Orbit Module

Directory List

Constellations DemoFuns Demos/GravityModels
Demos/OrbitControl Demos/OrbitCoord Demos/OrbitManeuver
Demos/OrbitMechanics Demos/OrbitPropagator Demos/OrbitSim
Demos/Visualization Glideslope GravityModels
LowThrust Optimization OrbitControl
OrbitCoord OrbitData OrbitManeuver
OrbitMechanics OrbitPropagatorGUI OrbitSim
RHSOrbit Visualization


Constellations

Create a cross scale constellation
Compute orbital elements for a Walker constellation.

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DemoFuns

Propagate and plot the Zermelo trajectory.
Zermelo's differential equation right hand side.
Computes the analytical cost for Zermelo's problem.
Computes the analytical lambda for Zermelo's problem.
Cost function of Zermelo's differential equations.

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Demos/GravityModels

Compare gravity models

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Demos/OrbitControl

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.
DragCompensationDemo.matOP Data for drag compensation maneuvers.
GEO Stationkeeping Example
Low thrust geo transfer
Low thrust geo transfer simulation
Demonstrate a Hohmann Transfer in simulation
Computes the insertion delta-V for a Hohmann transfer.
DV limits from fuel tank mass ratio
Simulate a low-thrust orbit raising from an ISS orbit
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.
Demo of J2 Orbit Effects in Simulation
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.
DragDemo.matDrag reentry demo OP data.
Demonstrate using an external gravity model with PropagateOrbitPlugIn.
Integration Accuracy for PropagateOrbitPlugin.
Demonstrate low thrust transfer using PropagateOrbitPlugIn.
LowThrustDemo.matLow thrust demo OP data.
LunarModelDemo.matOP Data for propagating with lunar gravity model.
Demonstrate using PropgateOrbitPlugin in batch
OPDemo.matOP Data for batch mode demo.
OrbitIntegrationAccuracy.matOP Data for accuracy demo.
Integration accuracy study comparing RK4, RK45, and ode113.
Compare various orbit propagators with a Topex ephemeris.

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Demos/OrbitSim

Simple demo to compute drag over one orbit
Simulates a spacecraft in earth orbit with spherical harmonics.
Using a spherical harmonic gravity model
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.
Simulates two orbits and plots their relative positions.
Investigate orbit coordinate systems.
Simulate an orbit using the variational equations.

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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.
Calculate delta-Vs for glideslope rendezvous.
Compute the glide slope angle.
Calculate delta-Vs for a pulsed circumnavigation.
Guidance trajectory where range rate is proportional to range.
Calculate sequential glideslope maneuvers for planning purposes.
Cost function for glideslope period solver
Derivative for glideslope period solver

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GravityModels

EGM100x100.matFirst 100 coefficients of Earth EGM2008 model (normalized).
EGM50x50.matFirst 50 coefficients of Earth EGM2008 model (normalized).
EarthGravityModel.matEarth GEMT1 model in a mat file (unnormalized).
GEMT1.geoGEMT1 gravity model circa 1987.
Create a gravity map from a gravity model.
JGM2.geoEarth JGM2 70-term gravity model, circa 1993.
JGM3.geoEarth JGM3 70-term gravity model, circa 1995.
Load the GEMT1 data.
Load a spherical harmonic gravity model (.geo) from GSFC/U. of Texas at Austin.
Generate a normalization matrix for spherical harmonics
Process an ascii file of spherical harmonic coefficients.
Remove normalization from a gravity model
WGS84.geoEarth WGS84 gravity model, 1984.

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LowThrust

Low thrust delta v between two circular orbits.
Delta-V from a circular to noncoplanar circular orbit.
Low-thrust transfer between two circular, nonplanar orbits
Delta v of a low thrust spiral between two circular orbits.
Compute the delta-V required for a low thrust escape.
Simulate low thrust spacecraft.

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Optimization

Cost function for 2D low thrust trajectory optimization.
Computes sail partials using a first difference approximation
Derivatives for the low-thrust planar orbit problem.
Propagate and plot the planar trajectory from costates (indirect optimization).
Size a spacecraft from acceleration time history
Performs indirect trajectory optimization on costates with fminsearch.

