Naar aanleiding van een aantal vragen van luisteraar Bas, kijken we in deze ietwat lange aflevering naar hoe planeten rond sterren cirkelen. The mass-period distribution of close-in exoplanets: https://www.aanda.org/articles/aa/full_html/2011/04/aa15774-10/aa15774-10.html Halting Planet Migration In The Evacuated Centers Of Protoplanetary Disks: https://iopscience.iop.org/article/10.1086/342370/pdf Orbital migration of the planetary companion of 51 Pegasi to its present location: https://pages.astro.umd.edu/~dcr/reprints/lin_nature380,606.pdf Connecting the dots II: Phase changes in the climate dynamics of tidally locked terrestrial exoplanets: https://arxiv.org/pdf/1508.00419 The climate and habitability of planets with eternal day and night sides: https://serious-science.org/the-climate-and-habitability-of-planets-with-eternal-day-and-night-sides-5289 import numpy as np import matplotlib.pyplot as plt import matplotlib.ticker as ticker a = 1.0 # semi-major axis (AU) M2 = 1.0 # mass of the central body # M1: mass of the orbiting body, from 0 to 1 M1 = np.linspace(0, 1, 500) # Newton's law T = np.sqrt(a**3 / (M1 + M2)) fig, ax = plt.subplots(figsize=(9, 5.5)) fig.patch.set_facecolor("#0d1117") ax.set_facecolor("#0d1117") # Gradient-ish line via a LineCollection from matplotlib.collections import LineCollection points = np.array([M1, T]).T.reshape(-1, 1, 2) segments = np.concatenate([points[:-1], points[1:]], axis=1) norm = plt.Normalize(T.min(), T.max()) lc = LineCollection(segments, cmap="cool", norm=norm, linewidth=2.5, zorder=3) lc.set_array(T) ax.add_collection(lc) ax.scatter([0], [np.sqrt(a**3 / M2)], color="#ff6b9d", s=70, zorder=5, label=f"Test-particle limit (M₁→0, T={np.sqrt(a**3/M2):.3f} yr)") T_eq = np.sqrt(a**3 / (M2 + M2)) ax.scatter([M2], [T_eq], color="#ffd166", s=70, zorder=5, label=f"Equal masses (M₁=M₂={M2}, T={T_eq:.3f} yr)") for spine in ax.spines.values(): spine.set_edgecolor("#30363d") ax.tick_params(colors="#8b949e", labelsize=10) ax.xaxis.label.set_color("#c9d1d9") ax.yaxis.label.set_color("#c9d1d9") ax.set_xlabel("M₁ — Mass of orbiting body (M☉)", fontsize=12, labelpad=10) ax.set_ylabel("Orbital Period T (years)", fontsize=12, labelpad=10) ax.set_title("Orbital Period vs. Mass of Orbiting Body\n" r"$T = \sqrt{\,a^3\,/\,(M_1+M_2)\,}$" f" [a = {a} AU, M₂ = {M2} M☉]", color="#e6edf3", fontsize=13, pad=14) ax.set_xlim(-0.01, 1.01) ax.set_ylim(T.min() * 0.97, T.max() * 1.03) ax.grid(color="#21262d", linestyle="--", linewidth=0.7, zorder=0) ax.legend(facecolor="#161b22", edgecolor="#30363d", labelcolor="#c9d1d9", fontsize=10, loc="upper right") plt.tight_layout() plt.show() De Zimmerman en Space podcast is gelicenseerd onder een Creative Commons CC0 1.0 licentie. http://creativecommons.org/publicdomain/zero/1.0
