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Diffstat (limited to 'macros/latex/contrib/exam-n/sample/dynamical1.tex')
-rw-r--r-- | macros/latex/contrib/exam-n/sample/dynamical1.tex | 8 |
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 |