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OrbitControl

Compute two delta-v's to raise the apogee and circularize the orbit.
Perform targeting in Earth orbit using the Lambert algorithm.
Compute accelerations for a point to point trajectory.
Updates orbital elements based on an impulsive delta-V
Creates a linear quadratic relative orbit controller.
Use Lambert with optimization of start and transfer time
Compute control acceleration for low thrust orbit raising
Compute delta-Vs for rendezvous.
Converts the transfer time to delta-V for a rendezvous.

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OrbitCoord

Computes the apogee radius from a and e.
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.
Convert an Alfriend orbital element set into the standard orbital element set
Transformation matrix from ecliptic to Sun-Earth rotating frame.
Transformation matrix from equinoctial to cartesian coordinates.
Transformation matrix from the perifocal frame to the inertial frame.
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.
Compute the transformation matrix that rotates ECEF to ECI coordinates.
This function takes a position vector and orbit normal vector in ECI
Transform from ECI to Rotating Libration Point Coordinates
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 orbital elements to r and v for an elliptic orbit.
Planar elements to flight path states
Transforms Keplerian elements to modified equinoctial elements.
Converts equinoctial elements to Keplerian elements.
Converts equinoctial elements to r and v for an elliptic orbit.
Compute the initial quaternion and body rates for a circular orbit,
Compute range and azimuth angle between two points on a sphere.
Determine the locus of visibility for a satellite above a planet.
Transform to ECI frame from tangential coordinates.
Transforms modified equinoctial elements to Keplerian elements.
Transforms modified equinoctial elements to r and v.
Computes the differences between orbital element vectors.
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 planet centered orbital elements.
Transform (range,azimuth) to (latitude,longitude) coordinates.
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 position vector in the perifocal plane.
Converts perigee and velocity at perigee to a and e
Computes the semimajor axis given position and velocity magnitudes.
Converts R and V to a, e, rP and rA.
Converts Cartesian state to Keplerian orbital elements.
Converts R and V to Equinoctial elements
Right ascension and declination with their rates from position and velocity vectors.
Batch form of RV2El.
Transforms elements r and v to modified equinoctial.
Given the reference absolute state, converts a relative orbit state to absolute.
Computes relative coordinates between two orbits.
Find the relative coordinate state vector between x2 and x1.
Computes the matrix from TEME to the pseudo-earth fixed frame.
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

Earth.txtHORIZONS ephemeris data for Earth.
LEOData.matSample LEO orbit data.
Messenger.txtHORIZONS ephemeris data for Messenger.
MirNORAD.txtMir NORAD two-line elements data.
NewHorizons.txtHORIZONS ephemeris data for New Horizons.
Reads in JPL Horizons data.
earthmap.fig3D Earth map in Normalized Earth-Fixed Coordinates.
mir.txtMir NORAD elements.
sdp.txtSDP NORAD 2 line elements test data
sgp.txtSGP 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.
Find a coplanar orbit with a different altitude
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
Compute Hohmann transfer between two elliptical coplanar orbits.
Compute impulses for an eccentric Hohmann transfer with a plane change.
Computes inclination drift for geosynchronous orbits.
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.
Solve the Linear Terminal Velocity Constraint problem.
Compute maneuver duration given constant thrust.
Compute the maneuver envelope for a spacecraft rotating around another.
Returns the maximum velocity change fraction
Optimal inclination corrections for a Hohmann transfer with a plane change.
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.
Computes semi-major axis from revisit and swath angle.
Two impulse optimal orbit transfer.
Three impulse orbit transfer.
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

