A pure Python library to solve common orbital mechanics problem
The Orbit class includes a few class methods which allows for fast and easy Orbit generation. Regardless of the input elements all orbits requires the following inputs :
- primBody = a Body object used to determine the gravitational parameter
- name = Every orbit created needs a name
This uses the basic set of keplerian elements :
- Semi-major Axis (a)
- Eccentricity (e)
- Inclination (i)
- Longitude of the ascending node (lAn)
- Argument of Periapsis (aPe)
- True Anomaly (tAn)
from orbits.orbit import Orbit
from examples import Sun
import numpy as np
earthOrbit = Orbit.fromElements(a=149597887.1558, e=0.01671022, i = np.radians(0.00005), lAn = np.radians(348.7394), primBody=Sun, aPe=np.radians(114.2078), tAn=6.23837308813, name="Earth Orbit")
print(earthOrbit)Which prints :
ID - Earth Orbit
primBody - Sun
a - 149597887.1558
e - 0.01671022
i - 8.726646259971648e-07
lAn - 6.086650761429513
aPe - 1.99330214145918
tAn - 6.23837308813
epoch - 2000-01-01 00:00:00.000
fromApsis replaces the semimajor axis and the eccentricity by the height of the Apoapsis (hPa) and Periapsis (hPe)
marsOrbit = Orbit.fromApsis(hPa = 247644270.465, hPe=220120745.788, i = np.radians(1.85061), lAn = np.radians(49.57854), primBody=Sun, aPe=np.radians(286.4623), tAn=0.40848952017, name="Mars Orbit")
print(marsOrbit)Which prints :
ID - Mars Orbit
primBody - Sun
a - 233882508.1265
e - 0.05884049409567938
i - 0.03229923767033226
lAn - 0.8653087613317094
aPe - 4.999710317835753
tAn - 0.40848952017
epoch - 2000-01-01 00:00:00.000
This replaces the set of keplerian elements by a position 3D vector and a velocity 3D vector
from examples import Earth
testOrbit = Orbit.fromStateVector((-6045, -3490, 2500), (-3.457, 6.618, 2.533), primBody=Earth, name = "State Vector Demo")
print(testOrbit)Which prints :
ID - State Vector Demo
primBody - Earth
a - 8788.081767279667
e - 0.17121118195416898
i - 2.6747036137846094
lAn - 4.455464041223287
aPe - 0.35025511728002945
tAn - 0.496472955354359
epoch - 2000-01-01 00:00:00.000
Orbits can also be generated using a multi revolution universal Lambert solver. It uses the following inputs:
- r1 - 3D position vector
- r2 - 3D position vector
- tof - Time of flight between r1 and r2 in seconds
And the following are optional :
- nRev - The number of full revolution completed (default is 0)
- DM - The direction of motion, if left empty the solver will determine the optimal one
lambertDemo = Orbit.fromLambert((5000,10000,2100), (-14600,2500,7000), 3600, primBody=Earth, name="Lambert Demo")
print(lambertDemo)Which will output :
ID - Lambert Demo
primBody - Earth
a - 20002.884935993607
e - 0.4334874513211504
i - 0.5269331332631371
lAn - 0.7784202841672524
aPe - 0.535923312928038
tAn - 6.123135458171056
epoch - 2000-01-01 00:00:00.000
The universal solver also supports hyperbolic trajectory :
from orbits.hyperbola import Hyperbola
lambertDemo = Hyperbola.fromLambert((5000,10000,2100), (-14600,2500,7000), 1500, primBody=Earth, name="Lambert Hyperbola")
print("SMA - {}, eccentricity - {}".format(lambertDemo.a, lambertDemo.e))Will output :
SMA - -2918.7342956582274, eccentricity - 4.215326772456562
It also supports multi-rev generation :
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