deploy: bb1d8a5

.buildinfo

@@ -1,4 +1,4 @@
 # Sphinx build info version 1
 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
-config: 872b768ca72aa162fa98caa2ca5da611
+config: eb783ae0f49d501bdcceefc61597e519
 tags: 645f666f9bcd5a90fca523b33c5a78b7

_sources/classical-orbital-elements/orbital-elements-and-the-state-vector.md

@@ -83,7 +83,9 @@ Next, we need to calculate the orbital angular momentum. By definition, $\vector
 :::
 ::::
 
+<!-- markdownlint-disable MD033 -->
 We find $\vector{h} =$ {glue:text}`orbital-elements-h_vec-I:.0f` $\uvec{I}$ + {glue:text}`orbital-elements-h_vec-J:.0f` $\uvec{J}$ - {glue:text}`orbital-elements-h_vec-K:.0f` $\uvec{K}$ km<sup>2</sup>/s and $h =$ {glue:text}`orbital-elements-h:.3f` km<sup>2</sup>/s. Notice that the $Z$ component of the angular momentum is negative. This means the momentum vector is pointing down and the orbit is retrograde. The magnitude of the orbital angular momentum is the first orbital element.
+<!-- markdownlint-enable MD033 -->
 
 ### Step 3—Inclination
 
@@ -328,8 +330,10 @@ The sequence of rotations to convert from the perifocal frame to the inertial fr
 
 ::::{grid} 1
 ---
+
 gutter: 2
 ---
+
 :::{grid-item-card} Step 2.1—Rotate Until $\uvec{p}$ is Aligned With the Node Line
 
 By definition, the $\uvec{p}$ vector points towards periapsis. Therefore, it is also aligned with the eccentricity vector. If we rotate the frame around the $\uvec{w}$ axis until $\uvec{p}$ is aligned with the node line, this will align $\vector{e}$ with $\vector{N}$. This rotation is the negative of the argument of periapsis, $\omega$.
@@ -353,6 +357,7 @@ These three angles ($\omega$, $i$, and $\Omega$) are called [**Euler angles**](h
 
 ::::{tab-item} PYTHON
 ---
+
 sync: PYTHON
 ---
 
@@ -371,8 +376,10 @@ To actually perform the rotation, we need to multiply the position and velocity
 
 ::::{tab-item} MATLAB
 ---
+
 sync: MATLAB
 ---
+
 :::{literalinclude} scripts/orbital_elements_and_the_state_vector.m
 :start-after: "[section-9]"
 :end-before: "[section-10]"

_sources/constants-of-orbital-motion/angular-momentum-is-conserved.md

@@ -1,4 +1,5 @@
 (sec:conservation-of-angular-momentum)=
+
 # Angular Momentum Is Conserved In Orbital Motion
 
 The two masses $m_1$ and $m_2$ in the two-body problem form a _system_, so they must follow all of the conservation laws:

_sources/constants-of-orbital-motion/energy-is-conserved-in-orbital-motion.md

@@ -1,4 +1,5 @@
 (sec:conservation-of-energy)=
+
 # Energy Is Conserved In Orbital Motion
 
 The two masses $m_1$ and $m_2$ in the two-body problem form a _system_, so they must follow all of the conservation laws:

_sources/intro/reference-frames.md

@@ -12,6 +12,7 @@ The two types of reference frames are:
 Profound.
 
 (sec:inertial-reference-frame)=
+
 ### Inertial Reference Frame
 
 An **inertial** reference frame is one that is not _accelerating_. It may be moving at constant velocity, but there can be absolutely no acceleration, _including rotation!_

