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The orbit of a planet sweeps out equal areas in equal times.

A field is basically a function of space itself:

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A sphere is just the subset of flat space that we get from fixing the radial coordinate r to be some specific value R.

The idea of taking a complicated expression and writing it as the sum of infinite terms, as in (3.9), is a technique that is applicable to a wide variety of problems.

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But fluids are characterized by more than just the energy density at each point. There can also be pressure, which can be thought of as the amount of force the fluid would exert on the walls of a container.