diff --git a/.github/workflows/deploy-book.yml b/.github/workflows/deploy-book.yml index 36afc693..7fd2df17 100644 --- a/.github/workflows/deploy-book.yml +++ b/.github/workflows/deploy-book.yml @@ -7,26 +7,29 @@ on: pull_request: branches: [main] -# This job installs dependencies, build the book, and pushes it to `gh-pages` +env: + PYDEVD_DISABLE_FILE_VALIDATION: 1 + +# This job installs dependencies, builds the book, and pushes it to `gh-pages` jobs: deploy-book: runs-on: ubuntu-latest steps: - - uses: actions/checkout@v2 + - uses: actions/checkout@v4 - name: Setup PDM - uses: pdm-project/setup-pdm@v3 + uses: pdm-project/setup-pdm@v4 with: cache: true - python-version: "3.10" + python-version: "3.11" - name: Install dependencies - run: pdm sync --prod --no-self + run: pdm sync --prod # Build the book - name: Build the book run: pdm run jupyter-book build -vv -W . # Push the book's HTML to github-pages - name: GitHub Pages action if: github.ref == 'refs/heads/main' - uses: peaceiris/actions-gh-pages@v3.9.2 + uses: peaceiris/actions-gh-pages@v3.9.3 with: github_token: ${{ secrets.GITHUB_TOKEN }} publish_dir: ./_build/html diff --git a/.markdownlint-cli2.jsonc b/.markdownlint-cli2.jsonc new file mode 100644 index 00000000..9b305b25 --- /dev/null +++ b/.markdownlint-cli2.jsonc @@ -0,0 +1,7 @@ +{ + "globs": ["**/*.md", "!.venv"], + "config": { + "MD013": false, + "MD037": false + } +} diff --git a/.mise.toml b/.mise.toml new file mode 100644 index 00000000..350f455e --- /dev/null +++ b/.mise.toml @@ -0,0 +1,8 @@ +[tools] +python = { version = "3.11", virtualenv = ".venv" } +markdownlint-cli2 = "latest" +pdm = "latest" + +[plugins] +pdm = "https://github.com/1oglop1/asdf-pdm" +markdownlint-cli2 = "https://github.com/paulo-ferraz-oliveira/asdf-markdownlint-cli2" diff --git a/.vscode/settings.json b/.vscode/settings.json index 8516b3e0..e638ce01 100644 --- a/.vscode/settings.json +++ b/.vscode/settings.json @@ -1,9 +1,4 @@ { - "python.formatting.provider": "black", - "python.linting.enabled": true, - "python.linting.mypyEnabled": true, - "python.linting.flake8Enabled": true, - "python.linting.lintOnSave": true, "cSpell.words": [ "apoapsis", "deorbit", diff --git a/INSTALL.md b/INSTALL.md new file mode 100644 index 00000000..dcdf9924 --- /dev/null +++ b/INSTALL.md @@ -0,0 +1,5 @@ +# Install/Build the Book + +The repo is set up to use [mise](https://mise.jdx.dev) to install required tools. Once `mise` is installed, changing into this directory should install the correct tools with the right versions. + +After that, running `pdm install` should install the dependencies. Then `doit build_jb` will build the book. diff --git a/LICENSE.txt b/LICENSE.txt new file mode 100644 index 00000000..7d4f96c5 --- /dev/null +++ b/LICENSE.txt @@ -0,0 +1,427 @@ +Attribution-ShareAlike 4.0 International + +======================================================================= + +Creative Commons Corporation ("Creative Commons") is not a law firm and +does not provide legal services or legal advice. Distribution of +Creative Commons public licenses does not create a lawyer-client or +other relationship. Creative Commons makes its licenses and related +information available on an "as-is" basis. Creative Commons gives no +warranties regarding its licenses, any material licensed under their +terms and conditions, or any related information. 