Orbit Propagator Kepler (unperturbed)

Performs unperturbed orbit calculations of one or more spacecraft using the universal formulation of Kepler’s variables.

blockType: SubSystem

Path in the library:

/Aerospace/Spacecraft/Spacecraft Dynamics/Orbit Propagator Kepler (unperturbed)

Description

The Orbit Propagator Kepler (unperturbed) block calculates the orbit of one or more spacecraft based on the universal formulation of Kepler’s variables. The block does not take into account atmospheric drag, gravitational influence of third bodies and light pressure. The number of spacecraft is determined by the size of the given initial conditions.

Ports

Output

# X_icrf (m) — spacecraft position
`vector 3 to 1

Details

The position of the spacecraft in the ICRF reference frame or in a fixed reference frame.

Data types	`Float64`.
Complex numbers support	No

# V_icrf (m/s) — velocity
vector 3 to 1

Details

The velocity of a spacecraft in a reference frame or in a stationary frame of reference.

Data types	`Float64`.
Complex numbers support	No

# t_utc (JD) — time at the current time step
scalar

Details

The time at the current time step, returned as a Julian date.

Data types	`Float64`.
Complex numbers support	No

Parameters

Main

# Start data/time (UTC Julian data)) — initial date and time of modelling

Details

The starting date and time of the simulation, specified in the Julian system.

Default value	`2458850.0`
Program usage name	`start_time`
Tunable	No
Evaluatable	Yes

Orbit

# Initial state format — method of input of initial orbit states
ICRF state vector | Orbital elements

Details

A method for inputting initial states of an orbit.

Values	`ICRF state vector` \| `Orbital elements`
Default value	`Orbital elements`
Program usage name	`state_format`
Tunable	No
Evaluatable	Yes

# Orbit type — orbital classification
Keplerian | Elliptical equatorial | Circular inclined | Circular equatorial

Details

Classification of orbits.

Dependencies

To use this parameter, set the parameter Initial state format to Orbital elements.

Values	`Keplerian` \| `Elliptical equatorial` \| `Circular inclined` \| `Circular equatorial`
Default value	`Keplerian`
Program usage name	`orbit_type`
Tunable	No
Evaluatable	Yes

# ICRF position (m) — spacecraft position vector

Details

Spacecraft position vector in the ICRF coordinate system.

Dependencies

To use this parameter, set the parameter Initial state format to ICRF state vector.

Default value	`[3.6497e6, 3.3082e6, -4.6766e6]`
Program usage name	`pos_eci`
Tunable	No
Evaluatable	Yes

# ICRF velocity (m/s) — spacecraft velocity vector

Details

Spacecraft velocity vector in the ICRF coordinate system.

Dependencies

To use this parameter, set the parameter Initial state format to ICRF state vector.

Default value	`[-2750.8, 6666.4, 2573.4]`
Program usage name	`vel_eci`
Tunable	No
Evaluatable	Yes

# Semi-major axis (m) — half of the major axis of the ellipse

Details

Half of the major axis of the ellipse. For parabolic orbits, this block interprets this parameter as the radius of the pericentre (distance from the pericentre to the focal point of the orbit). For hyperbolic orbits, this block interprets this parameter as the distance from the pericentre to the centre of the hyperbola.

Dependencies

To use this parameter, set the Initial state format parameters to Orbital elements.

Default value	`6.786e6`
Program usage name	`sma`
Tunable	No
Evaluatable	Yes

# Eccentricity — orbital deviation

Details

The deviation of an orbit from a perfect circle.

Dependencies

To use this parameter, set the Initial state format parameters to Orbital elements and the Orbit type parameters to Keplerian or Elliptical equatorial.

Default value	`0.01`
Program usage name	`ecc`
Tunable	No
Evaluatable	Yes

# Inclination (deg) — orbital plane inclination angle

Details

Vertical inclination of the ellipse relative to the reference plane.

Dependencies

To use this parameter, set the Initial state format parameters to Orbital elements and the Orbit type parameters to Keplerian or Circular inclined.

Default value	`50.0`
Program usage name	`inc`
Tunable	No
Evaluatable	Yes

# RAAN (deg) — angular distance in the equatorial plane

Details

The angular distance along the reference plane from the ICRF X-axis to the location of the ascending node (the point at which the spacecraft crosses the reference plane from south to north).

