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November 12, 2025 01:55
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Simulate astrometry for a Gaia exoplanet
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "id": "a6c2b132", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import astropy.coordinates as coord\n", | |
| "import astropy.units as u\n", | |
| "import matplotlib as mpl\n", | |
| "import matplotlib.pyplot as plt\n", | |
| "import numpy as np\n", | |
| "\n", | |
| "%matplotlib inline\n", | |
| "from scipy.spatial.transform import Rotation\n", | |
| "\n", | |
| "import jax\n", | |
| "\n", | |
| "jax.config.update(\"jax_enable_x64\", True)\n", | |
| "from jaxoplanet.orbits.keplerian import Central, System, Body" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "3d814809", | |
| "metadata": {}, | |
| "source": [ | |
| "# Simulate an astrometric orbit with `jaxoplanet`" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "effa93d9", | |
| "metadata": {}, | |
| "source": [ | |
| "Units should be: (solar mass, solar radius, day)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 88, | |
| "id": "962762c1", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "P = (1.84 * u.year).to_value(u.day)\n", | |
| "M1 = 1.0 # Msun\n", | |
| "M2 = (10.0 * u.Mjup).to_value(u.Msun)\n", | |
| "\n", | |
| "sys = System(Central(mass=M1, radius=1.0))\n", | |
| "sys = sys.add_body(Body(period=P, mass=M2, eccentricity=0.0, omega_peri=0.0))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 89, | |
| "id": "0041340e", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "(3, 5000)" | |
| ] | |
| }, | |
| "execution_count": 89, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "time_grid = np.arange(0, 5, 0.001) * 365 # 5 years, i.e. Gaia DR4\n", | |
| "star_orb_xyz = np.stack([x[0] for x in sys.central_position(time_grid)], axis=0)\n", | |
| "star_orb_vxyz = np.stack([x[0] for x in sys.central_velocity(time_grid)], axis=0)\n", | |
| "star_orb_xyz.shape" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 90, | |
| "id": "4aacf1ea", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "from astropy.constants import G\n", | |
| "\n", | |
| "a = np.cbrt((P * u.day) ** 2 * G * (M1 + M2) * u.Msun / (4 * np.pi**2)).to(u.Rsun)\n", | |
| "assert np.isclose(a.value, sys.bodies[0].semimajor)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 91, | |
| "id": "b2a221b7", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "star_a = a.value * 1 / (1 + M1 / M2)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 92, | |
| "id": "90520987", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "Text(0, 0.5, 'star orbit y [$\\\\mathrm{R_{\\\\odot}}$]')" | |
| ] | |
| }, | |
| "execution_count": 92, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 432x432 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "image/png": { | |
| "height": 431, | |
| "width": 440 | |
| } | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = plt.subplots()\n", | |
| "ax.plot(star_orb_xyz[0], star_orb_xyz[2], ls=\"\")\n", | |
| "ax.add_artist(plt.Circle((0, 0), star_a, color=\"tab:blue\", alpha=0.5))\n", | |
| "ax.set_aspect(\"equal\")\n", | |
| "ax.set_xlabel(f\"star orbit x [{u.Rsun:latex_inline}]\")\n", | |
| "ax.set_ylabel(f\"star orbit y [{u.Rsun:latex_inline}]\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "5f92de57", | |
| "metadata": {}, | |
| "source": [ | |
| "### Simulate astrometry with astropy\n", | |
| "\n", | |
| "Generate a position and velocity of the star (well, barycenter) with respect to the Sun (ICRS frame). Also set the orientation of the two-body system using the standard orbital elements." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 93, | |
| "id": "80444865", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Position = [ 6.0943416 -20.79968212 15.00902392] pc, Distance = 26.36358425718516 pc\n", | |
| "Velocity = [ 14.10847075 -29.26552783 -19.5326926 ] km / s\n", | |
| "Inclination = 1.0212746299596132 rad Omega = 0.8049616944763924 rad omega = 4.938987693414485 rad\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "rng = np.random.default_rng(seed=42)\n", | |
| "\n", | |
| "# Note: This makes the star close! Just for testing\n", | |