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Except for the limited purpose of indicating that +material is shared under a Creative Commons public license or as +otherwise permitted by the Creative Commons policies published at +creativecommons.org/policies, Creative Commons does not authorize the +use of the trademark "Creative Commons" or any other trademark or logo +of Creative Commons without its prior written consent including, +without limitation, in connection with any unauthorized modifications +to any of its public licenses or any other arrangements, +understandings, or agreements concerning use of licensed material. For +the avoidance of doubt, this paragraph does not form part of the +public licenses. + +Creative Commons may be contacted at creativecommons.org. diff --git a/_config.yml b/_config.yml index a243cd55..2b304ae2 100644 --- a/_config.yml +++ b/_config.yml @@ -12,6 +12,7 @@ exclude_patterns: - chapter-4 - .venv - .pytest_cache + - INSTALL.md latex: latex_engine: xelatex diff --git a/classical-orbital-elements/right-ascension-declination.md b/classical-orbital-elements/right-ascension-declination.md index 90ba8962..4171b483 100644 --- a/classical-orbital-elements/right-ascension-declination.md +++ b/classical-orbital-elements/right-ascension-declination.md @@ -29,7 +29,7 @@ Another way to view the equinox is as the line generated by the intersection of As seen from the Northern Hemisphere on Earth, any objects with a declination of approximately 90° - $\phi$, where $\phi$ is the observers latitude, will remain above the horizon all the time. These objects will appear to trace circles around the north celestial pole. The closer an object's declination is to +90°, the smaller the circle it traces. The star Polaris is currently quite close to the north celestial pole and is known as the North Star. Likewise, the constellation Usra Minor (the Little Dipper) never sets. -Other constellations, such as Orion (and the stars Belegeuse and Rigel) have declinations of only about +7.5°, so from New England they appear to rise and set each night. +Other constellations, such as Orion (and the stars Betelgeuse and Rigel) have declinations of only about +7.5°, so from New England they appear to rise and set each night. 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+ "poliastro>=0.18.dev0", + "scipy>=1.12.0", + "skyfield>=1.47", + "sphinx-design>=0.5.0", + "sympy>=1.12", + "wheel>=0.42.0", +] +# Numba 0.58.1 requires Python < 3.12 +requires-python = ">=3.10,<3.12" +name = "orbital-mechanics-notes" +version = "2024.01.0" +description = "Orbital Mechanics Notes built with JupyterBook" +authors = [ + {name = "Bryan Weber", email = "bryan.w.weber@gmail.com"}, +] +license = {text = "CC-BY-SA-4.0"} + [tool.pdm] +distribution = false + [tool.pdm.dev-dependencies] dev = [ - "black[jupyter]>=23.1.0", - "flake8>=6.0.0", "doit>=0.36.0", - "pyyaml>=6.0", - "mypy>=0.991", + "pyyaml>=6.0.1", + "mypy>=1.8.0", + "ruff>=0.1.14", ] +[tool.pdm.resolution.overrides] +# Unfortunately, poliastro is no longer maintained. I updated some dependencies on my +# fork to be able to upgrade some other things like astropy. Nothing seems to be broken +# but I'll need a replacement here at some point. +"poliastro" = "https://github.com/bryanwweber/poliastro/archive/main.zip" -[project] -# PEP 621 project metadata -# See https://www.python.org/dev/peps/pep-0621/ -name = "orbital-mechanics-notes" -dependencies = [ - "astropy", - "docutils>=0.17,!=0.18.*,!=0.19.*", - "ipympl", - "jupyter-book~=0.15.0", - "matplotlib", - "myst-nb-bokeh>=1.0", - "myst-nb>=0.17.1,<0.18", - "numpy", - "pint>=0.20.1", - "plotly", - "poliastro", - "scipy", - "skyfield>=1.45", - "sphinx-design>=0.3.0", - "sympy", - "wheel>=0.38.4", +[tool.ruff] +extend-include = ["*.ipynb"] +select = [ + "E", # pycodestyle + "W", # pycodestyle + "F", # pyflakes + "I", # isort + "UP", # pyupgrade + "NPY", # NumPy rules + "RUF", # Ruff rules ] -requires-python = ">=3.9,<3.11" diff --git a/time-since-periapsis-and-keplers-equation/universal-lagrange-coefficients-example.md