In [1]:
import matplotlib.pyplot as plt
plt.ion()
from astropy import units as u
from astropy.time import Time
In [2]:
from astropy.utils.data import conf
conf.dataurl
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In [3]:
conf.remote_timeout
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First, we need to increase the timeout time to allow the download of data occur properly
In [4]:
conf.remote_timeout = 10000
In [5]:
from astropy.coordinates import solar_system_ephemeris
solar_system_ephemeris.set("jpl")
from poliastro.bodies import *
from poliastro.twobody import Orbit
from poliastro.plotting import OrbitPlotter, plot
EPOCH = Time("2017-09-01 12:05:50", scale="tdb")
In [6]:
earth = Orbit.from_body_ephem(Earth, EPOCH)
earth
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In [7]:
plot(earth, label=Earth)
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In [8]:
from poliastro.neos import neows
In [9]:
florence = neows.orbit_from_name("Florence")
florence
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Two problems: the epoch is not the one we desire, and the inclination is with respect to the ecliptic!
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florence.epoch
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In [11]:
florence.epoch.iso
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In [12]:
florence.inc
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We first propagate:
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florence = florence.propagate(EPOCH)
florence.epoch.tdb.iso
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And now we have to convert to another reference frame, using http://docs.astropy.org/en/stable/coordinates/.
In [14]:
from astropy.coordinates import (
ICRS, GCRS,
CartesianRepresentation, CartesianDifferential
)
from poliastro.frames import HeliocentricEclipticJ2000
The NASA servers give the orbital elements of the asteroids in an Heliocentric Ecliptic frame. Fortunately, it is already defined in Astropy:
In [15]:
florence_heclip = HeliocentricEclipticJ2000(
x=florence.r[0], y=florence.r[1], z=florence.r[2],
v_x=florence.v[0], v_y=florence.v[1], v_z=florence.v[2],
representation=CartesianRepresentation,
differential_type=CartesianDifferential,
obstime=EPOCH
)
florence_heclip
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Now we just have to convert to ICRS, which is the "standard" reference in which poliastro works:
In [16]:
florence_icrs_trans = florence_heclip.transform_to(ICRS)
florence_icrs_trans.representation = CartesianRepresentation
florence_icrs_trans
Out[16]:
In [17]:
florence_icrs = Orbit.from_vectors(
Sun,
r=[florence_icrs_trans.x, florence_icrs_trans.y, florence_icrs_trans.z] * u.km,
v=[florence_icrs_trans.v_x, florence_icrs_trans.v_y, florence_icrs_trans.v_z] * (u.km / u.s),
epoch=florence.epoch
)
florence_icrs
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In [18]:
florence_icrs.rv()
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Let us compute the distance between Florence and the Earth:
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from poliastro.util import norm
In [20]:
norm(florence_icrs.r - earth.r) - Earth.R
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In [21]:
from IPython.display import HTML
HTML(
"""<blockquote class="twitter-tweet" data-lang="en"><p lang="es" dir="ltr">La <a href="https://twitter.com/esa_es">@esa_es</a> ha preparado un resumen del asteroide <a href="https://twitter.com/hashtag/Florence?src=hash">#Florence</a> 😍 <a href="https://t.co/Sk1lb7Kz0j">pic.twitter.com/Sk1lb7Kz0j</a></p>— AeroPython (@AeroPython) <a href="https://twitter.com/AeroPython/status/903197147914543105">August 31, 2017</a></blockquote>
<script async src="//platform.twitter.com/widgets.js" charset="utf-8"></script>"""
)
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And now we can plot!
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frame = OrbitPlotter()
frame.plot(earth, label="Earth")
frame.plot(Orbit.from_body_ephem(Mars, EPOCH))
frame.plot(Orbit.from_body_ephem(Venus, EPOCH))
frame.plot(Orbit.from_body_ephem(Mercury, EPOCH))
frame.plot(florence_icrs, label="Florence")
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The difference between doing it well and doing it wrong is clearly visible:
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frame = OrbitPlotter()
frame.plot(earth, label="Earth")
frame.plot(florence, label="Florence (Ecliptic)")
frame.plot(florence_icrs, label="Florence (ICRS)")
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And now let's do something more complicated: express our orbit with respect to the Earth! For that, we will use GCRS, with care of setting the correct observation time:
In [24]:
florence_gcrs_trans = florence_heclip.transform_to(GCRS(obstime=EPOCH))
florence_gcrs_trans.representation = CartesianRepresentation
florence_gcrs_trans
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In [25]:
florence_hyper = Orbit.from_vectors(
Earth,
r=[florence_gcrs_trans.x, florence_gcrs_trans.y, florence_gcrs_trans.z] * u.km,
v=[florence_gcrs_trans.v_x, florence_gcrs_trans.v_y, florence_gcrs_trans.v_z] * (u.km / u.s),
epoch=EPOCH
)
florence_hyper
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Notice that the ephemerides of the Moon is also given in ICRS, and therefore yields a weird hyperbolic orbit!
In [26]:
moon = Orbit.from_body_ephem(Moon, EPOCH)
moon
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In [27]:
moon.a
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moon.ecc
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So we have to convert again.
In [29]:
moon_icrs = ICRS(
x=moon.r[0], y=moon.r[1], z=moon.r[2],
v_x=moon.v[0], v_y=moon.v[1], v_z=moon.v[2],
representation=CartesianRepresentation,
differential_type=CartesianDifferential
)
moon_icrs
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In [30]:
moon_gcrs = moon_icrs.transform_to(GCRS(obstime=EPOCH))
moon_gcrs.representation = CartesianRepresentation
moon_gcrs
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In [31]:
moon = Orbit.from_vectors(
Earth,
[moon_gcrs.x, moon_gcrs.y, moon_gcrs.z] * u.km,
[moon_gcrs.v_x, moon_gcrs.v_y, moon_gcrs.v_z] * (u.km / u.s),
epoch=EPOCH
)
moon
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And finally, we plot the Moon:
In [32]:
plot(moon, label=Moon)
plt.gcf().autofmt_xdate()
And now for the final plot:
In [33]:
frame = OrbitPlotter()
# This first plot sets the frame
frame.plot(florence_hyper, label="Florence")
# And then we add the Moon
frame.plot(moon, label=Moon)
plt.xlim(-1000000, 8000000)
plt.ylim(-5000000, 5000000)
plt.gcf().autofmt_xdate()