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-rw-r--r--macros/latex/contrib/exam-n/sample/dynamical1.tex8
1 files changed, 4 insertions, 4 deletions
diff --git a/macros/latex/contrib/exam-n/sample/dynamical1.tex b/macros/latex/contrib/exam-n/sample/dynamical1.tex
index e3a51a803b..c371e9f900 100644
--- a/macros/latex/contrib/exam-n/sample/dynamical1.tex
+++ b/macros/latex/contrib/exam-n/sample/dynamical1.tex
@@ -23,20 +23,20 @@ $a(t)$ is the semimajor axis at time $t$)
\begin{equation*}
\frac{a(t)}{a_0}=\left[1-\frac{t\Delta V}{2^{1/2}\pi
a_0(1-e_0)^{1/2}}\right]^2
+\partmarks{2}
\end{equation*}
-\partmarks*{2}
and
\begin{equation*}
\frac{T(t)}{T_0}=\left[1-\frac{t\Delta V}{2^{1/2}\pi
a_0(1-e_0)^{1/2}}\right]^3
+\partmarks{1}
\end{equation*}
-\partmarks*{1}
and the eccentricity satisfies (with $e_0=e(0)$)
\begin{equation*}
e(t)=1-\frac{1-e_0}{\left[1-\frac{t\Delta V}{2^{1/2}\pi
a_0(1-e_0)^{1/2}}\right]^2}.
+\partmarks{2}
\end{equation*}
-\partmarks*{2}
Show that, once the orbit is circular, its radius decays
exponentially with time on timescale $m_0/2\dot{m}$ where $m_0$
@@ -62,8 +62,8 @@ passage distances for the system, show that this leads to a natural
time $T$ for the system, where
\begin{equation*}
T\propto\frac{\bar{u}u^2}{m^2\nu\log N}.
+\partmarks{5}
\end{equation*}
-\partmarks*{5}
\begin{questiondata}
You may assume that the sphere of influence radius of a star is