Orbit Functions

Orbit Module

Directory List

Constellations Demos/GravityModels Demos/Interplanetary
Demos/OrbitControl Demos/OrbitCoord Demos/OrbitManeuver
Demos/OrbitMechanics Demos/OrbitPropagator Demos/OrbitSim
Demos/ThreeBody Demos/Visualization Glideslope
GravityModels Interplanetary LowEnergyManeuver
OrbitControl OrbitCoord OrbitData
OrbitManeuver OrbitMechanics OrbitPropagator
OrbitSim RHSOrbit ThreeBody
Visualization


Constellations

Compute orbital elements for a Walker constellation.

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Demos/GravityModels

Compare gravity models

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Demos/Interplanetary

Set up and run a heliocentric trajectory simulation with two objects.
Spiral to a Hohmann Transfer to Apophis.

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Demos/OrbitControl

Compute a transfer from earth orbit to the asteroid Apophis.
Simulates two orbits and applies a relative controller.
Demonstrates the Lambert targeting function DVTarget.

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Demos/OrbitCoord

Test ComputeTLE

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Demos/OrbitManeuver

Plan the AKM burn by looking at the AKM thrust variations as a function of temperature.
Demonstrates drag compensation maneuvers.
GEO Stationkeeping Example
Low thrust geo transfer
Low thrust geo transfer
Computes the insertion delta-V for a Hohmann transfer.
Compute the total delta-V for the JIMO mission
Compute the delta-V for a low thrust mission to Mars synchronous orbit.
Perform an optimal transfer from earth to mars orbits.
Hohmann transfer to Mars.
Runs demonstrations of selected orbit maneuver functions.
Inclination Change
Orbit separation simulation with discrete delta-Vs
Orbit separation demo
Demonstrate the various orbit change functions.
Compute delta-v dispersions given declination and velocity errors.
Delta-V for a Hohmann transfer between LEO and GEO.
Computes a preliminary design of a two stage to orbit vehicle.

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Demos/OrbitMechanics

Demonstrate a fuel budget for the ComStar satellite.
Propagate an orbit about the moon. Show the visibility sun, earth, moon.
Sun-Synchronous Orbit Demo
Demo two of the five NORAD element propagators.
Generates two orbits and plots their relative positions

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Demos/OrbitPropagator

Demonstrate drag reentry.
Demonstrate using an external gravity model with PropagateOrbitPlugIn.
Integration Accuracy for PropagateOrbitPlugin.
Demonstrate low thrust transfer using PropagateOrbitPlugIn.
Demonstrate using PropgateOrbitPlugin in batch
Integration accuracy study comparing RK4, RK45, and ode113.
Compare various orbit propagators with a Topex ephemeris.

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Demos/OrbitSim

Simulate a spacecraft in orbit near the earth and moon.
Simple demo to compute drag over one orbit
Simulates a spacecraft in earth orbit with spherical harmonics.
Using a spherical harmonic gravity model
Interstellar mission simulation with a sun gravity assist.
Perform LEOP (Launch and Early Analysis Phase) analysis.
Linear orbit simulation. This compares nonlinear with linear.
Simulates a low thrust escape from an earth orbit.
Perform a helicocentric simulation from one circular orbit to another.
Simulate the solar system using an n-body model
Simulates two orbits and plots their relative positions.
Orbit simulation of a solar sail.
Investigate orbit coordinate systems.
Simulate an orbit using the variational equations.

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Demos/ThreeBody

Simulates a spiral out from LEO.

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Demos/Visualization

Generates a Mars orbit plot.
Demonstrate the OrbView function.
Visualize relative orbital motion in the inertial frame.
Demonstrate a high order gravity model.

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Glideslope

Visualize a set of maneuvers propagated with Clohessy-Wiltshire equations.
A special formulation of the Clohessy-Wiltshire equations.
Form:
Form:
Form:
Calculate sequential glideslope maneuvers for planning purposes.
Form:
Form:

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GravityModels

EarthGravityModel.mat - Earth GEMT1 model in a mat file.
GEMT1.geo - GEMT1 gravity model.
Create a gravity map from a gravity model.
JGM2.geo - JGM2 gravity model.
JGM3.geo - JGM3 gravity model.
Load the GEMT1 data.
Load a spherical harmonic gravity model from GSFC/University of Texas at Austin.
Load the LP150Q Lunar gravity model.
Load the SGM150 Lunar gravity model.
LunarGravityModel.mat - Gravity model based on Lunar Prospector, 75x75
Generate a normalization matrix for spherical harmonics
Process an ascii file of spherical harmonic coefficients.
Computes the acceleration due to the Sun and the Earth/Moon.
Remove normalization from a gravity model
WGS84.geo - WGS84 gravity model.
jgl075g1.sha - Lunar spherical harmonic ASCII file

