API Reference¶
poliastro.twobody package¶
poliastro.twobody.angles module¶
Angles and anomalies.
-
poliastro.twobody.angles.
nu_to_E
(nu, ecc)¶ Eccentric anomaly from true anomaly.
New in version 0.4.0.
Parameters: Returns: E – Eccentric anomaly.
Return type:
-
poliastro.twobody.angles.
E_to_nu
(E, ecc)¶ True anomaly from eccentric anomaly.
New in version 0.4.0.
Parameters: Returns: nu – True anomaly (rad).
Return type:
-
poliastro.twobody.angles.
M_to_E
(M, ecc)¶ Eccentric anomaly from mean anomaly.
New in version 0.4.0.
Parameters: Returns: E – Eccentric anomaly.
Return type:
-
poliastro.twobody.angles.
E_to_M
(E, ecc)¶ Mean anomaly from eccentric anomaly.
New in version 0.4.0.
Parameters: Returns: M – Mean anomaly (rad).
Return type:
-
poliastro.twobody.angles.
M_to_nu
(M, ecc)¶ True anomaly from mean anomaly.
New in version 0.4.0.
Parameters: Returns: nu – True anomaly (rad).
Return type: Examples
>>> nu = M_to_nu(np.radians(30.0), 0.06) >>> np.rad2deg(nu) 33.673284930211658
-
poliastro.twobody.angles.
nu_to_M
(nu, ecc)¶ Mean anomaly from true anomaly.
New in version 0.4.0.
Parameters: Returns: M – Mean anomaly (rad).
Return type:
poliastro.twobody.classical module¶
Functions to define orbits from classical orbital elements.
-
poliastro.twobody.classical.
rv_pqw
(k, p, ecc, nu)¶ Returns r and v vectors in perifocal frame.
-
poliastro.twobody.classical.
coe2rv
(k, p, ecc, inc, raan, argp, nu)¶ Converts from classical orbital elements to vectors.
Parameters:
-
poliastro.twobody.classical.
coe2mee
(p, ecc, inc, raan, argp, nu)¶ Converts from classical orbital elements to modified equinoctial orbital elements.
The definition of the modified equinoctial orbital elements is taken from [Walker, 1985].
Parameters: Note
The conversion equations are taken directly from the original paper.
-
class
poliastro.twobody.classical.
ClassicalState
(attractor, a, ecc, inc, raan, argp, nu)¶ State defined by its classical orbital elements.
-
a
¶ Semimajor axis.
-
ecc
¶ Eccentricity.
-
inc
¶ Inclination.
-
raan
¶ Right ascension of the ascending node.
-
argp
¶ Argument of the perigee.
-
nu
¶ True anomaly.
-
to_vectors
()¶ Converts to position and velocity vector representation.
-
to_classical
()¶ Converts to classical orbital elements representation.
-
to_equinoctial
()¶ Converts to modified equinoctial elements representation.
-
poliastro.twobody.decorators module¶
Decorators.
poliastro.twobody.equinoctial module¶
Functions to define orbits from modified equinoctial orbital elements.
-
poliastro.twobody.equinoctial.
mee2coe
(p, f, g, h, k, L)¶ Converts from modified equinoctial orbital elements to classical orbital elements.
The definition of the modified equinoctial orbital elements is taken from [Walker, 1985].
Note
The conversion is always safe because arctan2 works also for 0, 0 arguments.
poliastro.twobody.orbit module¶
-
class
poliastro.twobody.orbit.
Orbit
(state, epoch)¶ Position and velocity of a body with respect to an attractor at a given time (epoch).
-
state
= None¶ Position and velocity or classical elements
-
epoch
= None¶ Epoch of the orbit
-
classmethod
from_vectors
(attractor, r, v, epoch=<Time object: scale='tdb' format='jyear_str' value=J2000.000>)¶ Return Orbit from position and velocity vectors.
Parameters:
-
classmethod
from_classical
(attractor, a, ecc, inc, raan, argp, nu, epoch=<Time object: scale='tdb' format='jyear_str' value=J2000.000>)¶ Return Orbit from classical orbital elements.