b/time-since-periapsis-and-keplers-equation/universal-lagrange-coefficients-example.md index 84b02d09..444faf81 100644 --- a/time-since-periapsis-and-keplers-equation/universal-lagrange-coefficients-example.md +++ b/time-since-periapsis-and-keplers-equation/universal-lagrange-coefficients-example.md @@ -82,8 +82,8 @@ Since $\alpha$ is positive, this must be an elliptical orbit. Now we have enough information to solve the universal Kepler equation. ```{code-cell} ipython3 -def stumpff_0(z): - """Solve the Stumpff function C(z) = c0(z). The input z should be +def stumpff_2(z): + """Solve the Stumpff function C(z) = c2(z). The input z should be a scalar value. """ if z > 0: @@ -93,8 +93,8 @@ def stumpff_0(z): else: return 1/2 -def stumpff_1(z): - """Solve the Stumpff function S(z) = c1(z). The input z should be +def stumpff_3(z): + """Solve the Stumpff function S(z) = c3(z). The input z should be a scalar value. """ if z > 0: @@ -106,13 +106,13 @@ def stumpff_1(z): def universal_kepler(chi, r_0, v_r0, alpha, delta_t, mu): """Solve the universal Kepler equation in terms of the universal anomaly chi. - + This function is intended to be used with an iterative solution algorithm, such as Newton's algorithm. """ z = alpha * chi**2 - first_term = r_0 * v_r0 / np.sqrt(mu) * chi**2 * stumpff_0(z) - second_term = (1 - alpha * r_0) * chi**3 * stumpff_1(z) + first_term = r_0 * v_r0 / np.sqrt(mu) * chi**2 * stumpff_2(z) + second_term = (1 - alpha * r_0) * chi**3 * stumpff_3(z) third_term = r_0 * chi fourth_term = np.sqrt(mu) * delta_t return first_term + second_term + third_term - fourth_term @@ -120,8 +120,8 @@ def universal_kepler(chi, r_0, v_r0, alpha, delta_t, mu): def d_universal_d_chi(chi, r_0, v_r0, alpha, delta_t, mu): """The derivative of the universal Kepler equation in terms of the universal anomaly.""" z = alpha * chi**2 - first_term = r_0 * v_r0 / np.sqrt(mu) * chi * (1 - z * stumpff_1(z)) - second_term = (1 - alpha * r_0) * chi**2 * stumpff_0(z) + first_term = r_0 * v_r0 / np.sqrt(mu) * chi * (1 - z * stumpff_3(z)) + second_term = (1 - alpha * r_0) * chi**2 * stumpff_2(z) third_term = r_0 return first_term + second_term + third_term @@ -141,8 +141,8 @@ Now we can solve the equations to find the Lagrange coefficients, and then the p ```{code-cell} ipython3 z = alpha * chi**2 -f = 1 - chi**2 / r_0 * stumpff_0(z) -g = delta_t - chi**3 / np.sqrt(mu) * stumpff_1(z) +f = 1 - chi**2 / r_0 * stumpff_2(z) +g = delta_t - chi**3 / np.sqrt(mu) * stumpff_3(z) vec_r = f * vec_r_0 + g * vec_v_0 r = np.sqrt(vec_r.dot(vec_r)) @@ -151,8 +151,8 @@ print(round(r, 3), "km") ``` ```{code-cell} ipython3 -fdot = chi * np.sqrt(mu) / (r * r_0) * (z * stumpff_1(z) - 1) -gdot = 1 - chi**2 / r * stumpff_0(z) +fdot = chi * np.sqrt(mu) / (r * r_0) * (z * stumpff_3(z) - 1) +gdot = 1 - chi**2 / r * stumpff_2(z) vec_v = fdot * vec_r_0 + gdot * vec_v_0 v = np.sqrt(vec_v.dot(vec_v)) diff --git a/time-since-periapsis-and-keplers-equation/universal-variables-example.md b/time-since-periapsis-and-keplers-equation/universal-variables-example.md index 083673aa..edc804ea 100644 --- a/time-since-periapsis-and-keplers-equation/universal-variables-example.md +++ b/time-since-periapsis-and-keplers-equation/universal-variables-example.md @@ -89,7 +89,7 @@ where $z = \alpha\chi^2$. The derivative of this function is: $$f'(\chi) = \frac{r_0v_{r,0}}{\sqrt{\mu}} \chi\left(1 - z S(z)\right) + \left(1 - \alpha r_0\right) \chi^2 C(z) + r_0$$ -The Stumpff functions $C(z) = c_0(z)$ and $S(z) = c_1(z)$ are: +The Stumpff functions $C(z) = c_2(z)$ and $S(z) = c_3(z)$ are: $$C(z) = \begin{cases}\displaystyle \frac{1 - \cos\sqrt{z}}{z} & \left(z > 0\right)\\ \displaystyle\frac{\cosh\sqrt{-z} - 1}{-z} & \left(z < 0\right) \\ \displaystyle\frac{1}{2} & \left(z = 0\right)\end{cases}$$ @@ -98,8 +98,8 @@ and $$S(z) =\begin{cases}\displaystyle \frac{\sqrt{z} - \sin\sqrt{z}}{\left(\sqrt{z}\right)^3} & \left(z > 0\right)\\ \displaystyle \frac{\sinh\sqrt{-z} - \sqrt{-z}}{\left(\sqrt{-z}\right)^3} & \left(z < 0\right) \\ \displaystyle \frac{1}{6} & \left(z = 0\right)\end{cases}$$ ```{code-cell} ipython3 -def stumpff_0(z): - """Solve the Stumpff function C(z) = c0(z). The input z should be +def stumpff_2(z): + """Solve the Stumpff function C(z) = c2(z). The input z should be a scalar value. """ if z > 0: @@ -109,8 +109,8 @@ def stumpff_0(z): else: return 1/2 -def stumpff_1(z): - """Solve the Stumpff function S(z) = c1(z). The input z should be +def stumpff_3(z): + """Solve the Stumpff function S(z) = c3(z). The input z should be a scalar value. """ if z > 0: @@ -122,13 +122,13 @@ def stumpff_1(z): def universal_kepler(chi, r_0, v_r0, alpha, delta_t, mu): """Solve the universal Kepler equation in terms of the universal anomaly chi. - + This function is intended to be used with an iterative solution algorithm, such as Newton's algorithm. """ z = alpha * chi**2 - first_term = r_0 * v_r0 / np.sqrt(mu) * chi**2 * stumpff_0(z) - second_term = (1 - alpha * r_0) * chi**3 * stumpff_1(z) + first_term = r_0 * v_r0 / np.sqrt(mu) * chi**2 * stumpff_2(z) + second_term = (1 - alpha * r_0) * chi**3 * stumpff_3(z) third_term = r_0 * chi fourth_term = np.sqrt(mu) * delta_t return first_term + second_term + third_term - fourth_term @@ -136,8 +136,8 @@ def universal_kepler(chi, r_0, v_r0, alpha, delta_t, mu): def d_universal_d_chi(chi, r_0, v_r0, alpha, delta_t, mu): """The derivative of the universal Kepler equation in terms of the universal anomaly.""" z = alpha * chi**2 - first_term = r_0 * v_r0 / np.sqrt(mu) * chi * (1 - z * stumpff_1(z)) - second_term = (1 - alpha * r_0) * chi**2 * stumpff_0(z) + first_term = r_0 * v_r0 / np.sqrt(mu) * chi * (1 - z * stumpff_3(z)) + second_term = (1 - alpha * r_0) * chi**2 * stumpff_2(z) third_term = r_0 return first_term + second_term + third_term ``` diff --git a/time-since-periapsis-and-keplers-equation/universal-variables.md b/time-since-periapsis-and-keplers-equation/universal-variables.md index 49d16d92..c889ec56 100644 --- a/time-since-periapsis-and-keplers-equation/universal-variables.md +++ b/time-since-periapsis-and-keplers-equation/universal-variables.md @@ -48,13 +48,13 @@ Then, we will define the universal variable, or universal anomaly $\chi$, which Using the universal anomaly, we can find the position and velocity of the orbiting mass at any future time via: :::{math} -:label: +:label: eq:radius-velocity-universal-anomaly \begin{aligned}\vector{r} &= \left[1 - \frac{\chi^2}{r_0}C\left(\alpha\chi^2\right)\right]\vector{r}_0 + \left[\left(t - t_0\right) - \frac{\chi^3}{\sqrt{\mu}}S\left(\alpha\chi^2\right)\right]\vector{v}_0\\\vector{v} &= \frac{\chi\sqrt{\mu}}{r r_0}\left[\alpha\chi^2S\left(\alpha\chi^2\right) - 1\right]\vector{r}_0 + \left[1 - \frac{\chi^2}{r}C\left(\alpha\chi^2\right)\right]\vector{v}_0\end{aligned} ::: -where $\alpha = 1/a$ and we will define $C(z)$ and $S(z)$ shortly. Note that $\alpha < 0$ for hyperbolas, $\alpha = 0$ for parabolas ($a\rightarrow\infty$) and $\alpha > 0$ for ellipses. Interestingly, this gives $\chi$ dimensions of square root of length, such that $\alpha\chi^2$ is dimensionless. +where $\alpha = 1/a$ and we will define $C(z)$ and $S(z)$ shortly. Note that $\alpha < 0$ for hyperbolas, $\alpha = 0$ for parabolas ($a\rightarrow\infty$) and $\alpha > 0$ for ellipses. This gives $\chi$ dimensions of square root of length, such that $\alpha\chi^2$ is dimensionless. -In a [previous section](./the-lagrange-coefficients.md), we