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9

You can use this fundamental formula in spherical astronomy[1] $$\sin a=\sin \phi \sin \delta + \cos \phi \cos \delta \cos H$$ where $a$ is the wanted altitude, $\phi$ is your latitude, $\delta$ is the declination of the star, and $H$ is the hour angle, measured in the clockwise direction. Pay attention to the units! (Don't mix degrees, radians and grads. ...

-1

If you were free to set the galaxies in this cluster at any desired positions and in any desired states of motion, then you could easily violate the virial theorem. If the cluster was then left alone for a long enough time, then it would converge to a state in which it was bound and obeyed the virial theorem, and it would stay in that state for a very long (...

12

A slightly modified version of the virial theorem that you cite states that for a system of N bodyes (galaxies in a cluster) autogravotating $${1 \over 2} \ddot I = 2K + V$$ Where $K$ is the total kinetic energy, $V$ is the total potential energy and $I$ is the "scalar moment of inertia" of the system, defined as $$I = \sum_i^N m_i r_i^2.$$ When \$\...

9

According to the Wikipedia article on the Virial Theorem: The word virial for the right-hand side of the equation derives from vis, the Latin word for "force" or "energy", and was given its technical definition by Rudolf Clausius in 1870. Investigating this further, one can see from the original publication of Rudolf Clausius that ...

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