CelestLab


Table of Contents

I. About
CelestLabGeneral presentation of CelestLab
Reference Frames and time scales Presentation of Reference Frames and time scales used in CelestLab
II. Coordinates and frames
CL_co_car2ell — Cartesien to elliptical coordinates
CL_co_car2sph — Cartesien to spherical coordinates
CL_co_ell2car — Elliptical to cartesien coordinates
CL_co_sph2car — Spherical to cartesien coordinates
CL_dat_cal2cjd — Calendar date to CNES Julian Day
CL_dat_cal2jd — Calendar date to Julian Date
CL_dat_cjd2cal — CNES Julian date to calendar date
CL_dat_cjd2jd — CNES Julian date to Julian date
CL_dat_cjd2mjd — CNES Julian date to Modified Julian date
CL_dat_jd2cal — Julian Date to calendar date
CL_dat_jd2cjd — Julian date to CNES Julian date
CL_dat_mjd2cjd — Modified Julian Date to CNES Julian date
CL_dat_tai2utc — TAI to UTC conversion
CL_dat_utc2tai — UTC to TAI conversion
CL_fr_G502J2000 — Gamma50 (Veis) to EME2000 (J2000) frame vector transformation
CL_fr_G502J2000Mat — Gamma50 (Veis) to EME2000 (J2000) matrix
CL_fr_G502ter — Gamma50 (Veis) to terrestrial frame vector transformation
CL_fr_G502terMat — Gamma50 (Veis) to terrestrial matrix
CL_fr_H0n2J2000Mat — H0-n to EME2000 matrix
CL_fr_J20002G50 — EME2000 (J2000) to Gamma50 (Veis) frame vector transformation
CL_fr_J20002ter — EME2000 (J2000) to terrestrial frame vector transformation
CL_fr_inertial2qsw — Inertial to local orbital frame (q,s,w) vector transformation
CL_fr_inertial2tnw — Inertial to local orbital frame (t,n,w) vector transformation
CL_fr_lvlhMat — Local orbital frame (LVLH) definition in an inertial frame
CL_fr_qsw2inertial — Local orbital (q,s,w) to inertial frame vector transformation
CL_fr_qswMat — Local orbital frame (q,s,w) definition in an inertial frame
CL_fr_teme2J2000Mat — TEME to J2000 matrix
CL_fr_ter2G50 — Gamma50 (Veis) to G50restrial frame vector transformation
CL_fr_ter2J2000 — Terrestrial to EME2000 (J2000) frame vector transformation
CL_fr_ter2J2000Mat — Terrestrial to EME2000 (J2000) matrix
CL_fr_ter2topoN — Terrestrial to topocentric north frame vector transformation
CL_fr_tnw2inertial — Local orbital (t,n,w) to inertial frame vector transformation
CL_fr_tnwMat — Local orbital frame (t,n,w) definition in an inertial frame
CL_fr_topoN2ter — Topocentric north to terrestrial frame vector transformation
CL_fr_topoNMat — Local topocentric north frame
CL_oe_car2cir — Cartesien to circular adapted orbital elements
CL_oe_car2cirEqua — Cartesien to circular equatorial adapted orbital elements
CL_oe_car2kep — Cartesien to keplerian orbital elements
CL_oe_cir2car — Circular adapted to cartesien orbital elements
CL_oe_cirEqua2car — Circular equatorial adapted to cartesien orbital elements
CL_oe_cirEqua2kep — Circular equatorial adapted to keplerian orbital elements
CL_oe_kep2car — Keplerian to cartesian orbital elements
CL_oe_kep2cirEqua — Keplerian to circular equatorial adapted orbital elements
CL_rot_angles2matrix — Rotation angles matrix
CL_rot_angularVelocity — Rotation angles to velocity and acceleration vectors
CL_rot_axAng2quat — Rotation axis and angle to quaternion
CL_rot_defQuat — Quaternion definition from its real or imaginary components
CL_rot_eul2quat — Euler '123' angles to quaternion
CL_rot_matrix2quat — Matrix to quaternion
CL_rot_quat2eul — Quaternion to Euler '123' angles
CL_rot_quat2matrix — Quaternion to matrix
CL_rot_quatSlerp — Spherical linear interpolation between 2 quaternions
CL_rot_rotVect — Rotation(defined by a quaternion) of a vector
III. Geometry and events
CL_ev_defEvent — Events definition
CL_ev_defSensor — Sensor definition
CL_ev_defStation — Station definition
CL_ev_events — Events computation
CL_gm_beta2raan — Beta to right ascension of ascending node angle
CL_gm_betaEclipse — Eclipse angular semi amplitude wrt beta angle for circular orbits.
