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Physics: Problems and Solutions

Kepler's laws

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Kepler's laws are a set of three laws that describe the orbits of bodies around a much larger body (for example, planets around the sun).

  • The orbit of a body is a conic section, with the sun at a/the focus.
  • The line between the body and sun sweeps out an equal area during equal time spans, regardless of where the body is in its orbit.
  • The square of the orbital period is proportional to the cube of the semi-major axis (that is, the farthest the body is from the sun). This can be formulated as
P^2 = \frac{4 \pi^2 a^3}{G(M+m)}\approx \frac{4 \pi^2 a^3}{GM}

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