Formatting

chapter-4/7-effects-of-the-earths-oblateness.md

@@ -30,6 +30,7 @@ Therefore, it is sufficient to define any two of $a$, $b$, or $f$ to define the
 
 The parameters specified in the WGS84 standard are:
 
+<!-- markdownlint-disable MD033 -->
 | Parameter | Value |
 |----------------|----------------------------------------------------------------------------------|
 | $a$ | 6,378,137.0 m |
@@ -38,14 +39,17 @@ The parameters specified in the WGS84 standard are:
 | Zero Longitude | [IERS Reference Meridian](https://en.wikipedia.org/wiki/IERS_Reference_Meridian) |
 | $\mu$ | 3986004.418×10<sup>8</sup> m³/s². |
 | $\omega_E$ | 72.92115×10<sup>−6</sup> rad/s |
+<!-- markdownline-enable MD033 -->
 
 For even more accurate orbit calculations, particularly over longer time scales, it is necessary to map the variations in the earth's gravitational field due to things such as the tides, mountain ranges, oceans, and more. These effects are represented in a model called the [**Earth Gravitational Model**](https://en.wikipedia.org/wiki/Earth_Gravitational_Model) (EGM). The most recent EGM is from 2008 and relies on high accuracy satellite measurements of Earth's gravitational field.
 
 [EGM2008](https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2011JB008916) specifies the geoid of the earth to very high accuracy, as low as 10 cm in places. The EGM2008 is a model fit to the available experimental data, using [spherical harmonic equations](https://en.wikipedia.org/wiki/Spherical_harmonics) of extremely high order, resulting in [many millions of coefficients](https://earth-info.nga.mil/GandG/wgs84/gravitymod/new_egm/new_egm.html) in the model.
 
 ## Effect of Oblateness on Orbits
 
+<!-- markdownlint-disable MD033 -->
 The effect of planetary oblateness on orbits is captured in the dimensionless parameter called $J_2$, the **second zonal harmonic**. The zonal harmonics are values that depend on the particular planet. For Earth, $J_2 =$ 1.08263×10<sup>-3</sup> {cite}`Vallado2013` (Page 1039).
+<!-- markdownlint-enable MD033 -->
 
 The effect of oblateness is to cause the right ascension of the ascending node and the argument of the periapsis to change as a function of time. The average rate of change of these variables is:
 

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]"

classical-orbital-elements/scripts/definition_of_argument_of_periapsis.py

@@ -1,18 +1,17 @@
 #!/usr/bin/env python
-# coding: utf-8
 
-# **The canonical version of this is in `classical-orbital-elements/scripts/definition-of-raan.py`.**
+# **The canonical version of this is in
+# `classical-orbital-elements/scripts/definition-of-raan.py`.**
 #
 # This Notebook is here for interactive experimentation.
 
 # In[1]:
 
 
-import plotly.graph_objects as go
 import numpy as np
+import plotly.graph_objects as go
 from scipy.spatial.transform import Rotation as R
 
-
 # In[2]:
 
 
@@ -70,9 +69,9 @@ def arrow(start, end, fig=None, **kwargs):
 
 a = 100
 e = 0.4
-b = a * np.sqrt(1 - e ** 2)
+b = a * np.sqrt(1 - e**2)
 r_p = a * (1 - e)
-p = a * (1 - e ** 2)
+p = a * (1 - e**2)
 
 inclination = 30
 raan = 30
@@ -83,7 +82,7 @@ def arrow(start, end, fig=None, **kwargs):
 theta = np.arange(0, 2 * np.pi, step=0.01)
 phi = 0
 # https://math.stackexchange.com/a/819533
-r = a * (1 - e ** 2) / (1 - e * np.cos(theta - phi))
+r = a * (1 - e**2) / (1 - e * np.cos(theta - phi))
 x = r * np.cos(theta)
 y = r * np.sin(theta)
 z = np.zeros_like(x)

classical-orbital-elements/scripts/definition_of_inclination.py

@@ -1,14 +1,12 @@
 #!/usr/bin/env python
-# coding: utf-8
 
 # In[1]:
 
 
-import plotly.graph_objects as go
 import numpy as np
+import plotly.graph_objects as go
 from scipy.spatial.transform import Rotation as R
 