Parameters: - attractor (Body) – Main attractor.
- a (Quantity) – Semi-major axis.
- ecc (Quantity) – Eccentricity.
- inc (Quantity) – Inclination
- raan (Quantity) – Right ascension of the ascending node.
- argp (Quantity) – Argument of the pericenter.
- nu (Quantity) – True anomaly.
- epoch (Time, optional) – Epoch, default to J2000.
-
classmethod
from_equinoctial
(attractor, p, f, g, h, k, L, epoch=<Time object: scale='tdb' format='jyear_str' value=J2000.000>)¶ Return Orbit from modified equinoctial elements.
Parameters: - attractor (Body) – Main attractor.
- p (Quantity) – Semilatus rectum.
- f (Quantity) – Second modified equinoctial element.
- g (Quantity) – Third modified equinoctial element.
- h (Quantity) – Fourth modified equinoctial element.
- k (Quantity) – Fifth modified equinoctial element.
- L (Quantity) – True longitude.
- epoch (Time, optional) – Epoch, default to J2000.
-
classmethod
from_body_ephem
(body, epoch=None)¶ Return osculating Orbit of a body at a given time.
-
classmethod
circular
(attractor, alt, inc=<Quantity 0.0 deg>, raan=<Quantity 0.0 deg>, arglat=<Quantity 0.0 deg>, epoch=<Time object: scale='tdb' format='jyear_str' value=J2000.000>)¶ Return circular Orbit.
Parameters: - attractor (Body) – Main attractor.
- alt (Quantity) – Altitude over surface.
- inc (Quantity, optional) – Inclination, default to 0 deg (equatorial orbit).
- raan (Quantity, optional) – Right ascension of the ascending node, default to 0 deg.
- arglat (Quantity, optional) – Argument of latitude, default to 0 deg.
- epoch (Time, optional) – Epoch, default to J2000.
-
classmethod
parabolic
(attractor, p, inc, raan, argp, nu, epoch=<Time object: scale='tdb' format='jyear_str' value=J2000.000>)¶ Return parabolic Orbit.
Parameters: - attractor (Body) – Main attractor.
- p (Quantity) – Semilatus rectum or parameter.
- inc (Quantity, optional) – Inclination.
- raan (Quantity) – Right ascension of the ascending node.
- argp (Quantity) – Argument of the pericenter.
- nu (Quantity) – True anomaly.
- epoch (Time, optional) – Epoch, default to J2000.
-
propagate
(time_of_flight, rtol=1e-10)¶ Propagate this Orbit some time and return the result.
-
apply_maneuver
(maneuver, intermediate=False)¶ Returns resulting Orbit after applying maneuver to self.
Optionally return intermediate states (default to False).
Parameters:
-
rv
()¶ Position and velocity vectors.
-
coe
()¶ Classical orbital elements.
-
pqw
()¶ Perifocal frame (PQW) vectors.
-
attractor
¶ Main attractor body.
-
r
¶ Position vector.
-
v
¶ Velocity vector.
-
a
¶ Semimajor axis.
-
p
¶ Semilatus rectum.
-
r_p
¶ Radius of pericenter.
-
r_a
¶ Radius of apocenter.
-
ecc
¶ Eccentricity.
-
inc
¶ Inclination.
-
raan
¶ Right ascension of the ascending node.
-
argp
¶ Argument of the perigee.
-
nu
¶ True anomaly.
-
f
¶ Second modified equinoctial element.
-
g
¶ Third modified equinoctial element.
-
h
¶ Fourth modified equinoctial element.
-
k
¶ Fifth modified equinoctial element.
-
L
¶ True longitude.
-
period
¶ Period of the orbit.
-
n
¶ Mean motion.
-
energy
¶ Specific energy.
-
e_vec
¶ Eccentricity vector.
-
h_vec
¶ Specific angular momentum vector.
-
arglat
¶ Argument of latitude.