| "star_xyz = rng.normal(scale=20.0, size=3) * u.pc\n", | |
| "star_vxyz = rng.normal(scale=15.0, size=3) * u.km / u.s\n", | |
| "\n", | |
| "incl = np.arccos(rng.uniform(-1, 1)) * u.rad\n", | |
| "omega = rng.uniform(0, 2 * np.pi) * u.rad\n", | |
| "Omega = rng.uniform(0, 2 * np.pi) * u.rad\n", | |
| "\n", | |
| "print(f\"Position = {star_xyz}, Distance = {np.linalg.norm(star_xyz)}\")\n", | |
| "print(f\"Velocity = {star_vxyz}\")\n", | |
| "print(\"Inclination =\", incl, \"Omega =\", Omega, \"omega =\", omega)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 94, | |
| "id": "60820d3e", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "R = (\n", | |
| " Rotation.from_euler(\"z\", Omega.to_value(u.radian))\n", | |
| " * Rotation.from_euler(\"x\", incl.to_value(u.radian))\n", | |
| " * Rotation.from_euler(\"z\", omega.to_value(u.radian))\n", | |
| ").as_matrix()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 95, | |
| "id": "3e2e7e93", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "/var/folders/67/2zgxpmyd2z183j4k6r33nf740000gr/T/ipykernel_75264/3977179411.py:1: RuntimeWarning: divide by zero encountered in matmul\n", | |
| " star_orb_xyz_R = R @ star_orb_xyz\n", | |
| "/var/folders/67/2zgxpmyd2z183j4k6r33nf740000gr/T/ipykernel_75264/3977179411.py:1: RuntimeWarning: overflow encountered in matmul\n", | |
| " star_orb_xyz_R = R @ star_orb_xyz\n", | |
| "/var/folders/67/2zgxpmyd2z183j4k6r33nf740000gr/T/ipykernel_75264/3977179411.py:1: RuntimeWarning: invalid value encountered in matmul\n", | |
| " star_orb_xyz_R = R @ star_orb_xyz\n", | |
| "/var/folders/67/2zgxpmyd2z183j4k6r33nf740000gr/T/ipykernel_75264/3977179411.py:2: RuntimeWarning: divide by zero encountered in matmul\n", | |
| " star_orb_vxyz_R = R @ star_orb_vxyz\n", | |
| "/var/folders/67/2zgxpmyd2z183j4k6r33nf740000gr/T/ipykernel_75264/3977179411.py:2: RuntimeWarning: overflow encountered in matmul\n", | |
| " star_orb_vxyz_R = R @ star_orb_vxyz\n", | |
| "/var/folders/67/2zgxpmyd2z183j4k6r33nf740000gr/T/ipykernel_75264/3977179411.py:2: RuntimeWarning: invalid value encountered in matmul\n", | |
| " star_orb_vxyz_R = R @ star_orb_vxyz\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "star_orb_xyz_R = R @ star_orb_xyz\n", | |
| "star_orb_vxyz_R = R @ star_orb_vxyz" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 96, | |
| "id": "94aec047", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Note: turn this on to see proper motion effect\n", | |
| "# star_linear_motion = star_vxyz[None] * time_grid[:, None] * u.day\n", | |
| "star_linear_motion = 0 * u.pc\n", | |
| "\n", | |
| "total_xyz = (\n", | |
| " star_xyz + star_orb_xyz_R.T * u.Rsun + star_linear_motion\n", | |
| ")\n", | |
| "total_vxyz = star_orb_vxyz_R.T * u.Rsun / u.day + star_vxyz\n", | |
| "\n", | |
| "rep = coord.CartesianRepresentation(total_xyz.T)\n", | |
| "dif = coord.CartesianDifferential(total_vxyz.T)\n", | |
| "c = coord.SkyCoord(rep.with_differentials(dif), frame=\"icrs\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 97, | |
| "id": "a7920699", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "Text(0, 0.5, 'On sky offset (mas)')" | |
| ] | |
| }, | |
| "execution_count": 97, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 432x432 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "image/png": { | |
| "height": 440, | |
| "width": 440 | |
| } | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "c_fr = c.transform_to(coord.SkyOffsetFrame(origin=c[0]))\n", | |
| "\n", | |
| "plt.plot(c_fr.lon.to(u.mas), c_fr.lat.to(u.mas))\n", | |
| "plt.xlabel(\"On sky offset (mas)\")\n", | |
| "plt.ylabel(\"On sky offset (mas)\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "id": "a7c557ee", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "scratch", | |
| "language": "python", | |
| "name": "python3" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 3 | |
| }, | |
| "file_extension": ".py", | |
| "mimetype": "text/x-python", | |
| "name": "python", | |
| "nbconvert_exporter": "python", | |
| "pygments_lexer": "ipython3", | |
| "version": "3.12.10" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 5 | |
| } |
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