-
 # In[2]:
 
 
@@ -66,7 +64,7 @@ def arrow(start, end, fig=None, **kwargs):
 
 a = 100
 e = 0.4
-b = a * np.sqrt(1 - e ** 2)
+b = a * np.sqrt(1 - e**2)
 r_p = a * (1 - e)
 
 inclination = 30
@@ -77,7 +75,7 @@ def arrow(start, end, fig=None, **kwargs):
 
 theta = np.arange(0, 2 * np.pi, step=0.01)
 phi = 0
-r = a * (1 - e ** 2) / (1 - e * np.cos(theta - phi))
+r = a * (1 - e**2) / (1 - e * np.cos(theta - phi))
 x = r * np.cos(theta)
 y = r * np.sin(theta)
 z = np.zeros_like(x)

classical-orbital-elements/scripts/definition_of_raan.py

@@ -1,18 +1,17 @@
 #!/usr/bin/env python
-# coding: utf-8
 
-# **The canonical version of this is in `classical-orbital-elements/scripts/definition-of-raan.py`.**
+# **The canonical version of this is in
+# `classical-orbital-elements/scripts/definition-of-raan.py`.**
 #
 # This Notebook is here for interactive experimentation.
 
 # In[1]:
 
 
-import plotly.graph_objects as go
 import numpy as np
+import plotly.graph_objects as go
 from scipy.spatial.transform import Rotation as R
 
-
 # In[2]:
 
 
@@ -70,9 +69,9 @@ def arrow(start, end, fig=None, **kwargs):
 
 a = 100
 e = 0.4
-b = a * np.sqrt(1 - e ** 2)
+b = a * np.sqrt(1 - e**2)
 r_p = a * (1 - e)
-p = a * (1 - e ** 2)
+p = a * (1 - e**2)
 
 inclination = 30
 raan = 30
@@ -83,7 +82,7 @@ def arrow(start, end, fig=None, **kwargs):
 theta = np.arange(0, 2 * np.pi, step=0.01)
 phi = 0
 # https://math.stackexchange.com/a/819533
-r = a * (1 - e ** 2) / (1 - e * np.cos(theta - phi))
+r = a * (1 - e**2) / (1 - e * np.cos(theta - phi))
 x = r * np.cos(theta)
 y = r * np.sin(theta)
 z = np.zeros_like(x)

classical-orbital-elements/scripts/orbital_elements_and_the_state_vector.py

@@ -8,7 +8,7 @@
 r = np.linalg.norm(r_vec)
 v = np.linalg.norm(v_vec)
 v_r = np.dot(r_vec / r, v_vec)
-v_p = np.sqrt(v ** 2 - v_r ** 2)
+v_p = np.sqrt(v**2 - v_r**2)
 
 # [section-2]
 h_vec = np.cross(r_vec, v_vec)
@@ -34,7 +34,7 @@
 nu = np.arccos(np.dot(r_vec / r, e_vec / e))
 
 # [section-8]
-r_w = h ** 2 / mu / (1 + e * np.cos(nu)) * np.array((np.cos(nu), np.sin(nu), 0))
+r_w = h**2 / mu / (1 + e * np.cos(nu)) * np.array((np.cos(nu), np.sin(nu), 0))
 v_w = mu / h * np.array((-np.sin(nu), e + np.cos(nu), 0))
 
 # [section-9]

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:

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:

dodo.py

@@ -1,8 +1,9 @@
 from pathlib import Path
-from doit.action import CmdAction
-import yaml
 from textwrap import dedent
 
+import yaml
+from doit.action import CmdAction
+
 from raw_svg import render_math_svg
 
 HERE = Path(__file__).parent