-
poliastro.twobody.propagation module¶
Propagation algorithms.
-
poliastro.twobody.propagation.
func_twobody
(t0, u_, k, ad)¶ Differential equation for the initial value two body problem.
This function follows Cowell’s formulation.
Parameters:
-
poliastro.twobody.propagation.
cowell
(k, r0, v0, tof, rtol=1e-10, *, ad=None, callback=None, nsteps=1000)¶ Propagates orbit using Cowell’s formulation.
Parameters: - k (float) – Gravitational constant of main attractor (km^3 / s^2).
- r0 (array) – Initial position (km).
- v0 (array) – Initial velocity (km).
- ad (function(t0, u, k), optional) – Non Keplerian acceleration (km/s2), default to None.
- tof (float) – Time of flight (s).
- rtol (float, optional) – Maximum relative error permitted, default to 1e-10.
- nsteps (int, optional) – Maximum number of internal steps, default to 1000.
- callback (callable, optional) – Function called at each internal integrator step.
Raises: RuntimeError
– If the algorithm didn’t converge.Note
This method uses a Dormand & Prince method of order 8(5,3) available in the
scipy.integrate.ode
module.
-
poliastro.twobody.propagation.
kepler
(k, r0, v0, tof, rtol=1e-10, *, numiter=35)¶ Propagates Keplerian orbit.
Parameters: - k (float) – Gravitational constant of main attractor (km^3 / s^2).
- r0 (array) – Initial position (km).
- v0 (array) – Initial velocity (km).
- tof (float) – Time of flight (s).
- rtol (float, optional) – Maximum relative error permitted, default to 1e-10.
- numiter (int, optional) – Maximum number of iterations, default to 35.
Raises: RuntimeError
– If the algorithm didn’t converge.Note
This algorithm is based on Vallado implementation, and does basic Newton iteration on the Kepler equation written using universal variables. Battin claims his algorithm uses the same amount of memory but is between 40 % and 85 % faster.
-
poliastro.twobody.propagation.
propagate
(orbit, time_of_flight, *, method=<function kepler>, rtol=1e-10, **kwargs)¶ Propagate an orbit some time and return the result.
poliastro.iod package¶
poliastro.iod.izzo module¶
Izzo’s algorithm for Lambert’s problem
-
poliastro.iod.izzo.
lambert
(k, r0, r, tof, M=0, numiter=35, rtol=1e-08)¶ Solves the Lambert problem using the Izzo algorithm.
New in version 0.5.0.
Parameters: - k (Quantity) – Gravitational constant of main attractor (km^3 / s^2).
- r0 (Quantity) – Initial position (km).
- r (Quantity) – Final position (km).
- tof (Quantity) – Time of flight (s).
- M (int, optional) – Number of full revolutions, default to 0.
- numiter (int, optional) – Maximum number of iterations, default to 35.
- rtol (float, optional) – Relative tolerance of the algorithm, default to 1e-8.
Yields: v0, v (tuple) – Pair of velocity solutions.
poliastro.iod.vallado module¶
Initial orbit determination.
-
poliastro.iod.vallado.
lambert
(k, r0, r, tof, short=True, numiter=35, rtol=1e-08)¶ Solves the Lambert problem.
New in version 0.3.0.
Parameters: - k (Quantity) – Gravitational constant of main attractor (km^3 / s^2).
- r0 (Quantity) – Initial position (km).
- r (Quantity) – Final position (km).
- tof (Quantity) – Time of flight (s).
- short (boolean, optional) – Find out the short path, default to True. If False, find long path.
- numiter (int, optional) – Maximum number of iterations, default to 35.
- rtol (float, optional) – Relative tolerance of the algorithm, default to 1e-8.
Raises: RuntimeError
– If it was not possible to compute the orbit.Note
This uses the universal variable approach found in Battin, Mueller & White with the bisection iteration suggested by Vallado. Multiple revolutions not supported.
poliastro.neos package¶
Code related to NEOs.
