# Detecting Events¶

It is a well-known fact that launching a satellite is a captial-intensive and fuel-exhaustive process. Moreover, maintaining high accuracy and precision in any satellite orbit analysis is paramount to be able to comprehend helpful information from them.

Detecing some peculiar phenomena associated with satellites, which we call “events”, could provide beneficial insights about their orbit dynamics for further treatment. While some could provide critical scientific information and help us formulate efficient space strategies and policies, the potentially disastrous ones, like satellite collisions, could help us take further steps to prevent such contingencies.

This notebook gives a glimpse of `hapsira`

’s event detection capabilities. The procedure to track an event during an orbit’s propagation is fairly simple:

Instantiate the desired event class/classes.

Pass the

`Event`

object(s) as an argument to`CowellPropagator`

.Detect events! Optionally, the

`terminal`

and`direction`

attributes can be set as required.

```
[1]:
```

```
# Imports
import numpy as np
from numpy.linalg import norm
import matplotlib.pyplot as plt
import astropy
import astropy.units as u
from astropy.time import Time
from astropy.coordinates import (
CartesianRepresentation,
get_body_barycentric_posvel,
)
from hapsira.bodies import Earth, Sun
from hapsira.twobody.events import (
AltitudeCrossEvent,
LatitudeCrossEvent,
NodeCrossEvent,
PenumbraEvent,
UmbraEvent,
)
from hapsira.twobody.orbit import Orbit
from hapsira.twobody.propagation import CowellPropagator
from hapsira.twobody.sampling import EpochsArray
from hapsira.util import time_range
```

## Altitude Crossing Event¶

Let’s define some natural perturbation conditions for our orbit so that its altitude decreases with time.

```
[2]:
```

```
from hapsira.constants import H0_earth, rho0_earth
from hapsira.core.perturbations import atmospheric_drag_exponential
from hapsira.core.propagation import func_twobody
R = Earth.R.to_value(u.km)
# Parameters of the body
C_D = 2.2 # Dimensionless (any value would do)
A_over_m = ((np.pi / 4.0) * (u.m**2) / (100 * u.kg)).to_value(
u.km**2 / u.kg
) # km^2/kg
# Parameters of the atmosphere
rho0 = rho0_earth.to_value(u.kg / u.km**3) # kg/km^3
H0 = H0_earth.to_value(u.km) # km
def f(t0, u_, k):
du_kep = func_twobody(t0, u_, k)
ax, ay, az = atmospheric_drag_exponential(
t0, u_, k, R=R, C_D=C_D, A_over_m=A_over_m, H0=H0, rho0=rho0
)
du_ad = np.array([0, 0, 0, ax, ay, az])
return du_kep + du_ad
```

We shall use the `CowellPropagator`

with the above perturbating conditions and pass the events we want to keep track of, in this case only the `AltitudeCrossEvent`

.

```
[3]:
```

```
tofs = np.arange(0, 2400, 100) << u.s
orbit = Orbit.circular(Earth, 150 * u.km)
# Define a threshold altitude for crossing.
thresh_alt = 50 # in km
altitude_cross_event = AltitudeCrossEvent(thresh_alt, R) # Set up the event.
events = [altitude_cross_event]
method = CowellPropagator(events=events, f=f)
rr, _ = orbit.to_ephem(
EpochsArray(orbit.epoch + tofs, method=method),
).rv()
print(
f"The threshold altitude was crossed {altitude_cross_event.last_t} after the orbit's epoch."
)
```

```
The threshold altitude was crossed 2063.6700936204934 s after the orbit's epoch.
```

Let’s see how did the orbit’s altitude vary with time:

```
[4]:
```

```
altitudes = np.apply_along_axis(
norm, 1, (rr << u.km).value
) - Earth.R.to_value(u.km)
plt.plot(tofs[: len(rr)].to_value(u.s), altitudes)
plt.title("Altitude variation")
plt.ylabel("Altitude (in km)")
plt.xlabel("Time (in s)")
```

```
[4]:
```

```
Text(0.5, 0, 'Time (in s)')
```

Refer to the API documentation of the events to check the default values for `terminal`

and `direction`

and change it as required.

## Latitude Crossing Event¶

Similar to the `AltitudeCrossEvent`

, just pass the threshold latitude while instantiating the event.

```
[5]:
```

```
orbit = Orbit.from_classical(
Earth,
6900 << u.km,
0.75 << u.one,
45 << u.deg,
0 << u.deg,
0 << u.deg,
130 << u.deg,
)
```

```
[6]:
```

```
thresh_lat = 35 << u.deg
latitude_cross_event = LatitudeCrossEvent(orbit, thresh_lat, terminal=True)
events = [latitude_cross_event]
tofs = np.arange(0, 20 * orbit.period.to_value(u.s), 150) << u.s
method = CowellPropagator(events=events)
rr, _ = orbit.to_ephem(EpochsArray(orbit.epoch + tofs, method=method)).rv()
print(
f"The threshold latitude was crossed {latitude_cross_event.last_t} s after the orbit's epoch"
)
```

```
The threshold latitude was crossed 5225.7148541757415 s s after the orbit's epoch
```

Let’s plot the latitude varying with time:

```
[7]:
```

```
from hapsira.core.spheroid_location import cartesian_to_ellipsoidal
latitudes = []
for r in rr:
position_on_body = (r / norm(r)) * Earth.R
_, lat, _ = cartesian_to_ellipsoidal(
Earth.R, Earth.R_polar, *position_on_body
)
latitudes.append(np.rad2deg(lat))
plt.plot(tofs[: len(rr)].to_value(u.s), latitudes)
plt.title("Latitude variation")
plt.ylabel("Latitude (in degrees)")
plt.xlabel("Time (in days)")
```

```
[7]:
```

```
Text(0.5, 0, 'Time (in days)')
```

The orbit’s latitude would not change after the event was detected since we had set `terminal=True`

.

Since the attractor is `Earth`

, we could use `GroundtrackPlotter`

for showing the groundtrack of the orbit on Earth.

```
[8]:
```

```
from hapsira.earth import EarthSatellite
from hapsira.earth.plotting import GroundtrackPlotter
from hapsira.plotting import OrbitPlotter
es = EarthSatellite(orbit, None)
# Show the groundtrack plot from
t_span = time_range(orbit.epoch, end=orbit.epoch + latitude_cross_event.last_t)
# Generate ground track plotting instance.
gp = GroundtrackPlotter()
gp.update_layout(title="Latitude Crossing")
# Plot the above-defined earth satellite.
gp.plot(
es,
t_span,
label="Orbit",
color="red",
marker={
"size": 10,
"symbol": "triangle-right",
"line": {"width": 1, "color": "black"},
},
)
```