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-\begin_body - -\begin_layout Title -Eclipse computations in nyx -\end_layout - -\begin_layout Author -Christopher Rabotin -\end_layout - -\begin_layout Standard -This computation assumes that all objects are spherical. -\end_layout - -\begin_layout Standard -\begin_inset CommandInset toc -LatexCommand tableofcontents - -\end_inset - - -\end_layout - -\begin_layout Section -Summary -\end_layout - -\begin_layout Standard -In short, we project the light source onto a plane which crosses the eclipsing - body perpendicularly to the direction between the spacecraft and the (potential -ly) eclipsing body. - We then find whether the disks representing the eclipsing body and the - light source on that plane overlap. - If they do not, then we're in full illumination. - If they do, we compute the overlapping area of both disks, and compute - the nominal apparent disk. - The ratio of these areas is used to compute the percentage of penumbra. -\end_layout - -\begin_layout Section -Derivation -\end_layout - -\begin_layout Subsection -Umbra or visibilis computation -\end_layout - -\begin_layout Standard -\begin_inset Float figure -placement h -wide false -sideways false -status collapsed - -\begin_layout Plain Layout -\align center -\begin_inset Graphics - filename eclipse_computation.jpg - width 25col% - -\end_inset - - -\end_layout - -\begin_layout Plain Layout -\begin_inset Caption Standard - -\begin_layout Plain Layout -Top-view of eclipsing problem -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -First, let's compute -\begin_inset Formula $\beta_{2}$ -\end_inset - - the angle between -\begin_inset Formula $\vec{r}_{\text{EB-LS}}$ -\end_inset - - and -\begin_inset Formula $\vec{r}_{\text{LS}}$ -\end_inset - -, respectively the vector from the eclipsing body to the light source and - the vector from the spacecraft to the light source. - If that angle is less than a right angle, then the light source is not - behind the eclipsing body, so we're in full illumination: -\emph on -visibilis -\emph default -. -\end_layout - -\begin_layout Standard -Then, we compute -\begin_inset Formula $\beta_{3}$ -\end_inset - - the angle between the spacecraft and the eclipsing body, and between the - spacecraft and the light source. - We need this to project the radius of the light source onto the plane centered - at the eclipsing geoid, and normal to the direction to the spacecraft. -\end_layout - -\begin_layout Standard -Using the triangle formed between the spacecraft, the center of the eclipsing - body, and the projection plane, we can compute -\begin_inset Formula $\vec{r^{\prime}}_{\text{LS}}$ -\end_inset - -, the vector from the spacecraft to the intersection point on the plane - in the direction of -\begin_inset Formula $\hat{\boldsymbol{r}}_{\text{LS}}$ -\end_inset - -. - We use -\begin_inset Formula $\beta_{3}$ -\end_inset - - for this computation as we know the length of that hypotenuse is -\begin_inset Formula -\[ -|\vec{r}_{\text{EB-LS}}|=|\vec{r^{\prime}}_{\text{LS}}|\cos\beta_{3} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -Using Thales' theorem, we can compute the -\begin_inset Quotes eld -\end_inset - -pseudo light source radius -\begin_inset Quotes erd -\end_inset - -, that is the radius of the light source as seen from an angle -\begin_inset Formula $\gamma$ -\end_inset - - from the plane. - Forming a triangle between the intersection point, the center of the eclipsing - body, and the orthogonal projection of that intersection point onto -\begin_inset Formula $\vec{r}_{\text{EB-LS}}$ -\end_inset - -, we can compute the actual radius of the light source on the projection - plane. -\end_layout - -\begin_layout Standard -Let -\begin_inset Formula $\vec{r}_{\text{Plane-LS}}$ -\end_inset - - be the vector from the center of the eclipsing body to the projected center - of the light source on the plane. - We now check for any overlap. - If the norm of -\begin_inset Formula $\vec{r}_{\text{Plane-LS}}$ -\end_inset - - minus the project radius is greater than the radius of the eclipsing body, - it means that, no matter what the direction is, the shaddow of the eclipsing - body -\emph on -ends -\emph default - before the closest point of the light source: the light source is fully - visible. - If the norm of -\begin_inset Formula $\vec{r}_{\text{Plane-LS}}$ -\end_inset - - plus the projected radius of the light source is less than the radius of - the eclipsing body, then the light source is fully behind the eclipsing - body, so we're in total eclipse ( -\emph on -umbra -\emph default -). - Note that we have ruled out the light source being in front of the eclipsing - body by computing the angle -\begin_inset Formula $\beta_{2}$ -\end_inset - - at the start. -\end_layout - -\begin_layout Subsection -Penumbra percentage -\end_layout - -\begin_layout Standard -\begin_inset Float figure -placement h -wide false -sideways false -status collapsed - -\begin_layout Plain Layout -\align center -\begin_inset Graphics - filename eclipse_penumbra.jpg - width 25col% - -\end_inset - - -\end_layout - -\begin_layout Plain Layout -\begin_inset Caption Standard - -\begin_layout Plain Layout -In plane view -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Plain Layout - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Both circles represent the light source and the eclipsing body. - We then use the -\begin_inset CommandInset href -LatexCommand href -name "Circle-Circle intersection" -target "http://mathworld.wolfram.com/Circle-CircleIntersection.html" -literal "false" - -\end_inset - - computation to compute the area of the asymmetric lens corresponding to - the overlap of both circles, -\begin_inset Formula $A_{\text{shadow}}$ -\end_inset - -. - Then, we compute the full area of the light source, -\begin_inset Formula $\mathcal{A_{\text{LS}}}$ -\end_inset - -. -\end_layout - -\begin_layout Standard -The penumbra value, -\begin_inset Formula $P$ -\end_inset - -, is such that a number close to one means that the light source is almost - in full visibility. - Conversely, if the number is close to zero, then we are near total umbra. -\end_layout - -\begin_layout Standard -\begin_inset Formula -\[ -P=\frac{\mathcal{A_{\text{LS}}}-\mathcal{A_{\text{shadow}}}}{\mathcal{A_{\text{LS}}}} -\] - -\end_inset - - -\end_layout - -\end_body -\end_document diff --git a/docs/eclipsing.pdf b/docs/eclipsing.pdf deleted file mode 100644 index d5e7d591..00000000 Binary files a/docs/eclipsing.pdf and /dev/null differ diff --git a/docs/index.html b/docs/index.html deleted file mode 100644 index eba225d2..00000000 --- a/docs/index.html +++ /dev/null @@ -1,10 +0,0 @@ - - -
-Redirecting ...
- - diff --git a/src/md/trajectory/traj.rs b/src/md/trajectory/traj.rs index c03c5572..406edb12 100644 --- a/src/md/trajectory/traj.rs +++ b/src/md/trajectory/traj.rs @@ -135,7 +135,11 @@ where /// Creates an iterator through the trajectory by the provided step size between the provided bounds pub fn every_between(&self, step: Duration, start: Epoch, end: Epoch) -> TrajIterator