Functions related with NEOs and different NASA APIs. All of them are coded as part of SOCIS 2017 proposal.
poliastro.neos.dastcom5 module¶
NEOs orbit from DASTCOM5 database.
-
poliastro.neos.dastcom5.
asteroid_db
()¶ Return complete DASTCOM5 asteroid database.
Returns: database – Database with custom dtype. Return type: numpy.ndarray
-
poliastro.neos.dastcom5.
comet_db
()¶ Return complete DASTCOM5 comet database.
Returns: database – Database with custom dtype. Return type: numpy.ndarray
-
poliastro.neos.dastcom5.
orbit_from_name
(name)¶ Return
Orbit
given a name.Retrieve info from JPL DASTCOM5 database.
Parameters: name (str) – NEO name. Returns: orbit – NEO orbits. Return type: list (Orbit)
-
poliastro.neos.dastcom5.
orbit_from_record
(record)¶ Return
Orbit
given a record.Retrieve info from JPL DASTCOM5 database.
Parameters: record (int) – Object record. Returns: orbit – NEO orbit. Return type: Orbit
-
poliastro.neos.dastcom5.
record_from_name
(name)¶ Search dastcom.idx and return logical records that match a given string.
Body name, SPK-ID, or alternative designations can be used.
Parameters: name (str) – Body name. Returns: records – DASTCOM5 database logical records matching str. Return type: list (int)
-
poliastro.neos.dastcom5.
read_headers
()¶ Read DASTCOM5 headers and return asteroid and comet headers.
Headers are two numpy arrays with custom dtype.
Returns: ast_header, com_header – DASTCOM5 headers. Return type: tuple (numpy.ndarray)
-
poliastro.neos.dastcom5.
read_record
(record)¶ Read DASTCOM5 record and return body data.
Body data consists of numpy array with custom dtype.
Parameters: record (int) – Body record. Returns: body_data – Body information. Return type: numpy.ndarray
-
poliastro.neos.dastcom5.
download_dastcom5
()¶ Downloads DASTCOM5 database.
Downloads and unzip DASTCOM5 file in default poliastro path (~/.poliastro).
-
poliastro.neos.dastcom5.
entire_db
()¶ Return complete DASTCOM5 database.
Merge asteroid and comet databases, only with fields related to orbital data, discarding the rest.
Returns: database – Database with custom dtype. Return type: numpy.ndarray
poliastro.neos.neows module¶
NEOs orbit from NEOWS and JPL SBDB
-
poliastro.neos.neows.
orbit_from_spk_id
(spk_id)¶ Return
Orbit
given a SPK-ID.Retrieve info from NASA NeoWS API, and therefore it only works with NEAs (Near Earth Asteroids).
Parameters: Returns: orbit – NEA orbit.
Return type:
poliastro.bodies module¶
Bodies of the Solar System.
Contains some predefined bodies of the Solar System:
- Sun (☉)
- Earth (♁)
- Moon (☾)
- Mercury (☿)
- Venus (♀)
- Mars (♂)
- Jupiter (♃)
- Saturn (♄)
- Uranus (⛢)
- Neptune (♆)
- Pluto (♇)
and a way to define new bodies (Body
class).
Data references can be found in constants
-
class
poliastro.bodies.
Body
(parent, k, name, symbol=None, R=<Quantity 0.0 km>, **kwargs)¶ Class to represent a generic body.
poliastro.constants module¶
Astronomical and physics constants.
This module complements constants defined in astropy.constants, with gravitational paremeters and radii.
Note that GM_jupiter and GM_neptune are both referred to the whole planetary system gravitational parameter.
Unless otherwise specified, gravitational and mass parameters were obtained from:
- Luzum, Brian et al. “The IAU 2009 System of Astronomical Constants: The Report of the IAU Working Group on Numerical Standards for Fundamental Astronomy.” Celestial Mechanics and Dynamical Astronomy 110.4 (2011): 293–304. Crossref. Web. DOI: 10.1007/s10569-011-9352-4
and radii were obtained from:
- Archinal, B. A. et al. “Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2009.” Celestial Mechanics and Dynamical Astronomy 109.2 (2010): 101–135. Crossref. Web. DOI: 10.1007/s10569-010-9320-4
poliastro.coordinates module¶
Functions related to coordinate systems and transformations.
