions. The fallacy comes from trying to add things that it doesn’t make sense to add, as suggested by the cartoon in figure g. We only add forces that are acting on the same object. It doesn’t make sense to say that the skaters’ forces on each other add up to zero, because it doesn’t make sense to add them.

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