identified the coefficients of $\vector{r}_0$ and $\vector{v}_0$ in similar equations as the **Lagrange coefficients**, in that case, in terms of the change of true anomaly. These equations give the Lagrange coefficients in terms of the universal anomaly. +In a [previous section](./the-lagrange-coefficients.md), we identified the coefficients of $\vector{r}_0$ and $\vector{v}_0$ in equations similar to {eq}`eq:radius-velocity-universal-anomaly` as the **Lagrange coefficients**, in that case, in terms of the change of true anomaly. Eqs. {eq}`eq:radius-velocity-universal-anomaly` give the Lagrange coefficients in terms of the universal anomaly. Now, we need a way to solve for $\chi$, the universal anomaly. We can write Kepler's equation in terms of the universal anomaly as: @@ -65,6 +65,8 @@ Now, we need a way to solve for $\chi$, the universal anomaly. We can write Kepl Like Kepler's equation in the ellipse and hyperbola specific forms, this equation is transcendental in $\chi$. If $\chi$ is known, the equation can be solved for the change in time interval, $t - t_0$. If the time interval is known instead, we must use numerical techniques to solve the equation. +Next, we need to define the functions $C(z)$ and $S(z)$. + ## Stumpff Functions The functions $C(z)$ and $S(z)$ are [**Stumpff functions**](https://en.wikipedia.org/wiki/Stumpff_function). They can be defined by infinite series of the form: @@ -74,7 +76,9 @@ The functions $C(z)$ and $S(z)$ are [**Stumpff functions**](https://en.wikipedia c_k(z) = \frac{1}{k!} - \frac{z}{\left(k + 2\right)!} + \frac{z^2}{\left(k + 4\right)!} - \cdots = \sum_{i=0}^{\infty}\frac{\left(-1\right)^{i} z^i}{\left(k + 2i\right)!} ::: -where $k$ is an integer that indicates the type of Stumpff function. Interestingly, the Stumpff functions are related to the Taylor series expansions of the circular and hyperbolic trigonometric functions. The first two Stumpff functions, $k=0$ and $k=1$ respectively, define our $C(z)$ and $S(z)$ functions from above. +where $k$ is an integer that indicates the type of Stumpff function. + +To solve Eq. {eq}`eq:universal-keplers-equation`, we don't want to work with the infinite series forms of the Stumpff equations. Instead, we will convert the Stumpff functions to trigonometric functions using the Taylor series expansions of the [circular](https://en.wikipedia.org/wiki/Trigonometric_functions#Power_series_expansion) and [hyperbolic](https://en.wikipedia.org/wiki/Hyperbolic_functions#Taylor_series_expressions) trigonometric functions. The first third and fourth Stumpff functions, $k=2$ and $k=3$ respectively, define our $C(z)$ and $S(z)$ functions from above. :::{math} :label: eq:stumpff-function-0 @@ -99,7 +103,7 @@ from functools import partial from myst_nb import glue as myst_glue glue = partial(myst_glue, display=False) -def stumpff_0(z): +def stumpff_2(z): x = np.full_like(z, np.nan) x[z > 0] = (1 - np.cos(np.sqrt(z[z > 0]))) / z[z > 0] x[z < 0] = (np.cosh(np.sqrt(-z[z < 0])) - 1) / (-z[z < 0]) @@ -107,7 +111,7 @@ def stumpff_0(z): return x -def stumpff_1(z): +def stumpff_3(z): x = np.full_like(z, np.nan) z_gt_0 = z[z > 0] z_lt_0 = z[z < 0] @@ -120,12 +124,12 @@ x_1 = np.linspace(-50, 0, 100) x_2 = np.linspace(0, 30, 100) x_3 = np.linspace(30, 500, 300) -y0_1 = stumpff_0(x_1) -y1_1 = stumpff_1(x_1) -y0_2 = stumpff_0(x_2) -y1_2 = stumpff_1(x_2) -y0_3 = stumpff_0(x_3) -y1_3 = stumpff_1(x_3) +y0_1 = stumpff_2(x_1) +y1_1 = stumpff_3(x_1) +y0_2 = stumpff_2(x_2) +y1_2 = stumpff_3(x_2) +y0_3 = stumpff_2(x_3) +y1_3 = stumpff_3(x_3) fig, (ax_1, ax_2, ax_3) = plt.subplots(figsize=(4, 6), dpi=200, nrows=3) ax_1.plot(x_1, y0_1, label="$C(z)$") ax_1.plot(x_1, y1_1, label="$S(z)$")