This module complements astropy.coordinates
.
-
poliastro.coordinates.
body_centered_to_icrs
(r, v, source_body, epoch=<Time object: scale='tdb' format='jyear_str' value=J2000.000>, rotate_meridian=False)¶ Converts position and velocity body-centered frame to ICRS.
Parameters: - r (Quantity) – Position vector in a body-centered reference frame.
- v (Quantity) – Velocity vector in a body-centered reference frame.
- source_body (Body) – Source body.
- epoch (Time, optional) – Epoch, default to J2000.
- rotate_meridian (bool, optional) – Whether to apply the rotation of the meridian too, default to False.
Returns: r, v – Position and velocity vectors in ICRS.
Return type:
-
poliastro.coordinates.
icrs_to_body_centered
(r, v, target_body, epoch=<Time object: scale='tdb' format='jyear_str' value=J2000.000>, rotate_meridian=False)¶ Converts position and velocity in ICRS to body-centered frame.
Parameters: Returns: r, v – Position and velocity vectors in a body-centered reference frame.
Return type:
-
poliastro.coordinates.
inertial_body_centered_to_pqw
(r, v, source_body)¶ Converts position and velocity from inertial body-centered frame to perifocal frame.
Parameters: Returns: r_pqw, v_pqw – Position and velocity vectors in ICRS.
Return type:
poliastro.cli module¶
Command line functions.
poliastro.ephem module¶
Planetary ephemerides.
-
poliastro.ephem.
get_body_ephem
(body, epoch)¶ Position and velocity vectors of a given body at a certain time.
The vectors are computed with respect to the Solar System barycenter.
New in version 0.3.0.
Parameters: Returns: r, v – Position and velocity vectors.
Return type:
poliastro.examples module¶
Example data.
-
poliastro.examples.
iss
= 6772 x 6790 km x 51.6 deg orbit around Earth (♁)¶ ISS orbit example
Taken from Plyades (c) 2012 Helge Eichhorn (MIT License)
-
poliastro.examples.
molniya
= 6650 x 46550 km x 63.4 deg orbit around Earth (♁)¶ Molniya orbit example
-
poliastro.examples.
soyuz_gto
= 6628 x 42328 km x 6.0 deg orbit around Earth (♁)¶ Soyuz geostationary transfer orbit (GTO) example
Taken from Soyuz User’s Manual, issue 2 revision 0
-
poliastro.examples.
churi
= 1 x 6 AU x 7.0 deg orbit around Sun (☉)¶ Comet 67P/Churyumov–Gerasimenko orbit example
poliastro.hyper module¶
Utility hypergeometric functions.
-
poliastro.hyper.
hyp2f1b
¶ Hypergeometric function 2F1(3, 1, 5/2, x), see [Battin].
poliastro.maneuver module¶
Orbital maneuvers.
-
class
poliastro.maneuver.
Maneuver
(*impulses)¶ Class to represent a Maneuver.
Each
Maneuver
consists on a list of impulses \(\Delta v_i\) (changes in velocity) each one applied at a certain instant \(t_i\). You can access them directly indexing theManeuver
object itself.>>> man = Maneuver((0 * u.s, [1, 0, 0] * u.km / u.s), ... (10 * u.s, [1, 0, 0] * u.km / u.s)) >>> man[0] (<Quantity 0 s>, <Quantity [1,0,0] km / s>) >>> man.impulses[1] (<Quantity 10 s>, <Quantity [1,0,0] km / s>)
-
__init__
(*impulses)¶ Constructor.
Parameters: impulses (list) – List of pairs (delta_time, delta_velocity) Notes
TODO: Fix docstring, *args convention
-
classmethod
impulse
(dv)¶ Single impulse at current time.
