# Catch that asteroid!¶

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

[1]:

from astropy.utils.data import conf

conf.dataurl

[1]:

'http://data.astropy.org/'

[2]:

conf.remote_timeout

[2]:

10.0

[3]:

conf.remote_timeout = 10000


Then, we do the rest of the imports:

[4]:

from astropy import units as u
from astropy.time import Time, TimeDelta
from astropy.coordinates import solar_system_ephemeris

solar_system_ephemeris.set("jpl")

from poliastro.bodies import Sun, Earth, Moon
from poliastro.ephem import Ephem
from poliastro.frames import Planes
from poliastro.plotting import StaticOrbitPlotter
from poliastro.plotting.misc import plot_solar_system
from poliastro.twobody import Orbit
from poliastro.util import norm, time_range

EPOCH = Time("2017-09-01 12:05:50", scale="tdb")
C_FLORENCE = "#000"
C_MOON = "#999"

[5]:

Earth.plot(EPOCH)

[5]:

([<matplotlib.lines.Line2D at 0x7f528a8ab0a0>],
<matplotlib.lines.Line2D at 0x7f528a8a7970>)


Our first option to retrieve the orbit of the Florence asteroid is to use Orbit.from_sbdb, which gives us the osculating elements at a certain epoch:

[6]:

florence_osc = Orbit.from_sbdb("Florence")
florence_osc

[6]:

1 x 3 AU x 22.1 deg (HeliocentricEclipticIAU76) orbit around Sun (☉) at epoch 2459800.50080073 (TDB)


However, the epoch of the result is not close to the time of the close approach we are studying:

[7]:

florence_osc.epoch.iso

[7]:

'2022-08-09 00:01:09.183'


Therefore, if we propagate this orbit to EPOCH, the results will be a bit different from the reality. Therefore, we need to find some other means.

Let’s use the Ephem.from_horizons method as an alternative, sampling over a period of 6 months:

[8]:

epochs = time_range(
EPOCH - TimeDelta(3 * 30 * u.day), end=EPOCH + TimeDelta(3 * 30 * u.day)
)

[9]:

florence = Ephem.from_horizons("Florence", epochs, plane=Planes.EARTH_ECLIPTIC)
florence

[9]:

Ephemerides at 50 epochs from 2017-06-03 12:05:50.000 (TDB) to 2017-11-30 12:05:50.000 (TDB)

[10]:

florence.plane

[10]:

<Planes.EARTH_ECLIPTIC: 'Earth mean Ecliptic and Equinox of epoch (J2000.0)'>


And now, let’s compute the distance between Florence and the Earth at that epoch:

[11]:

earth = Ephem.from_body(Earth, epochs, plane=Planes.EARTH_ECLIPTIC)
earth

[11]:

Ephemerides at 50 epochs from 2017-06-03 12:05:50.000 (TDB) to 2017-11-30 12:05:50.000 (TDB)

[12]:

min_distance = norm(florence.rv(EPOCH)[0] - earth.rv(EPOCH)[0]) - Earth.R
min_distance.to(u.km)

[12]:

$7060098.8 \; \mathrm{km}$

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

[13]:

abs((min_distance - 7060160 * u.km) / (7060160 * u.km)).decompose()

[13]:

$8.6636052 \times 10^{-6} \; \mathrm{}$
[14]:

from IPython.display import HTML

HTML(
)

[14]:


And now we can plot!

[15]:

frame = plot_solar_system(outer=False, epoch=EPOCH)
frame.plot_ephem(florence, EPOCH, label="Florence", color=C_FLORENCE)

[15]:

([<matplotlib.lines.Line2D at 0x7f52867851f0>],
<matplotlib.lines.Line2D at 0x7f5286785e80>)


Finally, we are going to visualize the orbit of Florence with respect to the Earth. For that, we set a narrower time range, and specify that we want to retrieve the ephemerides with respect to our planet:

[16]:

epochs = time_range(
EPOCH - TimeDelta(5 * u.day), end=EPOCH + TimeDelta(5 * u.day)
)

[17]:

florence_e = Ephem.from_horizons("Florence", epochs, attractor=Earth)
florence_e

[17]:

Ephemerides at 50 epochs from 2017-08-27 12:05:50.000 (TDB) to 2017-09-06 12:05:50.000 (TDB)


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

[18]:

moon = Ephem.from_body(Moon, epochs, attractor=Earth)
moon

[18]:

Ephemerides at 50 epochs from 2017-08-27 12:05:50.000 (TDB) to 2017-09-06 12:05:50.000 (TDB)

[19]:

plotter = StaticOrbitPlotter()
plotter.set_attractor(Earth)
plotter.set_body_frame(Moon)
plotter.plot_ephem(moon, EPOCH, label=Moon, color=C_MOON)

[19]:

([<matplotlib.lines.Line2D at 0x7f52865b65b0>],
<matplotlib.lines.Line2D at 0x7f52865b6820>)


And now, the glorious final plot:

[20]:

from matplotlib import pyplot as plt

frame = StaticOrbitPlotter()

frame.set_attractor(Earth)
frame.set_orbit_frame(Orbit.from_ephem(Earth, florence_e, EPOCH))

frame.plot_ephem(florence_e, EPOCH, label="Florence", color=C_FLORENCE)
frame.plot_ephem(moon, EPOCH, label=Moon, color=C_MOON)

[20]:

([<matplotlib.lines.Line2D at 0x7f5284d2a5b0>],
<matplotlib.lines.Line2D at 0x7f5284d23fd0>)