Catch that asteroid!

[1]:
from astropy import units as u
from astropy.time import Time
[2]:
from astropy.utils.data import conf
conf.dataurl
[2]:
'http://data.astropy.org/'
[3]:
conf.remote_timeout
[3]:
10.0

First, we need to increase the timeout time to allow the download of data occur properly

[4]:
conf.remote_timeout = 10000

Then, we do the rest of the imports and create our initial orbits.

[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 OrbitPlotter2D
from poliastro.plotting.misc import plot_solar_system

EPOCH = Time("2017-09-01 12:05:50", scale="tdb")
[6]:
earth = Orbit.from_body_ephem(Earth, EPOCH)
earth
[6]:
1 x 1 AU x 23.4 deg (ICRS) orbit around Sun (☉) at epoch 2017-09-01 12:05:50.000 (TDB)
[7]:
earth.plot(label=Earth)
/home/juanlu/Development/poliastro/poliastro-library/src/poliastro/twobody/propagation.py:230: UserWarning:

Frame <class 'astropy.coordinates.builtin_frames.icrs.ICRS'> does not support 'obstime', time values were not returned

[8]:
from poliastro.neos import neows
[9]:
florence = neows.orbit_from_name("Florence")
florence
[9]:
1 x 3 AU x 22.1 deg (HeliocentricEclipticJ2000) orbit around Sun (☉) at epoch 2458600.5 (TDB)

Two problems: the epoch is not the one we desire, and the inclination is with respect to the ecliptic!

[10]:
florence.rv()
[10]:
(<Quantity [-2.76132873e+08, -1.71570015e+08, -1.09377634e+08] km>,
 <Quantity [13.17478674, -9.82584125, -1.48126639] km / s>)
[11]:
florence.epoch
[11]:
<Time object: scale='tdb' format='jd' value=2458600.5>
[12]:
florence.epoch.iso
[12]:
'2019-04-27 00:00:00.000'
[13]:
florence.inc
[13]:
$22.142394 \; \mathrm{{}^{\circ}}$

We first propagate:

[14]:
florence = florence.propagate(EPOCH)
florence.epoch.tdb.iso
[14]:
'2017-09-01 12:05:50.000'

And now we have to convert to the same frame that the planetary ephemerides are using to make consistent comparisons, which is ICRS:

[15]:
florence_icrs = florence.to_icrs()
florence_icrs.rv()
[15]:
(<Quantity [ 1.46404761e+08, -5.35736589e+07, -2.05640225e+07] km>,
 <Quantity [ 7.33453685, 23.48471466, 24.12478169] km / s>)

Let us compute the distance between Florence and the Earth:

[16]:
from poliastro.util import norm
[17]:
norm(florence_icrs.r - earth.r) - Earth.R
[17]:
$6966586.7 \; \mathrm{km}$

This value is consistent with what ESA says! \(7\,060\,160\) km

[18]:
abs(((norm(florence_icrs.r - earth.r) - Earth.R) - 7060160 * u.km) / (7060160 * u.km))
[18]:
$0.013253715 \; \mathrm{}$
[19]:
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>&mdash; AeroPython (@AeroPython) <a href="https://twitter.com/AeroPython/status/903197147914543105">August 31, 2017</a></blockquote>
<script src="//platform.twitter.com/widgets.js" charset="utf-8"></script>"""
)
[19]:

And now we can plot!

[20]:
frame = plot_solar_system(outer=False, epoch=EPOCH)
frame.plot(florence_icrs, label="Florence")
/home/juanlu/Development/poliastro/poliastro-library/src/poliastro/twobody/propagation.py:230: UserWarning:

Frame <class 'astropy.coordinates.builtin_frames.icrs.ICRS'> does not support 'obstime', time values were not returned

The difference between doing it well and doing it wrong is clearly visible:

[21]:
frame = OrbitPlotter2D()

frame.plot(earth, label="Earth")

frame.plot(florence, label="Florence (Ecliptic)")
frame.plot(florence_icrs, label="Florence (ICRS)")

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:

[22]:
from astropy.coordinates import GCRS, CartesianRepresentation
[23]:
florence_heclip = florence.frame.realize_frame(
    florence.represent_as(CartesianRepresentation)
)
[24]:
florence_gcrs_trans_cart = florence_heclip.transform_to(
    GCRS(obstime=EPOCH)
).represent_as(CartesianRepresentation)

florence_gcrs_trans_cart
[24]:
<CartesianRepresentation (x, y, z) in km
    (5099783.89297201, -4712095.67900917, 640778.03222918)
 (has differentials w.r.t.: 's')>
[25]:
florence_hyper = Orbit.from_vectors(
    Earth,
    r=florence_gcrs_trans_cart.xyz,
    v=florence_gcrs_trans_cart.differentials['s'].d_xyz,
    epoch=EPOCH
)
florence_hyper
[25]:
6969288 x -6973635 km x 104.2 deg (GCRS) orbit around Earth (♁) at epoch 2017-09-01 12:05 (TDB)

We now retrieve the ephemerides of the Moon, which are given directly in GCRS:

[26]:
moon = Orbit.from_body_ephem(Moon, EPOCH)
moon
[26]:
367937 x 405209 km x 19.4 deg (GCRS) orbit around Earth (♁) at epoch 2017-09-01 12:05 (TDB)
[27]:
moon.plot(label=Moon)

And now for the final plot:

[28]:
import matplotlib.pyplot as plt
plt.ion()

from poliastro.plotting.static import StaticOrbitPlotter
[29]:
frame = StaticOrbitPlotter()

# 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()
../_images/examples_Catch_that_asteroid!_41_0.png

Per Python ad astra!