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For a circular orbit, the law of periods then amounts to a statement that T 2 is proportional to r3 , where r is the radius. If all the planets were moving in their orbits at the same speed, then the time for one orbit would only increase with the circumference of the circle, so we would have a simple proportionality between T and r. Since this is not the case, we can interpret the law of periods to mean that different planets orbit the sun at different speeds. In fact, the outer planets move more slowly than the inner ones.

The difficulty of their task is suggested by figure q, which shows how the relatively simple orbital motions of the earth and Mars combine so that as seen from earth Mars appears to be staggering in loops like a drunken sailor. 52 Chapter 2 Conservation of Momentum 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. Brahe, the last of the great naked-eye astronomers, collected extensive data on the motions of the planets over a period of many years, taking the giant step from the previous observations’ accuracy of about 10 minutes of arc (10/60 of a degree) to an unprecedented 1 minute.

What do you notice about the change in velocity when you compare the three tables? Answer, p. 173 Accounting works because money is conserved. Apparently, something is also conserved when the balls collide. We call it momentum. Momentum is not the same as velocity, because conserved quantities have to be additive. Our pool balls are like identical atoms, but atoms can be stuck together to form molecules, people, and planets. Because conservation laws work by addition, two atoms stuck together and moving at a certain velocity must have double the momentum that a single atom would have had.

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Conceptual Physics by Crowell B.

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