poliastro.twobody.orbit.creation

Module Contents

Classes

OrbitCreationMixin

Mixin-class containing class-methods to create Orbit objects

class poliastro.twobody.orbit.creation.OrbitCreationMixin(*_, **__)

Mixin-class containing class-methods to create Orbit objects

classmethod from_vectors(cls, attractor, r, v, epoch=J2000, plane=Planes.EARTH_EQUATOR)

Return Orbit from position and velocity vectors.

Parameters
  • attractor (Body) – Main attractor.

  • r (Quantity) – Position vector wrt attractor center.

  • v (Quantity) – Velocity vector.

  • epoch (Time, optional) – Epoch, default to J2000.

  • plane (Planes) – Fundamental plane of the frame.

classmethod from_coords(cls, attractor, coord, plane=Planes.EARTH_EQUATOR)

Creates an Orbit from an attractor and astropy SkyCoord or BaseCoordinateFrame instance.

This method accepts position and velocity in any reference frame unlike Orbit.from_vector which can accept inputs in only inertial reference frame centred at attractor. Also note that the frame information is lost after creation of the orbit and only the inertial reference frame at body centre will be used for all purposes.

Parameters
  • attractor (Body) – Main attractor

  • coord (SkyCoord or BaseCoordinateFrame) – Position and velocity vectors in any reference frame. Note that coord must have a representation and its differential with respect to time.

  • plane (Planes, optional) – Final orbit plane, default to Earth Equator.

classmethod from_classical(cls, attractor, a, ecc, inc, raan, argp, nu, epoch=J2000, plane=Planes.EARTH_EQUATOR)

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.

  • plane (Planes) – Fundamental plane of the frame.

classmethod from_equinoctial(cls, attractor, p, f, g, h, k, L, epoch=J2000, plane=Planes.EARTH_EQUATOR)

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.

  • plane (Planes) – Fundamental plane of the frame.

classmethod from_ephem(cls, attractor, ephem, epoch)

Create osculating orbit from ephemerides at a given epoch.

This will assume that the Ephem coordinates are expressed with respect the given body.

Parameters
  • ephem (Ephem) – Ephemerides object to use.

  • attractor (Body) – Body to use as attractor.

  • epoch (Time) – Epoch to retrieve the osculating orbit at.

classmethod from_sbdb(cls, name, **kwargs)

Return osculating Orbit by using SBDB from Astroquery.

Parameters
  • name (str) – Name of the body to make the request.

  • **kwargs – Extra kwargs for astroquery.

Returns

ss – Orbit corresponding to body_name

Return type

poliastro.twobody.orbit.Orbit

Examples

>>> from poliastro.twobody.orbit import Orbit
>>> apophis_orbit = Orbit.from_sbdb('apophis')  
classmethod circular(cls, attractor, alt, inc=0 * u.deg, raan=0 * u.deg, arglat=0 * u.deg, epoch=J2000, plane=Planes.EARTH_EQUATOR)

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.

  • plane (Planes) – Fundamental plane of the frame.

classmethod stationary(cls, attractor)

Return the stationary orbit for the given attractor and its rotational speed.

Parameters

attractor (Body) – Main attractor.

Returns

New orbit.

Return type

Orbit

classmethod synchronous(cls, attractor, period_mul=1 * u.one, ecc=0 * u.one, inc=0 * u.deg, argp=0 * u.deg, arglat=0 * u.deg, raan=0 * u.deg, epoch=J2000, plane=Planes.EARTH_EQUATOR)

Returns an orbit where the orbital period equals the rotation rate of the orbited body. The synchronous altitude for any central body can directly be obtained from Kepler’s Third Law by setting the orbit period Psync, equal to the rotation period of the central body relative to the fixed stars D*. In order to obtain this, it’s important to match orbital period with sidereal rotation period.

Parameters
  • attractor (Body) – Main attractor.

  • period_mul (Quantity) – Multiplier, default to 1 to indicate that the period of the body is equal to the sidereal rotational period of the body being orbited, 0.5 a period equal to half the average rotational period of the body being orbited, indicates a semi-synchronous orbit.

  • ecc (Quantity) – Eccentricity,default to 0 as a stationary orbit.

  • inc (Quantity) – Inclination,default to 0 deg.

  • raan (Quantity) – Right ascension of the ascending node,default to 0 deg.

  • argp (Quantity) – Argument of the pericenter,default to 0 deg.

  • arglat (Quantity, optional) – Argument of latitude, default to 0 deg.

  • epoch (Time, optional) – Epoch, default to J2000.

  • plane (Planes) – Fundamental plane of the frame.

Returns

New orbit.

Return type

Orbit

Raises

ValueError – If the pericenter is smaller than the attractor’s radius.

Notes

Thus:

\[ \begin{align}\begin{aligned}\begin{split}P_{s y n c}=D^{*} \\\end{split}\\\begin{split}a_{s y n c}=\left(\mu / 4 \pi^{2}\right)^{1 / 3}\left(D^{*}\right)^{2 / 3}\\\end{split}\\\begin{split}H_{s y n c}=a_{s y n c} - R_{p l a n e t}\\\end{split}\end{aligned}\end{align} \]
classmethod heliosynchronous(cls, attractor, a=None, ecc=None, inc=None, raan=0 * u.deg, argp=0 * u.deg, nu=0 * u.deg, epoch=J2000, plane=Planes.EARTH_EQUATOR)

Creates a Sun-Synchronous orbit.