CL_gm_eclipseCir — Analytic eclipse calculation for circular orbits
CL_gm_equatorialOverlap — Ratio between equatorial sensor swath and equatorial ground track
CL_gm_equatorialSwath — Satellite instrument swath to ensure overlap ratio of 1 at equator
CL_gm_inertial2orbitSph — Spherical coordinates conversion from inertial frame to orbital frame
CL_gm_intersectPlanes — Arguments of latitudes at the intersection of 2 planes
CL_gm_lat2locTime — Local time at given latitude for a sun synchronous orbit
CL_gm_locSolTime — Local solar time
CL_gm_orbit2inertialSph — Spherical coordinates conversion from orbital frame to inertial frame
CL_gm_orbitalNoon — Latitude argument of the orbital noon on the given orbit
CL_gm_pixelSize — Deformation ratio of a pixel for a given altitude and a given swath (tilt)
CL_gm_raan2beta — Right ascension of ascending node to beta angle
CL_gm_sphericDist — Great circle distance between 2 geographic coordinates
CL_gm_stationElevation — Ground stations elevations of satellites positions.
CL_gm_sunZenithAngle — Sun zenith angle and sun azimuth in function of latitude, sun declination and local hour of a Earth's point.
CL_gm_visiParams — Visibility parameters (angles, distance…) for a spherical planet
CL_gm_visibility — Geometric station visibilities start and end dates.
IV. Interplanetary
CL_3b_environment — Creates environment for 3-body problem functions
CL_3b_halo — Halo orbit
CL_3b_lissajous — Lissajous orbit
CL_3b_manifolds — Manifolds (divergent and convergent) from Halo and Lissajous
V. Models
CL_mod_atmUS76 — US 76 Atmosphere model
CL_mod_equinoxesEquation — Equation of the equinoxes (IERS 1996)
CL_mod_expDensity — Exponential density model
CL_mod_expDensityDrag — Atmospheric drag using exponential density model
CL_mod_meanObliquity — Mean obliquity (IERS 1996)
CL_mod_moonSunG50 — Moon and Sun coordinates in Gamma50 (Veis) frame
CL_mod_nutationAngles — Nutation angles (Wahr IAU 1980)
CL_mod_nutationArg — Fundamental arguments for nutation
CL_mod_nutationMatrix — Nutation matrix and rotation vectors (IERS 1996)
CL_mod_planetsG50ecl — Planets positions on Gamma50 (Veis) ecliptic
CL_mod_polarMotionMatrix — Polar motion matrix
CL_mod_precessionAngles — Precession angles (Lieske 1976)
CL_mod_precessionMatrix — Precession matrix and rotation vectors (IERS 1996)
CL_mod_sidTime — Greenwich mean sideral time (IERS 1996)
CL_mod_sidTimeG50 — Sideral time in Gamma50 (Veis) frame
VI. Orbit properties
CL_kp_E2M — Eccentric anomaly to mean anomaly for elliptic and hyperbolic orbits
CL_kp_E2v — Eccentric anomaly to true anomaly
CL_kp_M2E — Solution of kepler's equation (ecc,M to E)
CL_kp_M2Egene — Solution of generalized kepler's equation (ex, ey, M to E)
CL_kp_M2v — True anomaly to mean anomaly
CL_kp_characteristics — Various Keplerian characteristics
CL_kp_params — Orbit properties with a Keplerian motion (mean motion, period, longitude gap between 2 orbits)
CL_kp_v2E — True anomaly to eccentric anomaly
CL_kp_v2M — True anomaly to mean anomaly
CL_op_driftJ2 — Drift of orbital elements due to J2
CL_op_frozenOrbit — Eccentricity and perigee argument for a frozen orbit
CL_op_frozenOrbitDer — Eccentricity and perigee drift over time for an orbit close to a frozen orbit
CL_op_locTime — Local time or right ascension at date
CL_op_paramsJ2 — Orbit properties including J2 effects (mean motion, period, nodal period, longitude gap between 2 orbits)
CL_op_rarp2ae — Apoapsis radius and periapsis radius to semi major axis and eccentricity (elliptic orbits)
CL_op_rava2ae — Apoapsis radius and velocity to semi major axis and eccentricity (elliptic orbits)