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Interplanetary

Generate elements and orbit state for the asteroid Apophis.
Compute the position and velocity of Earth in the heliocentric frame.
Computes the heliocentric orbital elements after an Earth escape spiral.
Computes the ECI parking orbit plane for a heliocentric injection.
Simple thruster force model for orbit simulations
Calculate the heliocentric gravity for the position and date.
Initialize a heliocentric orbit from a planet centered orbit.
Transformation matrix from the heliocentric to B-plane frame.
Find the Julian Date for a straight line trajectory to the target
Double rendezvous problem between two planets.
Thruster force model producing zero force.
Plots planet alignments fur successive synodic periods.
Compute the phase angle in the ecliptic plane of a given planet at jD.
Compute Julian Dates for times when two planets are closest.
Compute and plot positions of planet1 and planet2 at the specified times.
Generate a Lambert transfer between two planets.
B-plane plots using HelioToBPlane.
Right-Hand-Side function for solar system object trajectories
Computes planet heliocentric states for a range of dates.
Computes the synodic period from planets.

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LowEnergyManeuver

Calculate from Jacobi constant from a scaled state vector
Check to see if MATLAB contains the Optimization Toolbox
Keplerian Energy with respect to the Moon
Compute a periodic orbit for a LET transfer. The orbit has nearest periapsis
Calculate the nominal transfer time for a low energy transfer
Compute a ballistic lunar capture trajectory from a circular orbit
Calculate a low energy transfer in a CRTBP.
Minimize the keplerian energy of the final state of a transfer orbit
Find a second perpendicular crossing of the x-axis
Plot the Low Energy Transfer
Plot the Low Energy Transfer for a 3 body problem in a Non-Rotating
Transfer a CRTBP LET to the restricted 3 body, non-planar problem.
Transfer a LET from the restricted 3BP to the Sun/Planet/Moon 4BP
Obtain a refined maneuver magnitude for transferring an orbit from the
Calculate an initial velocity from the jacobi constant

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OrbitControl

Compute two delta-v's to raise the apogee and circularize the orbit.
Perform targeting using the Lambert algorithm.
Compute accelerations for a point to point trajectory.
Updates orbital elements based on an impulsive delta-V
Right hand side for locally optimizing the Lambert time of flight problem.
Creates a linear quadratic relative orbit controller.
Use Lambert with Nelder-Meade simplex optimization of start and transfer time
Low thrust control.
Compute delta-Vs for rendezvous.
Converts the transfer time to delta-V for a rendezvous.