These orbits make use of the J2 perturbation to precess in order to be always towards Sun. At least two parameters of the set {a, ecc, inc} are needed in order to solve for these kind of orbits.

Relationships among them are given by:

\[\begin{split}\begin{align} a &= \left (\frac{-3R_{\bigoplus}J_{2}\sqrt{\mu}\cos(i)}{2\dot{\Omega}(1-e^2)^2} \right ) ^ {\frac{2}{7}}\\ e &= \sqrt{1 - \sqrt{\frac{-3R_{\bigoplus}J_{2}\sqrt{\mu}cos(i)}{2a^{\frac{7}{2}}\dot{\Omega}}}}\\ i &= \arccos{\left ( \frac{-2a^{\frac{7}{2}}\dot{\Omega}(1-e^2)^2}{3R_{\bigoplus}J_{2}\sqrt{\mu}} \right )}\\ \end{align}\end{split}\]
Parameters
  • attractor (SolarSystemPlanet) – 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.

  • plane (Planes) – Fundamental plane of the frame.

classmethod parabolic(cls, attractor, p, inc, raan, argp, nu, epoch=J2000, plane=Planes.EARTH_EQUATOR)

Return a 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.

  • plane (Planes) – Fundamental plane of the frame.

classmethod frozen(cls, attractor, alt, inc=None, argp=None, raan=0 * u.deg, arglat=0 * u.deg, ecc=None, epoch=J2000, plane=Planes.EARTH_EQUATOR)

Return a frozen Orbit. If any of the given arguments results in an impossibility, some values will be overwritten

To achieve frozen orbit these two equations have to be set to zero.

\[\dfrac {d\overline {e}}{dt}=\dfrac {-3\overline {n}J_{3}R^{3}_{E}\sin \left( \overline {i}\right) }{2a^{3}\left( 1-\overline {e}^{2}\right) ^{2}}\left( 1-\dfrac {5}{4}\sin ^{2}\overline {i}\right) \cos \overline {w}\]
\[\dfrac {d\overline {\omega }}{dt}=\dfrac {3\overline {n}J_{2}R^{2}_{E}}{a^{2}\left( 1-\overline {e}^{2}\right) ^{2}}\left( 1-\dfrac {5}{4}\sin ^{2}\overline {i}\right) \left[ 1+\dfrac {J_{3}R_{E}}{2J_{2}\overline {a}\left( 1-\overline {e}^{2}\right) }\left( \dfrac {\sin ^{2}\overline {i}-\overline {e}\cos ^{2}\overline {i}}{\sin \overline {i}}\right) \dfrac {\sin \overline {w}}{\overline {e}}\right]\]

The first approach would be to nullify following term to zero:

\[( 1-\dfrac {5}{4}\sin ^{2})\]

For which one obtains the so-called critical inclinations: i = 63.4349 or 116.5651 degrees. To escape the inclination requirement, the argument of periapsis can be set to w = 90 or 270 degrees to nullify the second equation. Then, one should nullify the right-hand side of the first equation, which yields an expression that correlates the inclination of the object and the eccentricity of the orbit:

\[\overline {e}=-\dfrac {J_{3}R_{E}}{2J_{2}\overline {a}\left( 1-\overline {e}^{2}\right) }\left( \dfrac {\sin ^{2}\overline {i}-\overline {e}\cos ^{2} \overline {i}}{\sin \overline {i}}\right)\]

Assuming that e is negligible compared to J2, it can be shown that:

\[\overline {e}\approx -\dfrac {J_{3}R_{E}}{2J_{2}\overline {a}}\sin \overline {i}\]

The implementation is divided in the following cases:

  1. When the user gives a negative altitude, the method will raise a ValueError

  2. When the attractor has not defined J2 or J3, the method will raise an AttributeError

  3. When the attractor has J2/J3 outside of range 1 to 10 , the method will raise an NotImplementedError. Special case for Venus.See “Extension of the critical inclination” by Xiaodong Liu, Hexi Baoyin, and Xingrui Ma

  4. If argp is not given or the given argp is a critical value:

    • if eccentricity is none and inclination is none, the inclination is set with a critical value and the eccentricity is obtained from the last formula mentioned

    • if only eccentricity is none, we calculate this value with the last formula mentioned

    • if only inclination is none ,we calculate this value with the formula for eccentricity with critical argp.

  5. If inc is not given or the given inc is critical:

    • if the argp and the eccentricity is given we keep these values to create the orbit

    • if the eccentricity is given we keep this value, if not, default to the eccentricity of the Moon’s orbit around the Earth

  6. if it’s not possible to create an orbit with the the argp and the inclination given, both of them are set to the critical values and the eccentricity is calculate with the last formula

Parameters
  • attractor (Body) – Main attractor.

  • alt (Quantity) – Altitude over surface.

  • inc (Quantity, optional) – Inclination, default to critical value.

  • argp (Quantity, optional) – Argument of the pericenter, default to critical value.

  • raan (Quantity, optional) – Right ascension of the ascending node, default to 0 deg.

  • arglat (Quantity, optional) – Argument of latitude, default to 0 deg.

  • ecc (Quantity) – Eccentricity, default to the eccentricity of the Moon’s orbit around the Earth

  • epoch (Time, optional) – Epoch, default to J2000.

  • plane (Planes) – Fundamental plane of the frame.