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3

Kepler's 3rd Law: The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. If we take Jupiter's semimajor axis of 5.2 AU (avg value), then objects at 2.5 AU, 2.82 AU, 2.95 AU, 3.25 AU have orbital periods shorter than Jupiter by a factor of 3:1, 5:2, 7/3 etc. The fact that the ratios for the deepest ...

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You would expect type Ia supernovas to be standard candles in neutrinos for the same reason they work that way in light. Alas, with the current detector packages they are only good in our local group (this would be considerably improved with the implementation of a GADZOOKS!-like scheme to gadolinium-doped superK or by several proposed but very expensive ...

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This is an integral, the number of stars of mass between $XM_{SUN}$ and $YM_{SUN}$ is : $N(XM_{SUN} \to YM_{SUN}) = \int_{XM_{SUN}}^{YM_{SUN}} \xi_0 (\frac{m}{M_{SUN}})^{-\alpha} \frac{dm}{M_{SUN}} = \int_X^Y \xi_0 (m')^{-\alpha} dm'$ So, it is clear that, with the additive properties of the integral, we have : \$N(XM_{SUN} \to ZM_{SUN}) = N(XM_{SUN} \to ...

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