Brian Jackson edited We_can_use_the_encounter__.tex  over 8 years ago

Commit id: 6a0053c4c8dce428f60b8dc51602e87838838c60

deletions | additions      

       

\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.