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@astrojuanlu
Created July 3, 2020 11:04
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import warnings\n",
"warnings.simplefilter(\"ignore\")\n",
"\n",
"from astropy.time import Time\n",
"from astropy import units as u\n",
"\n",
"import matplotlib.pyplot as plt\n",
"plt.style.use(\"seaborn\")\n",
"\n",
"from poliastro.bodies import Sun, Venus, Earth\n",
"from poliastro.ephem import Ephem\n",
"from poliastro.frames import Planes\n",
"from poliastro.maneuver import Maneuver\n",
"from poliastro.twobody import Orbit\n",
"from poliastro.plotting.static import StaticOrbitPlotter"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We use the current epoch, although it doesn't really matter:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<Time object: scale='tdb' format='datetime' value=2020-07-03 11:04:38.124402>"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"epoch = Time.now().tdb\n",
"epoch"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We retrieve the orbits for Ceres and Vesta:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"ceres = Orbit.from_sbdb(\"Ceres\")\n",
"vesta = Orbit.from_sbdb(\"Vesta\")"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3 x 3 AU x 10.6 deg (HeliocentricEclipticIAU76) orbit around Sun (☉) at epoch 2459000.5008007516 (TDB)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ceres"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2 x 3 AU x 7.1 deg (HeliocentricEclipticIAU76) orbit around Sun (☉) at epoch 2458600.5008007586 (TDB)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"vesta"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 1008x432 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plotter = StaticOrbitPlotter(plane=Planes.EARTH_ECLIPTIC)\n",
"plotter.plot_body_orbit(Venus, epoch=epoch)\n",
"plotter.plot_body_orbit(Earth, epoch=epoch)\n",
"plotter.plot(ceres, label=\"Ceres\", color=\"#666\")\n",
"ax = plotter.plot(vesta, label=\"Vesta\", color=\"#999\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now create osculating orbits for Earth and Venus at the current epoch:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"earth_i = Orbit.from_ephem(\n",
" Sun, Ephem.from_body(Earth, epoch, plane=Planes.EARTH_ECLIPTIC), epoch\n",
")\n",
"venus_i = Orbit.from_ephem(\n",
" Sun, Ephem.from_body(Venus, epoch, plane=Planes.EARTH_ECLIPTIC), epoch\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And compute the maneuver, assuming that both Ceres and Vesta are more or less circular:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"earth_ceres = Maneuver.hohmann(earth_i, ceres.a)\n",
"earth_vesta = Maneuver.hohmann(earth_i, vesta.a)\n",
"venus_ceres = Maneuver.hohmann(venus_i, ceres.a)\n",
"venus_vesta = Maneuver.hohmann(venus_i, vesta.a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First time is the time to pericenter, second is the actual transfer time:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$1.2709568 \\; \\mathrm{yr}$"
],
"text/plain": [
"<Quantity 1.27095683 yr>"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"earth_ceres[1][0].to(u.year)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$1.0688244 \\; \\mathrm{yr}$"
],
"text/plain": [
"<Quantity 1.0688244 yr>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"earth_vesta[1][0].to(u.year)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$1.1377234 \\; \\mathrm{yr}$"
],
"text/plain": [
"<Quantity 1.13772342 yr>"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"venus_ceres[1][0].to(u.year)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$0.94335186 \\; \\mathrm{yr}$"
],
"text/plain": [
"<Quantity 0.94335186 yr>"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"venus_vesta[1][0].to(u.year)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Confirmed! **Venus is \"closer\" to the asteroid belt, in the sense that it takes less time!**"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.8.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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