The virial theorem, maybe better described as bound body energetics, requires that an object has an inward central force $r^{-a}$ such as a gravitational force or an electromagnetic force. The theorem also requires a constant moment of inertia on average so that the object maintains its rough shape over whatever timescale is relevant. Most structures can be virialized such as Earth, the sun, and the galaxy. For virialized structures we can say that Kinetic energy (K)$= \frac{-1}{2}$ Potential Energy (U) Worksheet 8.1 #1 For a planet of mass m orbiting a star of mass M, at a distance a, start with the Virial Theorem and derive Kepler’s Third Law of motion. Assume that m is much less than M $U_g = \frac{-GmM}{a}$ $K=\frac {U_g}{2}=\frac{-GmM}{2a}$=$\frac {1}{2} mv_p^2$ $v_p= \frac{2 \pi a}{T}= (\frac{GM}{a})^{\frac{1}{2}}$ $\frac{4 \pi ^2 a^2}{T^2}= \frac{GM}{a}$ $T^2=\frac{4 \pi ^2a^3}{GM}$ #2 Consider a spherical distribution of particles, each with a mass $m_i$ and a total (coll...
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