_sources/orbital-maneuvers/nonimpulsive-maneuver-example.ipynb

@@ -36,14 +36,14 @@
  "metadata": {},
  "outputs": [],
  "source": [
- "import numpy as np\n",
- "from scipy.integrate import solve_ivp\n",
  "# %matplotlib notebook\n",
  "import matplotlib.pyplot as plt\n",
+ "import numpy as np\n",
  "from matplotlib.patches import Circle\n",
+ "from scipy.integrate import solve_ivp\n",
  "\n",
  "R_E = 6378 # km\n",
- "mu = 3.986E5 # km**3/s**2\n",
+ "mu = 3.986e5 # km**3/s**2\n",
  "\n",
  "r_LEO = R_E + 300 # km\n",
  "v_LEO = np.sqrt(mu / r_LEO) # km/s\n",
@@ -52,12 +52,12 @@
  "\n",
  "r_0 = np.array((r_LEO, 0, 0)) # km\n",
  "v_0 = np.array((0, v_LEO, 0)) # km/s\n",
- "m_0 = np.array((1000)) # kg\n",
+ "m_0 = np.array(1000) # kg\n",
  "Y_0 = np.hstack((r_0, v_0, m_0))\n",
  "\n",
- "T = 2.5E-3 # kN\n",
+ "T = 2.5e-3 # kN\n",
  "I_sp = 10_000 # s\n",
- "g_0 = 9.807E-3 # km/s**2"
+ "g_0 = 9.807e-3 # km/s**2"
  ]
  },
  {
@@ -75,7 +75,7 @@
  "source": [
  "def nonimpulsive_maneuver(t, Y, mu, T, I_sp, g_0, r_2):\n",
  " \"\"\"Residual function for non-impulsive maneuvers.\n",
- " \n",
+ "\n",
  " t: Current simulation time\n",
  " Y: State vector [x y z xdot ydot zdot m], km, km/s, kg\n",
  " mu: Gravitational parameter, km**3/s**2\n",
@@ -89,7 +89,7 @@
  " dY_dt = np.zeros(len(Y))\n",
  " dY_dt[0:3] = Y[3:6]\n",
  " dY_dt[3:6] = -mu * Y[0:3] / r**3 + T * Y[3:6] / (m * v)\n",
- " dY_dt[-1] = - T / (I_sp * g_0)\n",
+ " dY_dt[-1] = -T / (I_sp * g_0)\n",
  " return dY_dt"
  ]
  },
@@ -112,7 +112,7 @@
  "source": [
  "def reached_destination(t, Y, mu, T, I_sp, g_0, r_2):\n",
  " \"\"\"Determine if the spacecraft reaches the destination radius.\n",
- " \n",
+ "\n",
  " Returns the difference between the current orbital radius and the\n",
  " destination radius.\n",
  " \"\"\"\n",
@@ -152,12 +152,13 @@
  "source": [
  "def mass(t, Y, mu, T, I_sp, g_0, r_2):\n",
  " \"\"\"Return the current mass of the spacecraft.\n",
- " \n",
+ "\n",
  " The mass is stored in the last element of the solution vector.\n",
  " If this becomes zero, the integration should terminate.\n",
  " \"\"\"\n",
  " return Y[-1]\n",
  "\n",
+ "\n",
  "mass.terminal = True"
  ]
  },
@@ -180,10 +181,11 @@
  "source": [
  "def orbit(t, Y, mu, T, I_sp, g_0, r_2):\n",
  " \"\"\"Trigger when the y-component of the position crosses zero.\n",
- " \n",
+ "\n",
  " Useful to count the number of orbits.\"\"\"\n",
  " return Y[1]\n",
  "\n",
+ "\n",
  "# Only trigger when going from negative to positive\n",
  "orbit.direction = 1"
  ]
@@ -222,17 +224,17 @@
  ],
  "source": [
  "t_end = 2_000_000 # s\n",
- "t_eval = np.linspace(0, t_end, int(1E6))\n",
+ "t_eval = np.linspace(0, t_end, int(1e6))\n",
  "sol = solve_ivp(\n",
  " nonimpulsive_maneuver,\n",
  " t_span=(0, t_end),\n",
  " y0=Y_0,\n",
  " t_eval=t_eval,\n",
  " events=(reached_destination, mass, orbit),\n",
- " rtol=1E-12,\n",
- " atol=1E-15,\n",
+ " rtol=1e-12,\n",
+ " atol=1e-15,\n",
  " method=\"DOP853\",\n",
- " args=(mu, T, I_sp, g_0, r_2)\n",
+ " args=(mu, T, I_sp, g_0, r_2),\n",
  ")\n",
  "print(sol.status)"
  ]
@@ -281,9 +283,9 @@
  "outputs": [],
  "source": [
  "r_vec = sol.y[0:3].T\n",
- "r = np.sqrt(r_vec[:, 0]**2 + r_vec[:, 1]**2 + r_vec[:, 2]**2)\n",
+ "r = np.sqrt(r_vec[:, 0] ** 2 + r_vec[:, 1] ** 2 + r_vec[:, 2] ** 2)\n",
  "v_vec = sol.y[3:6].T\n",
- "v = np.sqrt(v_vec[:, 0]**2 + v_vec[:, 1]**2 + v_vec[:, 2]**2)\n",
+ "v = np.sqrt(v_vec[:, 0] ** 2 + v_vec[:, 1] ** 2 + v_vec[:, 2] ** 2)\n",
  "m = sol.y[-1]"
  ]
  },
@@ -325,7 +327,7 @@
  "ax.add_patch(Circle((0, 0), r_2, ec=\"C1\", fc=\"none\", lw=2, ls=\"--\"))\n",
  "ax.plot(r_vec[:, 0], r_vec[:, 1], color=\"C2\")\n",
  "orbit_crossings = sol.y_events[2][:, 0]\n",
- "ax.plot(orbit_crossings, np.zeros(orbit_crossings.shape), 'ko', fillstyle='none')"
+ "ax.plot(orbit_crossings, np.zeros(orbit_crossings.shape), \"ko\", fillstyle=\"none\")"
  ]
  },
  {
@@ -425,7 +427,7 @@
  }
  ],
  "source": [
- "h_t = np.sqrt(2 * mu * r_LEO*r_2/(r_LEO + r_2))\n",
+ "h_t = np.sqrt(2 * mu * r_LEO * r_2 / (r_LEO + r_2))\n",
  "delta_v_1 = h_t / r_LEO - v_LEO\n",
  "delta_v_2 = np.sqrt(mu / r_2) - h_t / r_2\n",
  "delta_v_t = delta_v_1 + delta_v_2\n",
@@ -434,8 +436,10 @@
  "delta_m = m_0 * (1 - np.exp(-delta_v_t / (300 * g_0)))\n",
  "print(f\"The Δm for a Hohmann transfer is: {delta_m:.4F} kg\")\n",
  "\n",
- "transit_t = np.pi / np.sqrt(mu) * ((r_LEO + r_2) / 2)**(3/2)\n",
- "print(f\"The time of flight for a Hohmann transfer is: {transit_t / (3600 * 24):.4F} days\")"
+ "transit_t = np.pi / np.sqrt(mu) * ((r_LEO + r_2) / 2) ** (3 / 2)\n",
+ "print(\n",
+ " f\"The time of flight for a Hohmann transfer is: {transit_t / (3600 * 24):.4F} days\"\n",
+ ")"
  ]
  },
  {

