Catch that asteroid!

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
Out[2]:
'http://data.astropy.org/'
In [3]:
conf.remote_timeout
Out[3]:
10.0

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

In [4]:
conf.remote_timeout = 10000

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

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
Out[6]:
1 x 1 AU x 23.4 deg (ICRS) orbit around Sun (☉)
In [7]:
plot(earth, label=Earth);
/home/juanlu/Development/poliastro/poliastro-library/src/poliastro/twobody/orbit.py:475: UserWarning:

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

../_images/examples_Catch_that_asteroid!_9_1.png
In [8]:
from poliastro.neos import neows
In [9]:
florence = neows.orbit_from_name("Florence")
florence
Out[9]:
1 x 3 AU x 22.1 deg (HeliocentricEclipticJ2000) orbit around Sun (☉)

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

In [10]:
florence.epoch
Out[10]:
<Time object: scale='tdb' format='jd' value=2458200.5>
In [11]:
florence.epoch.iso
Out[11]:
'2018-03-23 00:00:00.000'
In [12]:
florence.inc
Out[12]:
$22.144811 \; \mathrm{{}^{\circ}}$

We first propagate:

In [13]:
florence = florence.propagate(EPOCH)
florence.epoch.tdb.iso
Out[13]:
'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:

In [14]:
florence_icrs = florence.to_icrs()
florence_icrs.rv()
Out[14]:
(<Quantity [ 1.46265478e+08, -5.38817374e+07, -2.08986005e+07] km>,
 <Quantity [ 7.3998822 , 23.46299461, 24.12028277] km / s>)

Let us compute the distance between Florence and the Earth:

In [15]:
from poliastro.util import norm
In [16]:
norm(florence_icrs.r - earth.r) - Earth.R
Out[16]:
$7057830.8 \; \mathrm{km}$

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

In [17]:
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>"""
)
Out[17]:

And now we can plot!

In [18]:
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");
/home/juanlu/Development/poliastro/poliastro-library/src/poliastro/twobody/orbit.py:475: UserWarning:

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

../_images/examples_Catch_that_asteroid!_26_1.png

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

In [19]:
frame = OrbitPlotter()

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

frame.plot(florence, label="Florence (Ecliptic)")
frame.plot(florence_icrs, label="Florence (ICRS)");
/home/juanlu/Development/poliastro/poliastro-library/src/poliastro/twobody/orbit.py:475: UserWarning:

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

../_images/examples_Catch_that_asteroid!_28_1.png

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 [20]:
from astropy.coordinates import GCRS, CartesianRepresentation
In [21]:
florence_heclip = florence.frame.realize_frame(
    florence.represent_as(CartesianRepresentation)
)
In [22]:
florence_gcrs_trans_cart = (florence_heclip.transform_to(GCRS(obstime=EPOCH))
                            .represent_as(CartesianRepresentation))
florence_gcrs_trans_cart
Out[22]:
<CartesianRepresentation (x, y, z) in km
    (4960528.40227817, -5020204.24301458, 306195.40673516)
 (has differentials w.r.t.: 's')>
In [23]:
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
Out[23]:
7064205 x -7068561 km x 104.3 deg (GCRS) orbit around Earth (♁)

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

In [24]:
moon = Orbit.from_body_ephem(Moon, EPOCH)
moon
Out[24]:
367937 x 405209 km x 19.4 deg (GCRS) orbit around Earth (♁)
In [25]:
plot(moon, label=Moon)
plt.gcf().autofmt_xdate()
../_images/examples_Catch_that_asteroid!_36_0.png

And now for the final plot:

In [26]:
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()
../_images/examples_Catch_that_asteroid!_38_0.png

Per Python ad astra!