boinor.twobody.orbit.creation ============================= .. py:module:: boinor.twobody.orbit.creation .. autoapi-nested-parse:: module related to orbit creation in the twobody sub-package Classes ------- .. autoapisummary:: boinor.twobody.orbit.creation.OrbitCreationMixin Module Contents --------------- .. py:class:: OrbitCreationMixin(*_, **__) Mixin-class containing class-methods to create Orbit objects. .. py:method:: from_vectors(attractor, r, v, epoch=J2000, plane=Planes.EARTH_EQUATOR) :classmethod: Return `Orbit` from position and velocity vectors. :param attractor: Main attractor. :type attractor: Body :param r: Position vector wrt attractor center. :type r: ~astropy.units.Quantity :param v: Velocity vector. :type v: ~astropy.units.Quantity :param epoch: Epoch, default to J2000. :type epoch: ~astropy.time.Time, optional :param plane: Fundamental plane of the frame. :type plane: ~boinor.frames.Planes .. py:method:: apply_impulse(v) Apply impulse to `Orbit`. :param v: Velocity vector. :type v: ~astropy.units.Quantity :param epoch: Epoch, default to J2000. :type epoch: ~astropy.time.Time, optional :param plane: Fundamental plane of the frame. :type plane: ~poliastro.frames.Planes .. py:method:: from_coords(attractor, coord, plane=Planes.EARTH_EQUATOR) :classmethod: 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. :param attractor: Main attractor :type attractor: Body :param coord: Position and velocity vectors in any reference frame. Note that coord must have a representation and its differential with respect to time. :type coord: ~astropy.coordinates.SkyCoord or ~astropy.coordinates.BaseCoordinateFrame :param plane: Final orbit plane, default to Earth Equator. :type plane: ~boinor.frames.Planes, optional .. py:method:: from_classical(attractor, a, ecc, inc, raan, argp, nu, epoch=J2000, plane=Planes.EARTH_EQUATOR) :classmethod: Return `Orbit` from classical orbital elements. :param attractor: Main attractor. :type attractor: Body :param a: Semi-major axis. :type a: ~astropy.units.Quantity :param ecc: Eccentricity. :type ecc: ~astropy.units.Quantity :param inc: Inclination :type inc: ~astropy.units.Quantity :param raan: Right ascension of the ascending node. :type raan: ~astropy.units.Quantity :param argp: Argument of the pericenter. :type argp: ~astropy.units.Quantity :param nu: True anomaly. :type nu: ~astropy.units.Quantity :param epoch: Epoch, default to J2000. :type epoch: ~astropy.time.Time, optional :param plane: Fundamental plane of the frame. :type plane: ~boinor.frames.Planes .. py:method:: from_equinoctial(attractor, p, f, g, h, k, L, epoch=J2000, plane=Planes.EARTH_EQUATOR) :classmethod: Return `Orbit` from modified equinoctial elements. :param attractor: Main attractor. :type attractor: Body :param p: Semilatus rectum. :type p: ~astropy.units.Quantity :param f: Second modified equinoctial element. :type f: ~astropy.units.Quantity :param g: Third modified equinoctial element. :type g: ~astropy.units.Quantity :param h: Fourth modified equinoctial element. :type h: ~astropy.units.Quantity :param k: Fifth modified equinoctial element. :type k: ~astropy.units.Quantity :param L: True longitude. :type L: ~astropy.units.Quantity :param epoch: Epoch, default to J2000. :type epoch: ~astropy.time.Time, optional :param plane: Fundamental plane of the frame. :type plane: ~boinor.frames.Planes .. py:method:: from_ephem(attractor, ephem, epoch) :classmethod: Create osculating orbit from ephemerides at a given epoch. This will assume that the `Ephem` coordinates are expressed with respect the given body. :param attractor: Body to use as attractor. :type attractor: ~boinor.bodies.Body :param ephem: Ephemerides object to use. :type ephem: ~boinor.ephem.Ephem :param epoch: Epoch to retrieve the osculating orbit at. :type epoch: ~astropy.time.Time .. py:method:: from_sbdb(name, **kwargs) :classmethod: Return osculating `Orbit` by using `SBDB` from Astroquery. :param name: Name of the body to make the request. :type name: str :param \*\*kwargs: Extra kwargs for astroquery. :returns: **ss** -- Orbit corresponding to body_name :rtype: boinor.twobody.orbit.Orbit .. rubric:: Examples >>> from boinor.twobody.orbit import Orbit >>> apophis_orbit = Orbit.from_sbdb('apophis') # doctest: +REMOTE_DATA .. py:method:: circular(attractor, alt, inc=0 * u.deg, raan=0 * u.deg, arglat=0 * u.deg, epoch=J2000, plane=Planes.EARTH_EQUATOR) :classmethod: Return circular `Orbit`. :param attractor: Main attractor. :type attractor: Body :param alt: Altitude over surface. :type alt: ~astropy.units.Quantity :param inc: Inclination, default to 0 deg (equatorial orbit). :type inc: ~astropy.units.Quantity, optional :param raan: Right ascension of the ascending node, default to 0 deg. :type raan: ~astropy.units.Quantity, optional :param arglat: Argument of latitude, default to 0 deg. :type arglat: ~astropy.units.Quantity, optional :param epoch: Epoch, default to J2000. :type epoch: ~astropy.time.Time, optional :param plane: Fundamental plane of the frame. :type plane: ~boinor.frames.Planes .. py:method:: stationary(attractor) :classmethod: Return the stationary orbit for the given attractor and its rotational speed. :param attractor: Main attractor. :type attractor: Body :returns: New orbit. :rtype: Orbit .. py:method:: synchronous(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) :classmethod: 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 P\ :sub:`sync`, equal to the rotation period of the central body relative to the fixed stars D\ :sup:`*`. In order to obtain this, it's important to match orbital period with sidereal rotation period. :param attractor: Main attractor. :type attractor: Body :param period_mul: 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. :type period_mul: ~astropy.units.Quantity :param ecc: Eccentricity,default to 0 as a stationary orbit. :type ecc: ~astropy.units.Quantity :param inc: Inclination,default to 0 deg. :type inc: ~astropy.units.Quantity :param raan: Right ascension of the ascending node,default to 0 deg. :type raan: ~astropy.units.Quantity :param argp: Argument of the pericenter,default to 0 deg. :type argp: ~astropy.units.Quantity :param arglat: Argument of latitude, default to 0 deg. :type arglat: ~astropy.units.Quantity, optional :param epoch: Epoch, default to J2000. :type epoch: ~astropy.time.Time, optional :param plane: Fundamental plane of the frame. :type plane: ~boinor.frames.Planes :returns: New orbit. :rtype: Orbit :raises ValueError: If the pericenter is smaller than the attractor's radius. .. rubric:: Notes Thus: .. math:: P_{s y n c}=D^{*} \\ a_{s y n c}=\left(\mu / 4 \pi^{2}\right)^{1 / 3}\left(D^{*}\right)^{2 / 3}\\ H_{s y n c}=a_{s y n c} - R_{p l a n e t}\\ .. py:method:: heliosynchronous(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) :classmethod: 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: .. math:: \begin{aligned} 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{aligned} :param attractor: Attractor. :type attractor: ~boinor.bodies.SolarSystemPlanet :param a: Semi-major axis. :type a: ~astropy.units.Quantity :param ecc: Eccentricity. :type ecc: ~astropy.units.Quantity :param inc: Inclination. :type inc: ~astropy.units.Quantity :param raan: Right ascension of the ascending node. :type raan: ~astropy.units.Quantity :param argp: Argument of the pericenter. :type argp: ~astropy.units.Quantity :param nu: True anomaly. :type nu: ~astropy.units.Quantity :param epoch: Epoch, default to J2000. :type epoch: ~astropy.time.Time, optional :param plane: Fundamental plane of the frame. :type plane: ~boinor.frames.Planes .. py:method:: parabolic(attractor, p, inc, raan, argp, nu, epoch=J2000, plane=Planes.EARTH_EQUATOR) :classmethod: Return a parabolic `Orbit`. :param attractor: Main attractor. :type attractor: Body :param p: Semilatus rectum or parameter. :type p: ~astropy.units.Quantity :param inc: Inclination. :type inc: ~astropy.units.Quantity, optional :param raan: Right ascension of the ascending node. :type raan: ~astropy.units.Quantity :param argp: Argument of the pericenter. :type argp: ~astropy.units.Quantity :param nu: True anomaly. :type nu: ~astropy.units.Quantity :param epoch: Epoch, default to J2000. :type epoch: ~astropy.time.Time, optional :param plane: Fundamental plane of the frame. :type plane: ~boinor.frames.Planes .. py:method:: frozen(attractor, alt, inc=None, argp=None, raan=0 * u.deg, arglat=0 * u.deg, ecc=None, epoch=J2000, plane=Planes.EARTH_EQUATOR) :classmethod: 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. .. math:: \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} .. math:: \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: .. math:: ( 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: .. math:: \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: .. math:: \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 :param attractor: Main attractor. :type attractor: Body :param alt: Altitude over surface. :type alt: ~astropy.units.Quantity :param inc: Inclination, default to critical value. :type inc: ~astropy.units.Quantity, optional :param argp: Argument of the pericenter, default to critical value. :type argp: ~astropy.units.Quantity, optional :param raan: Right ascension of the ascending node, default to 0 deg. :type raan: ~astropy.units.Quantity, optional :param arglat: Argument of latitude, default to 0 deg. :type arglat: ~astropy.units.Quantity, optional :param ecc: Eccentricity, default to the eccentricity of the Moon's orbit around the Earth :type ecc: ~astropy.units.Quantity :param epoch: Epoch, default to J2000. :type epoch: ~astropy.time.Time, optional :param plane: Fundamental plane of the frame. :type plane: ~boinor.frames.Planes