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OrbitCoord

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Computes the perigee radius from a.
Convert angles to right ascension and declination
Converts semi-major axis and eccentricity to right perigee and apogee.
Computes v and r given a, e and nu.
Convert semi-major axis & ecc. to velocity, altitude, flight path angle
Converts semi-major axis, eccentricy and r to true anomaly.
[a,th,i,q1,q2,W] -> [a,i,W,w,e,M]
Computes the ECI position of the Earth-Moon Barycenter.
Transformation matrix from ecliptic to Sun-Earth rotating frame.
Transformation matrix from equinoctial to cartesian coordinates.
Scales CRTBP Jacobi coordinates to km and sec
Converts tangential accelerations into radial using the true anomaly.
Converts tangential accelerations into radial using the elements vector.
Converts tangential accelerations into radial using equinoctial elements.
Convert a cartesian orbit state to cylindrical orbit coordinates.
Compute inertial position and velocity given circular orbit elements
Compute two-line elements from osculating elements
Convert NORAD TLE string into a data structure.
Convert a cylindrical orbit state to a cartesian orbit.
Ratio of apogee radius to perigee radius given eccentricity for an ellipsew
Compute the transformation matrix that rotates ECEF to ECI coordinates.
This function takes a position vector and orbit normal vector in ECI
Convert ECI to Earth Moon rotating coordinates about the barycenter.
Transform from ECI to Rotating Libration Point Coordinates
Convert ECI to Sun Earth rotating coordinates about the barycenter.
Scale EMB system to be non-dimensional
Compute the transformation matrix that rotates ENU to ECEF coordinates.
Convert the standard orbital element set into an Alfriend orbital element set
Converts conventional elements to equinoctial elements.
Converts orbital elements to commonly used angular quantities
Converts equinoctial elements to Keplerian elements.
Converts equinoctial elements to r and v for an elliptic orbit.
Computes the flight path angle from eccentricity and true anomaly.
Computes the transformation matrix from heliocentric to planet fixed frame.
Compute the initial quaternion and body rates for a circular orbit,
Transform from J2000 to rotating-pulsating
Transform a state vector from the J2000 reference frame to a rotating
Converts eccentric longitude to true longitude
Transform from km and sec to Jacobi coordinates for circular restricted
Converts eccentric longitude to true longitude
Compute range and azimuth angle between two points on a sphere.
Determine the locus of visibility for a satellite above a planet.
Computes true anomaly from a series expansion
Eccentric longitude from the mean longitude by solving Kepler's equation.
Approximate eccentric longitude from the mean longitude.
Computes the differences between orbital element vectors.
Conmputes the orbit normal from orbital elements.
Computes the orbit normal from equinoctial elements.
Computes closest orbit point to points on the earth.
Display the orbital plane with the Earth.
Determine whether r is in a area on the surface of an Earth sphere
Computes the parameter for any orbit.
Computes planet centered orbital elements.
Computes the semi major axis from apogee and perigee radii
Computes the eccentricity from apogee and perigee radii
Transform (range,azimuth) to (latitude,longitude) coordinates.
Computes the orbit radius and the parameter from Keplerian elements.
Computes the orbit radius and the parameter from equinoctial elements.
Transform (range,azimuth) to (latitude,longitude) coordinates
Computes a collinear Lagrange point.
Computes the orbit radius.
Computes the orbit position vector in the perifocal plane.
Converts perigee and apogee to semi-major axis and eccentricity
Converts perigee and velocity at perigee to a and e
Computes true anomaly from semi-major axis, eccentricity and radius.
Converts R and V to a, e, rP and rA.
Converts R and V to Equinoctial elements
Right ascension and declination with their rates from position and velocity vectors.
Computes relative coordinates between two orbits.
Find the relative coordinate state vector between x2 and x1.
Transform a state vector from a rotating pulsating reference frame
Transform pos. and vel. from inertial heliocentric frame to
Transform from Sun-Earth/Moon rotating to inertial frame
Scale position and velocity in SEM system (rotating or inertial) by
Computes the semi-latus rectum.
Computes the matrix from TEME to the pseudo-earth fixed frame.
Transform ECI pos. and vel. to Earth Moon barycenter rotating frame.
Transform ECI pos. and vel. to Sun-Earth-Moon rotating (SEMR) frame.
Transform pos. and vel. from Earth Moon barycenter rotating frame to ECI
Transform Sun-Earth-Moon rotating (SEMR) state to ECI frame.
Transform Sun-Earth-Moon rotating (SEMR) state to the heliocentric frame.
Generates an array of true anomalies.
Computes the orbit velocity in the perifocal plane.
Computes sma and eccentricity given v and r.
Converts flight path angle, velocity and r to orbital elements.
Compute (VF,gammaF) at hF from (V0,gamma0) at h0.

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OrbitData

Specifies Earth-Moon system constants
LEOData.mat - Sample LEO orbit data.
MirNORAD.txt - Mir NORAD elements data.
Reads in JPL Horizons data.
Specifies Sun-Earth-Moon system constants.
earthmap.fig - 3D Earth map in Normalized Earth-Fixed Coordinates.
mir.txt - Mir NORAD elements.
sdp.txt - SDP NORAD 2 line elements test data
sgp.txt - SGP NORAD 2 line elements test data

