\contentsline {figure}{\numberline {1}{\ignorespaces An example of a synthetic trail generated by our code. The green axes show the directions defined as ``x'' and ``y'', and the red arrows indicate the synthetic trail, which has a 'stationary' $g'$ magnitude of $18.96\nobreakspace {}$mag, angle of motion of $29.62^\circ $ counter-clockwise from the x-axis, and rate of motion of $6.04\nobreakspace {}$deg/day. }}{8}{figure.1}
\contentsline {figure}{\numberline {2}{\ignorespaces A wire diagram of the analytical model used to fit trailed objects. The x and y axes (denoted in Fig\nobreakspace {}1) are indicated, as are the $x'$ and $y'$ axes, which are rotated by angle $\theta $ to line up with the trail's direction of motion. }}{9}{figure.2}
\contentsline {figure}{\numberline {3}{\ignorespaces Histogram of RMS on derived center point for generated synthetic trails. }}{10}{figure.3}
\contentsline {figure}{\numberline {4}{\ignorespaces Histogram of magnitudes of trails generated (dashed) and found (solid) for all trail lengths. }}{10}{figure.4}
\contentsline {figure}{\numberline {5}{\ignorespaces Trail fitting efficiency (derived/generated) vs magnitude. }}{11}{figure.5}
\contentsline {figure}{\numberline {6}{\ignorespaces Differences in x and y positions between the generated and derived synthetic trails. The black points are defined as derived trails that were less than $2$ pixels ($0.74\nobreakspace {}$arcsec) in x or y away from the generated trail center (inside the dotted-line box) while the red points are defined as derived trails between $2$ and $10$ pixels ($0.74$ and $3.7\nobreakspace {}$arcsec) in x or y away from the generated trail center. }}{11}{figure.6}
\contentsline {figure}{\numberline {7}{\ignorespaces Generated trail length compared to derived length. The red points indicate trails with large RMS in derived center position. }}{12}{figure.7}
\contentsline {figure}{\numberline {8}{\ignorespaces Generated angle (with respect to the pixel x axis) compared to derived angle. }}{12}{figure.8}
\contentsline {figure}{\numberline {9}{\ignorespaces Generated angle (with respect to the pixel x axis) compared to derived angle for trails with lengths between $5$ and $10$ degrees per day. }}{13}{figure.9}
\contentsline {figure}{\numberline {10}{\ignorespaces The scatter in derived angle compared to the generated length of the trail. Red points are those that show significant differences in derived center points. }}{13}{figure.10}
\contentsline {figure}{\numberline {11}{\ignorespaces Generated magnitude compared to derived magnitude. The derived magnitude has been shifted by $28.26$ magnitudes, corresponding to the Elixir-calculated zero-point of the images used. }}{14}{figure.11}
\contentsline {figure}{\numberline {12}{\ignorespaces The scatter in derived magnitude compared to the generated length of the trail. A negative value on the y-axis implies an object fitted to a fainter flux level than was generated. }}{14}{figure.12}