CL_op_repeat2smaInc — Repeat orbit parameters (N,P,Q) to semi major axis and inclination
CL_op_repeatGroundTracks — Longitudes of repeating ground tracks
CL_op_rpvinf2ae — Periapsis radius and velocity at infinity to semi major axis and eccentricity (hyperbolic orbits)
CL_op_rpvp2ae — Periapsis radius and velocity at periapsis to semi major axis and eccentricity
CL_op_searchRepeatOrbits — Search for repeat orbits
CL_op_ssoJ2 — Semi major axis, eccentricity or inclination for a sun synchronous orbit (J2)
VII. Relative motion
CL_cw_Mmatrix — Clohessy-Wiltshire M matrix
CL_cw_Nmatrix — Clohessy-Wiltshire N Matrix
CL_cw_ballisticPropa — Ballistic propagation of a chaser relatively to a target
CL_cw_circularDrift — Clohessy-Wiltshire circular drift
CL_cw_contPropa — Continuous thrust trajectory
CL_cw_diffDrag — Differential acceleration drag
CL_cw_hohmannLine — Hohmann line
CL_cw_impulPropa — Propagation of a chaser relatively to a target, with impulsives maneuvers
CL_cw_meanChaser — Mean chaser
CL_cw_twoImpulse — Two-impulse transfer
VIII. Trajectory and maneuvers
CL_dsp_covCoord — Change coordinates of covariance matrix
CL_dsp_kepCovPropa — Covariance propagation (Keplerian)
CL_ex_eckHech — Eckstein Hechler orbit extrapolation analytic model
CL_ex_kepler — Keplerian orbit extrapolation
CL_ex_lyddane — Lydanne orbit extrapolation analytic model
CL_ex_lyddaneMan — Lydanne orbit extrapolation analytic model with maneuvers
CL_ex_meanEckHech — Mean parameters of the Eckstein Hechler orbit extrapolation analytic model
CL_ex_meanLyddane — Mean parameters of the Lydanne orbit extrapolation model
CL_ex_secularJ2 — Secular J2 effects orbit propagation
CL_man_applyDv — Modification of osculating orbital elements after a maneuver defined in QSW frame.
CL_man_apsidesLine — Delta V for a maneuver to modify line of apsides
CL_man_biElliptic — Total delta V for a bi-elliptic Hohmann transfer
CL_man_consumption — Mass consumed, delta V, isp or initial mass
CL_man_hohmann — Delta V for a hohmann transfer
CL_man_hohmannG — Delta V for a generalized Hohmann transfer maneuver
CL_man_incRaanCirc — Inclination and RAAN maneuver for circular orbits
CL_man_inclination — Delta V for an inclination maneuver
CL_man_lambert — Lambert's problem
CL_man_sma — Delta V for an orbit shape modification (semi major axis)
CL_man_thrustDuration — Thrust duration, mass consumed, thrust value or propellant specific impulse
IX. Utilities
CL_colGcd — Greatest common divisor (gcd or pgcd) for 2 vectors of integers (elementwise)
CL_colMult — Multiplication of each columns of a matrix
CL_colNorm — Columnwise vectorized norm
CL_cor2cov — Correlation to covariance matrix
CL_cov2cor — Covariance to correlation matrix
CL_covDraw — Draw samples from covariance
CL_cross — Vector cross product
CL_dot — Vector scalar product
CL_evalPoly — Evaluate a matrix of polynoms
CL_init — Defines CelestLab constants as global and returns them
CL_intervInters — Intersection of intervals
CL_intervInv — "Inversion" of intervals
CL_intervUnion — Union of intervals
CL_matSort — Sorts increasingly or decreasingly a row or a column of a matrix
CL_plot_earthMap — Plots an earth map (continents, lakes and islands)
CL_plot_ephem — Plots ground tracks of the given position ephemeris
CL_rMod — Modulo between 2 values
CL_stat — Statistics on a matrix of samples
CL_stumpC — Stumpff function C(z)
CL_stumpS — Stumpff function S(z)
CL_unitVector — Vector normalization
CL_vectAngle — Angle between vectors

List of Figures

1. ITRF International Terrestrial Reference Frame
2. Earth Mean Equator and Mean Equinox of Epoch J2000
3. Rotation Terrestrial to Celestial
4. G50 (Veis) Reference Frame