Ugh dependencies

the-n-body-problem/lagrange-points.md

@@ -207,7 +207,7 @@ ax.plot([0, 1], [0, -1], lw=1.0, color="silver", ls="--", label="$m_2$")
 ax.set_xticks(np.arange(0, 1.1, 0.1))
 ax.set_yticks(np.arange(-1.5, 1.75, 0.25))
 ax.grid()
-ax.set_xlabel(r"$\pi_2$")
+ax.set_xlabel("$\pi_2$")
 ax.set_ylabel("$x^*$")
 ax.annotate("$m_2$", xy=(0.55, 0.5), ha="center", va="bottom")
 ax.annotate("$m_1$", xy=(0.55, -0.5), ha="center", va="bottom")
@@ -228,7 +228,7 @@ On this figure, the $x$ axis is $\pi_2$ and the $y$ axis is $x^*$. For a given v
 The solutions for $x^*$ for the collinear Lagrange points lie on the S-curve shape. For a given value of $\pi_2$, we can see there are 3 solutions of the function, corresponding to the three collinear Lagrange points for that system.
 
 By convention, the Lagrange points are numbered such that $L_1$ lies between $m_1$ and $m_2$, $L_2$ lies to the right of $m_2$, and $L_3$ lies to the left of $m_1$. Thus, we can see on the figure that the upper part of the S-curve is the solution for $L_2$. Below $x^{*} = 1.0$, the solution is for $L_1$, since that lies between $m_1$ and $m_2$. Finally, below $x^{*} = -1.0$, the solution is for $L_3$.
-<!--
+
 {numref}`fig:lagrange-points-animation` plots the five Lagrange points in non-dimensional coordinates as a function of the mass ratio $\pi_2$.
 
 ```{code-cell}
@@ -282,19 +282,20 @@ ann = ax.annotate("", xy=(1, 0.85), ha="center", va="center", fontsize=20)
 
 ax.legend(bbox_to_anchor=(0, 1, 1, 0), loc="lower left", mode="expand", ncol=7)
 
+
 def init():
  m2_orb.set_data([], [])
  m1_orb.set_data([], [])
  equil.set_data([], [])
  ann.set_text("")
  return (com, l, m2_orb, m1_orb, equil, ann)
 
-# Precompute the arrays, then index by "time step" to return lines, rather than solving on each one.
+
 def animate(pi_2):
- m_1 = [-pi_2]
- m_2 = [1 - pi_2]
- m1_line.set_data(m_1, [0])
- m2_line.set_data(m_2, [0])
+ m_1 = -pi_2
+ m_2 = 1 - pi_2
+ m1_line.set_data(m_1, 0)
+ m2_line.set_data(m_2, 0)
  x_2 = m_2 * cos
  y_2 = m_2 * sin
  x_1 = m_1 * cos
@@ -305,11 +306,11 @@ def animate(pi_2):
  L_1 = newton(func=collinear_lagrange, x0=0, args=(pi_2,))
  L_3 = newton(func=collinear_lagrange, x0=-1, args=(pi_2,))
  L_4 = L_5 = 0.5 - pi_2
- L1_line.set_data([L_1], [0])
- L2_line.set_data([L_2], [0])
- L3_line.set_data([L_3], [0])
- L4_line.set_data([L_4], [np.sqrt(3) / 2])
- L5_line.set_data([L_5], [-np.sqrt(3) / 2])
+ L1_line.set_data(L_1, 0)
+ L2_line.set_data(L_2, 0)
+ L3_line.set_data(L_3, 0)
+ L4_line.set_data(L_4, np.sqrt(3) / 2)
+ L5_line.set_data(L_5, -np.sqrt(3) / 2)
  equil.set_data([m_1, L_4, m_2, L_5, m_1], [0, np.sqrt(3) / 2, 0, -np.sqrt(3) / 2, 0])
  ann.set_text(fr"$\pi_2$ = {pi_2:.4G}")
 
@@ -328,7 +329,7 @@ glue("lagrange-points-animation", HTML(anim.to_jshtml()), display=False)
 Animation showing the position of the five Lagrange points as the value of $\pi_2$ goes from 0 to 1.
 :::
 
-{numref}`fig:lagrange-points-animation` shows that the solution of the equations of motion for the equilibrium points is symmetrical. We chose $m_1$ to be the larger mass at the start of the problem, but we can interchange $m_1$ and $m_2$ without any problems. -->
+{numref}`fig:lagrange-points-animation` shows that the solution of the equations of motion for the equilibrium points is symmetrical. We chose $m_1$ to be the larger mass at the start of the problem, but we can interchange $m_1$ and $m_2$ without any problems.
 
 For the Earth-Moon system, the value of $\pi_2$ is approximately 0.012.
 

the-orbit-equation/hyperbolic-trajectories.md

@@ -26,9 +26,9 @@ From the orbit equation, Eq. {eq}`eq:scalar-orbit-equation`, we see that the den
 
 As the true anomaly approaches $\nu_{\infty}$, $r$ approaches infinity. $\nu_{\infty}$ is restricted to be between 90° and 180°.
 
-For $-\nu_{\infty} < \nu < \nu_{\infty}$, the trajectory of $m_2$ follows the occupied or real trajectory. For $\nu_{\infty} < \nu < \left({360}^{\circ} - \nu_{\infty}\right)$, $m_2$ would occupy the virtual trajectory. This trajectory would require a repulsive gravitational force for a mass to actually follow it, so it is only a mathematical result.
+For $-\nu_{\infty} < \nu < \nu_{\infty}$, the trajectory of $m_2$ follows the occupied or real trajectory shown on the left in {numref}`fig:hyperbolic-trajectory-animation`. For $\nu_{\infty} < \nu < \left({360}^{\circ} - \nu_{\infty}\right)$, $m_2$ would occupy the virtual trajectory on the figure below. This trajectory would require a repulsive gravitational force for a mass to actually follow it, so it is only a mathematical result.
 
-<!-- ```{code-cell} ipython3
+```{code-cell} ipython3
 :tags: [remove-cell]
 
 from IPython.display import HTML
@@ -42,7 +42,7 @@ glue("hyperbolic-trajectory-animation", HTML(anim.to_jshtml()), display=False)
 :name: fig:hyperbolic-trajectory-animation
 
 Animation showing the hyperbolic trajectory and the value of the true anomaly for various positions on the occupied and virtual trajectories.
-::: -->
+:::
 
 Periapsis lies on the apse line, as usual, of the occupied trajectory. Interestingly, apoapsis lies on the virtual trajectory. Halfway between periapsis and apoapsis lies the center of a Cartesian coordinate system.