_sources/orbital-maneuvers/plane-change-maneuvers.md

@@ -153,7 +153,7 @@ glue("plane-change-pure-rotation", fig, display=False)
 The required velocity increment as a function of dihedral angle for pure rotation maneuvers.
 :::
 
-As we can see from {numref}`fig:plane-change-pure-rotation`, plane change of about 24° requires the same $\Delta v$ as is needed to increase the speed to the escape velocity from a circular orbit, $\Delta v / v \approx$ 0.414. 
+As we can see from {numref}`fig:plane-change-pure-rotation`, plane change of about 24° requires the same $\Delta v$ as is needed to increase the speed to the escape velocity from a circular orbit, $\Delta v / v \approx$ 0.414.
 
 Similarly, a plane change of 60° requires a $\Delta v$ equal to the current spacecraft velocity! In LEO, the velocity is approximately 7.5 km/s. A plane change of 60°, with an $I_{sp}$ of 300, would require over 90% of the spacecraft mass to be propellant.
 

_sources/reference/planetary-ephemeris.md

@@ -359,10 +359,10 @@ The default interface of HORIZONS is shown in {numref}`fig:horizons-default`
 The default web interface for HORIZONS.
 :::
 
-Each of the options can be changed by clicking the *Edit* buttons. For our purposes, we can change the following:
+Each of the options can be changed by clicking the _Edit_ buttons. For our purposes, we can change the following:
 
 1. _Ephemeris Type_: Either _Vector Table_ or _Osculating Orbital Elements_ is suitable, although the latter is more direct for this example
-2. _Target Body_: This option opens a pop-up where we can search for the body of interest. In the drop-down menu under *Choose a method for specifying the target body*, you can choose *Select from a list of major bodies*, then choose *Mercury*
+2. _Target Body_: This option opens a pop-up where we can search for the body of interest. In the drop-down menu under _Choose a method for specifying the target body_, you can choose _Select from a list of major bodies_, then choose *Mercury*
 3. _Center_: The default selection here is _Solar System Barycenter_, the center of gravity of the entire solar system. This is usually a little bit outside the sun, depending on the relative locations of the planets, especially Jupiter. In our case, we want the center of the Sun as the focus of the orbit, so click _Edit_ and then type `@sun` into the search box.
 4. _Time Span_: This can be used to generate a range of dates, or to input specific dates. We will choose _Specify a list of times_ for this example, and then input the date of interest, in JDT, {glue:text}`planetary-ephemeris-JDT`.
 5. _Table Settings_: Here, we want to change the units to _km and seconds_. Another useful option is the _Reference plane_. The default of _ecliptic x-y plane derived from reference plane_ is appropriate for this example. You may also want to set the CSV output option, depending on how you will use the data.

_sources/reference/planetary-parameters.md

@@ -13,6 +13,7 @@ kernelspec:
 ---
 
 (sec:planetary-parameters)=
+
 # Planetary Parameters
 
 ## Planetary Mass Parameters