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The relation $$ \frac{v}{c} \geq \frac{1}{\sin \theta + \cos \theta} $$ where c is the speed of light, gives the actual speeds for which superluminal motion is observed by O for a given $$ \theta $$. Invert the above relation to obtain the relation $$ \sin^{-1} \left[ \frac{1}{2\beta} \left(1 - \sqrt{2\beta^2 - 1}\right) \right] \leq \theta \leq \sin^{-1} \left[ \frac{1}{2\beta} \left(1 + \sqrt{2\beta^2 - 1}\right) \right] $$ where $$ \beta = v/c $$, and which gives the angles for which superluminal motion is observed by O for a given $$ \beta $$.

Name: the relation fracvc geq frac1sin theta cos theta where c is the speed of light gives the actual speeds for which superluminal motion is observed by o for a given theta invert the above relat 19248
Uploaded: 2022-09-22T02:21:54-08:00
Duration: 2 min 4 s
Channel: Timothy James
Description: the relation fracvc geq frac1sin theta cos theta where c is the speed of light gives the actual speeds for which superluminal motion is observed by o for a given theta invert the above relat 19248

          The relation
$$ \frac{v}{c} \geq \frac{1}{\sin \theta + \cos \theta} $$
where c is the speed of light, gives the actual speeds for which superluminal motion is observed by O for a given $$ \theta $$. Invert the above relation to obtain the relation
$$ \sin^{-1} \left[ \frac{1}{2\beta} \left(1 - \sqrt{2\beta^2 - 1}\right) \right] \leq \theta \leq \sin^{-1} \left[ \frac{1}{2\beta} \left(1 + \sqrt{2\beta^2 - 1}\right) \right] $$
where $$ \beta = v/c $$, and which gives the angles for which superluminal motion is observed by O for a given $$ \beta $$.

$the relation fracvc geq frac1sin theta cos theta where c is the speed of light gives the actual speeds for which superluminal motion is observed by o for a given theta invert the above relat 19248$

Added by Brianna J.

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