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.
Adjusts mean anomaly in an elements vector for a different start time.
Compute the ballistic coefficient from a CAD model.
Drag loss along the arc of a transfer orbit determined from flight path angle
Compute the drag loss over an orbit arc in planetary orbit.
Delta-V for an upper stage with two impulses to orbit
Converts eccentric anomaly to mean anomaly.
Computes the true anomaly from the eccentric or hyperbolic anomaly.
Ratio of apogee radius to perigee radius given eccentricity for an ellipse
Compute the energy for any orbit
Computes a fuel budget from a list of events.
Computes the flight path angle from eccentricity and true anomaly.
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 continuous-time relative dynamics for Gauss' variational equations
Retrieve fuel budget information from a CAD model.
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 - analytic model.
Converts eccentric longitude to true longitude
Converts eccentric longitude to true longitude
Compute the local time of the ascending node.
Solves the Lambert time of flight problem using Battin's method.
Computes the longitudinal motion due to an acceleration a
Computes the eccentric anomaly
Approximate root to Kepler's Equation for elliptical and hyperbolic orbits.
Eccentric anomaly for an ellipse.
Eccentric anomaly for a hyperbola.
Computes the true anomaly from the mean anomaly.
Computes the true anomaly from the mean anomaly without wrapping.
Generate the true anomaly from the mean anomaly for a parabola.
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.
Convert semi-major and semi-minor lengths to a and e
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.
Convert NORAD to Keplerian elements.
Dimensionalize or non-dimensionalize an orbit.
Converts true anomaly to eccentric or hyperbolic anomaly.
Converts true anomaly to mean anomaly.
Computes the mean anomaly from the true anomaly without wrapping btwn -pi / pi
Computes the asymptote angle for a hyperbola.
Approximate time for an orbit to decay based on an exponential atmosphere.
Conmputes the orbit normal from orbital elements.
Compute the orbital rate from distance and semi-major axis.
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 the parameter for any orbit.
Compute the period for an orbit.
Compute the semi major axis from the period
Compute perturbations due to other planets aside from the center.
Propagates the ephemeris one step.
Computes m, nu and E from r, a and e.
Computes the semi major axis from apogee and perigee radii
Computes the eccentricity from apogee and perigee radii
Computes the orbit radius and the parameter from Keplerian elements.
Computes the orbit radius.
Converts perigee and apogee to semi-major axis and eccentricity
Computes true anomaly from semi-major axis, eccentricity and radius.
Monte-Carlo orbit simulation.
Computes the semi-latus rectum.
Computes the sphere of influence ratio
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.
Time vector for a TLE
Computes the Hohman transfer time between two orbits
Computes the wait time at the target.
Time of flight in a hyperbola
Generates an array of true anomalies.
Compute the earth's gravitational potential.
Computes the escape velocity.
Computes the asymptotic velocity for a hyperbola (v infinity)
Generate RV from parameters v infinity and periapsis
Computes the orbital velocity from radius.
Computes the orbit velocity in the perifocal plane.
Computes the right hand side of the equinoctial variational equations (polar).
Computes the right hand side of the variational equations (tangential)
Computes the right hand side of the Gauss variational equations.
Variational Keplerian equations with the acceleration in tangential coordinates.

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OrbitPropagatorGUI

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

Propagate an ECI state into the future with the J2 perturbation.
Load a set of NORAD elements (TLEs) and convert to Cartesian states
Propagates the NORAD two line elements (TLE), ex. SGP, SGP4, SGP8.
Propagate an ECI state into the future with point mass orbit.
Propagate a low thrust trajectory with constant thrust
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.
Generate an orbit by propagating Keplerian elements.
High fidelity orbit simulation with drag and planetary perturbations.

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RHSOrbit

Right-hand-side of the cylindrical orbit equations about a mass point.
Computes the linearized orbit equations for a discrete system.
Computes the right-hand-side of the orbit equations about a mass point
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.
Events function for FOrbLEOP
Orbit model for low thrust escapes.
Right hand side of the planar orbit equations assuming constant thrust
Computes the right hand side of the variational equations.
Computes the linearized orbit equations.
RHS for 2D polar orbit
Right-hand-side for equinoctial elements.
Computes the right hand side for a gravity model.
Computes the right hand side for Earth gravity with J2.
Continuous form of linearized orbit (Hills equations).
Right hand side for a simple Cartesian orbit.
Two dimensional orbit dynamics.
Cartesian orbital equations in a planet fixed (rotating) frame.
Point mass orbit equations in equatorial spherical coordinates.

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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 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 Lambert transfer trajectory as computed by DVTarget
Create a plot page with 2D and 3D views of an orbit.
Plot two initial orbits and a transfer orbit.
Plot the state in 3D with an planet map.
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.
Displays spacecraft and moon in a trajectory about the Earth in real time.

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