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OrbitManeuver

Convert an acceleration vector into a thrust quaternion.
Delta-V to change apogee.
Compute the delta V required to change perigee
Compute maneuver profile for a circular maneuver.
Computes the temperature required to achieve the desired delta-V.
Computes the velocity and inclination errors for a delta V burn
Delta-V needed to control the longitudinal acceleration in geo.
Computes the delta-v for a coplanar Hohmann transfer
Computes two impulses needed to transfer between two elliptical coplanar orbits.
Computes inclination drift for geosynchronous orbits.
Delta-V from a circular to noncoplanar circular orbit.
Computes the optimal circular capture radius and delta-v.
Delta-v for injection into an interplanetary orbit using Olberth's method.
Computes the delta-V for reentry from a near-circular orbit.
Compute delta-Vs for rendezvous using Hohmann transfers.
Low thrust delta v between two circular orbits.
Solve the Linear Terminal Velocity Constraint problem.
Compute the delta-V required for a low thrust escape.
Compute maneuver duration given constant thrust.
Compute the maneuver envelope for a spacecraft rotating around another.
Delta-V for a bielliptic orbit maneuver between circular orbits.
Computes the delta-V for a 2-burn transfer to a circular orbit at rF.
Computes the delta-V for a Hohmann transfer between circular orbits.
Delta-V for a Hohmann transfer between circular non coplanar orbits.
Computes the delta-V for an inclination correction.
Computes the delta-V to insert into a planetary or lunar orbit.
Delta-V for an longitude and inclination change maneuver for a circular orbit.
Computes the delta-V for a longitude only maneuver for a circular orbit.
Computes the delta-V to lower apogee.
Computes the delta-V for a one-tangent transfer between coplanar orbits.
Compute the delta V required to change perigee.
Computes the delta-V for a phase change.
Computes the delta-V for a change in semi-major axis.
Helps design patched conic trajectories.
Computes semi-major axis from revisit and swath angle.
Computes the transfer and phase angle given transfer time.
Compute maneuver profile for a triangular maneuver.
Plans delta-v maneuvers to correct triaxial motion.
Computes the heliocentric departure vector for a spacecraft.

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OrbitMechanics

Low thrust delta v between two circular orbits.
Compute the gravitational acceleration in spherical coordinates.
Compute the gravitational acceleration in cartesian coordinates.
Perturbing acceleration due to a planet on a spacecraft.
Launch azimuth to achieve a desired orbit inclination.
Compute the ballistic coefficient from a CAD model.
Convert c3 to heliocentric velocity
Right-hand-side of the cylindrical orbit equations about a mass point.
Compute the drag loss over an orbit arc in planetary orbit.
Computes the parking orbit plane for a heliocentric injection.
Compute the energy for any orbit
Computes a fuel budget from a list of events.
Compute the flight path angle for a Cartesian state.
Compute the flight path angle from elements
Calculates orbital elements and perigee radius for a planetary flyby.
Compute the required orbital elements for a flyby
Compute continuous-time relative dynamics for Gauss' variational equations
Compute the power balance in a spacecraft.
Compute ground coverage for an orbit.
Computes orbit angular momentum from the elements vector.
Calculates the orbit angular momentum given the input in equinoctial elements
Computes the inclination rate of an earth orbit due to the sun.
Finds the inclination rate and orbit normal vector.
Compute J2 effects on the orbital elements.
Propagate an ECI state into the future with the J2 perturbation.
Compute the local time of the ascending node.
Solves the Lambert time of flight problem using Battin's method.
Load a set of historical NORAD elements and convert to Cartesian states.
Computes the longitudinal motion due to an acceleration a
Computes the mean anomaly from change in time
Computes the mean orbit rate for an elliptic orbit
Computes the semi-major axis given the mean orbit rate.
Propagates the NORAD two line elements, ex. SGP, SGP4, SGP8.
Convert NORAD to Keplerian elements.
Dimensionalize or non-dimensionalize an orbit.
Computes the asymptote angle for a hyperbola. If e is < 1 it substitutes 1.
Optimal inclination corrections for a Hohmann transfer with a plane change.
Approximate time for an orbit to decay based on an exponential atmosphere.
Approximate the acceleration due to drag over an orbit arc, h0 to hF.
Computes the elements of an orbit with the desired synodic period.
Compute orbit insertion velocity and flight path angle.
Computes the Jacobian for a spherical planet gravity model.
Compute (VF,gammaF) at hF from (v0,gamma0) at h0.
Computes the phase angles for a Hohmann intercept
Dynamic pressure on a satellite based on an exponential atmospheric model.
Compute the semi-major axis from an orbit period or mean motion.
Computes patched conic elements.
Compute perturbations due to other planets aside from the center.
Propagates the ephemeris one step.
Propagates the NORAD two line elements, ex. SGP, SGP4, SGP8.
Propagates a set of NORAD two line elements with a common time frame.
Generate an orbit by propagating Keplerian elements.
Batch form of RV2El.
Monte-Carlo orbit simulation.
Computes the sphere of influence ratio
Point mass orbit equations in equatorial spherical coordinates.
Computes the ratio of the sphere of influence for interplanetary
Compute the sun-synchronous inclination for an orbit.
Compute the ascending node for the desired local time.
Computes the synodic period between two orbits.
Computes the synodic period from semi-major axis.
Resolves the transfer angle ambiguity.
Computes all times for a Hohmann Transfer.
Computes the Hohman transfer time between two orbits
Computes the wait time at the target.
Two impulse optimal orbit transfer.
Three impulse orbit transfer.
Time of flight in a hyperbola
Compute the earth's gravitational potential.
Atmospheric velocity from position and planetary rate.
Computes the escape velocity.
Computes the asymptotic velocity for a hyperbola
Computes the right hand side of the equinoctial variational equations.
Computes the right hand side of the variational equations
Computes the right hand side of the Gauss variational equations.
Variational Keplerian equations with the acceleration in tangential coordinates.