Dependencies

To use this parameter, set the Initial state format parameters to Orbital elements and the Orbit type parameters to Keplerian or Circular inclined.

Default value	`95.0`
Program usage name	`raan`
Tunable	No
Evaluatable	Yes

# Argument of periapsis (deg) — angle from the spacecraft ascending node to the pericentre

Details

The angle from the spacecraft ascending node to the pericentre (the closest point in the orbit to the central body).

Dependencies

To use this parameter, set the Initial state format parameters to Orbital elements and the Orbit type parameters to Keplerian.

Default value	`93.0`
Program usage name	`aop`
Tunable	No
Evaluatable	Yes

# True anomaly (deg) — angle between the pericentre and the initial position of the spacecraft

Details

The angle between the pericentre (the closest point of the orbit to the central body) and the initial position of the spacecraft in orbit.

Dependencies

To use this parameter, set the Initial state format parameters to Orbital elements and the Orbit type parameters to Keplerian or Elliptical inclined.

Default value	`203.0`
Program usage name	`ta`
Tunable	No
Evaluatable	Yes

# Longitude of periasis (deg) — angle between the ICRF X-axis and the eccentricity vector

Details

The angle between the X axis of the ICRF and the eccentricity vector.

Dependencies

To use this parameter, set the Initial state format parameters to Orbital elements and the Orbit type parameters to Elliptical equatorial.

Default value	`0.0`
Program usage name	`lop`
Tunable	No
Evaluatable	Yes

# Argument of latitude (deg) — angle between the ascending node and the initial position of the spacecraft

Details

The angle between the ascending node and the initial position of the spacecraft in orbit.

Dependencies

To use this parameter, set the Initial state format parameter to Orbital elements and the Orbit type parameter to Circular inclined.

Default value	`0.0`
Program usage name	`aolat`
Tunable	No
Evaluatable	Yes

# True longitude (deg) — angle between the ICRF X-axis and the initial position of the spacecraft

Details

The angle between the X axis of the ICRF and the initial position of the spacecraft in its orbit.

Dependencies

To use this parameter, set the Initial state format parameters to Orbital elements and the Orbit type parameters to Circular equatorial.

Default value	`0.0`
Program usage name	`tlong`
Tunable	No
Evaluatable	Yes

Central body

Details

A celestial body around which a spacecraft revolves.

Values	`Earth` \| `Sun` \| `Moon` \| `Mercury` \| `Jupiter` \| `Venus` \| `Mars` \| `Saturn` \| `Uranus` \| `Neptune` \| `Custom`
Default value	`Earth`
Program usage name	`central_body`
Tunable	No
Evaluatable	Yes

# Gravitational parameter (m^3/s^2) — free-fall acceleration

Details

The free fall acceleration of a planet.

Dependencies

To use this parameter, set the parameter Central body to Custom.

Default value	`3.986004415e14`
Program usage name	`gm`
Tunable	No
Evaluatable	Yes

Literature

Vallado, David. Fundamentals of Astrodynamics and Applications, 4th ed. Hawthorne, CA: Microcosm Press, 2013.
Gottlieb, R. G., Fast Gravity, Gravity Partials, Normalised Gravity, Gravity Gradient Torque and Magnetic Field: Derivation, Code and Data, NASA Contractor Technical Report Report 188243, NASA Lyndon B. Johnson Space Centre, Houston, Texas, February 1993.
Konopliv, A. S., S. W. Asmar, E. Carranza, W. L. Sjogen, and D. N. Yuan, Recent Gravity Models as a Result of the Lunar Prospector Mission, Icarus, Vol. 150, no. 1, pp 1-18, 2001.
Lemoine, F. G., D. E. Smith, D. D. Rowlands, M. T. Zuber, G. A. Neumann, and D. S. Chinn, An improved solution of the gravity field of Mars (GMM-2B) from the Mars Global Surveyor, Journal Of Geophysical Research, Vol. 106, No. E10, pp 23359-23376, October 25, 2001.
Seidelmann, P.K., Archinal, B.A., A’hearn, M.F. et al. Report of the IAU/IAG Working Group on cartographic coordinates and rotational elements: 2006. Celestial Mech Dyn Astr 98, 155-180 (2007).
Montenbruck, Oliver, and Gill Eberhard. Satellite Orbits: Models, Methods, and Applications. Springer, 2000.