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Brian Jackson edited We_can_use_the_encounter__.tex
over 8 years ago
Commit id: 6a0053c4c8dce428f60b8dc51602e87838838c60
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diff --git a/We_can_use_the_encounter__.tex b/We_can_use_the_encounter__.tex
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\label{eqn:dp_dP_obs}
\dfrac{dp}{dP_{\rm obs}} = \left( \dfrac{P_{\rm act}}{P_{\rm obs}^2} \right) \left(\dfrac{\Gamma_{\rm act}}{2 b}\right)^2 = \left( \dfrac{P_{\rm act}}{P_{\rm obs}^2} \right) \left( \dfrac{P_{\rm min}}{P_{\rm act} - P_{\rm min}} \right).
\end{equation}
We also require that $P_{\rm obs} \le P_{\rm act}$.
Figure \ref{fig:distortion_probabilities} shows the probability densities for $\Gamma_{\rm obs}$ and $P_{\rm obs}$, given actual values, as well as the corresponding limits. Not surprisingly, because of the miss distance effect, $\Gamma_{\rm obs}$ tends toward larger values and $P_{\rm obs}$ toward smaller values.