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OrbitPropagator

The aero force model. This is a pure drag model.
Atmospheric density model function that calls the Jacchia J70 model.
Computes the engine force vector in the ECI frame.
High fidelity orbit model designed to work with ode113.
The plant noise model.
The solar force model for OrbitPropagator.
Main GUI for propagating an orbit using ode113 and user-selected models.
Reads a Topex Precision Orbit Ephemerides file.
Stopping conditions for an orbit.
Create a stopping conditions plug in for OrbitPropagator.

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OrbitSim

Simulate low thrust spacecraft.
Propagate a Sun-Earth 3BP with origin at the Earth system barycenter
Propagate a Sun-Earth-Moon 4BP with origin at the Earth-Moon barycenter
Propagate a low thrust trajectory assuming that the thrust is constant
Propagate n-bodies in an n-body problem.
High fidelity orbit simulation with drag and planetary perturbations.

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RHSOrbit

Computes the linearized orbit equations for a discrete system.
Gravity acceleration in the earth moon system
Orbit dynamics with spherical harmonic models of the Earth and Moon gravity.
Orbit equations for InterstellarSim.
Computes the right-hand-side of the orbit equations about a mass point
Computes the right-hand-side of a spherical harmonic orbit (Cartesian).
High fidelity orbit model right-hand-side.
High fidelity orbit model designed to work with ode113.
Orbit model for Launch and Early Orbit Operations.
Its companion function is FOrbLEOP
Orbit model for low thrust escapes.
Right hand side of the planar orbit equations assuming constant thrust
Solar sail simulation right hand side.
Computes the right hand side of the variational equations.
Computes the linearized orbit equations.
Computes the right hand side for a gravity model.
Computes the right hand side for Earth gravity with J2.
Right hand side for a heliocentric system with a thruster.
Two dimensional orbit dynamics.
Cartesian orbital equations in a planet fixed (rotating) frame.

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ThreeBody

Compute the Jacobi constant for a state in the CRTBP system.
Compute linear system matrix for the circular restricted 3 body problem
Right-hand-side for the circular restricted three body problem.
Simulate an escape trajectory from Earth using CRTBPRHS.
Right-hand-side for the forced circular restricted three body problem.
Compute and plot a family of stable HALO orbits in the given system
Compute a stable initial state for a HALO orbit
Approximate an initial state for a HALO orbit given the orbit size
Simulate the Earth orbit to L2 point low thrust transfer.
Design a low thrust transfer from Earth orbit to Sun/Earth-Moon L2 point
Stoppping Function for the circular restricted three body problem.
Generate a family of planar Lyapunov orbits
Compute a stable initial state for a Lyapunov orbit
Propagate an arbitrary CRTBP with origin at the secondary body.
Propagate the CRTBP initial state to the next perigee
Compute the RHS of the CRTBP equations of motion.

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Visualization

Draw attitude frames. You can add these to any 3D picture.
Draw an orbit plane. You can add this to any 3D plot.
Plot an orbit track in the Earth/Moon System.
Plot an orbit track in the Earth/Moon Rotating System.
Generate a plot of a HALO trajectory
Simulate and plot an Earth orbit to L2 point low thrust transfer.
Plot a planet-fixed orbit track in 2D or 3D.
Plot an orbit track in the ECI frame.
View orbit related parameters on a quad chart.
Plot a trajectory in the Earth-Moon system
Create a plot page with 2D and 3D views of an orbit.
Plot the two initial orbits and the transfer orbit.
Plot an orbit track in the Sun/Earth-Moon Rotating System.
View a set of satellite TLEs in Earth orbit, using TLEs from celestrak.
A GUI to view / select from a list of TLE groups at www.celestrak.com.
Draws a 2D or 3D trajectory plot.

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SVN Revision: 42425


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