-
classmethod
hohmann
(orbit_i, r_f)¶ Compute a Hohmann transfer between two circular orbits.
-
classmethod
bielliptic
(orbit_i, r_b, r_f)¶ Compute a bielliptic transfer between two circular orbits.
-
get_total_time
()¶ Returns total time of the maneuver.
-
get_total_cost
()¶ Returns total cost of the maneuver.
-
poliastro.patched_conics module¶
Patched Conics Computations
Contains methods to compute interplanetary trajectories approximating the three body problem with Patched Conics.
-
poliastro.patched_conics.
compute_soi
(body, a=None)¶ Approximated radius of the Laplace Sphere of Influence (SOI) for a body.
Parameters: Returns: Approximated radius of the Sphere of Influence (SOI) [m]
Return type:
poliastro.plotting module¶
Plotting utilities.
-
poliastro.plotting.
plot
(state, label=None)¶ Plots a
State
.For more advanced tuning, use the
OrbitPlotter
class.
-
class
poliastro.plotting.
OrbitPlotter
(ax=None, num_points=100)¶ OrbitPlotter class.
This class holds the perifocal plane of the first
State
plotted in it usingplot()
, so all following plots will be projected on that plane. Alternatively, you can callset_frame()
to set the frame before plotting.-
__init__
(ax=None, num_points=100)¶ Constructor.
Parameters:
-
set_frame
(p_vec, q_vec, w_vec)¶ Sets perifocal frame if not existing.
Raises: ValueError
– If the vectors are not a set of mutually orthogonal unit vectors.NotImplementedError
– If the frame was already set up.
-
set_attractor
(orbit)¶ Sets plotting attractor.
Parameters: orbit (Orbit) – orbit with attractor to plot.
-
plot
(orbit, label=None)¶ Plots state and osculating orbit in their plane.
-
poliastro.stumpff module¶
Stumpff functions.
-
poliastro.stumpff.
c2
¶ Second Stumpff function.
For positive arguments:
\[c_2(\psi) = \frac{1 - \cos{\sqrt{\psi}}}{\psi}\]
-
poliastro.stumpff.
c3
¶ Third Stumpff function.
For positive arguments:
\[c_3(\psi) = \frac{\sqrt{\psi} - \sin{\sqrt{\psi}}}{\sqrt{\psi^3}}\]
poliastro.util module¶
Function helpers.
-
poliastro.util.
circular_velocity
(k, a)¶ Compute circular velocity for a given body (k) and semimajor axis (a).
-
poliastro.util.
rotate
(vector, angle, axis='z', unit=None)¶ Rotates a vector around axis a right-handed positive angle.
This is just a convenience function around
astropy.coordinates.matrix_utilities.rotation_matrix()
.Parameters: - vector (array_like) – Dimension 3 vector.
- angle (convertible to Angle) – Angle of rotation.
- axis (str or 3-sequence) – Either ‘x’,’y’, ‘z’, or a (x,y,z) specifying an axis to rotate about. If ‘x’,’y’, or ‘z’, the rotation sense is counterclockwise looking down the + axis (e.g. positive rotations obey left-hand-rule).
- unit (UnitBase, optional) – If angle does not have associated units, they are in this unit. If neither are provided, it is assumed to be degrees.
Note
This is just a convenience function around
astropy.coordinates.matrix_utilities.rotation_matrix()
. This performs a so-called active or alibi transformation: rotates the vector while the coordinate system remains unchanged. To do the opposite operation (passive or alias transformation) call the function asrotate(vec, ax, -angle, unit)
or use the convenience functiontransform()
, see [1].References
[1] http://en.wikipedia.org/wiki/Rotation_matrix#Ambiguities
-
poliastro.util.
transform
(vector, angle, axis='z', unit=None)¶ Rotates a coordinate system around axis a positive right-handed angle.
Note
This is a convenience function, equivalent to
rotate(vec, -angle, axis, unit)
. Refer to the documentation ofrotate()
for further information.
-
poliastro.util.
norm
(vec)¶ Norm of a Quantity vector that respects units.