Card 6k - Orbit Definition

This optional card defines orbital parameters.

Parameters: L, ORIENT, ALB, NINT, SUNDECL, ORBINCL, E, SMAR, OMEGA, ANGPER, PER, N1

This Card generates equivalent Card 6b - Solar View Factor Request and Card 6d - Earth from the orbital parameters. Additional optional orbital parameters may be defined on that card that immediately follow: Card 6l - Additional Orbital Parameters ORBADD. The planet does not have to be Earth.

L

L is an orbit generation code.

  • L = ORBS1 (or 19) generates them with shadowing.
  • L = ORBN1 (or 20) generates them with no shadowing.
  • L = ORBSALL (or 21) generates them for all elements with shadowing. N1 = blank.
  • L = ORBNALL (or 22) generates them for all elements with no shadowing. N1 = blank.

ORIENT

ORIENT is the vehicle coordinate system orientation flag. Different orientation flags may not be mixed within a single data deck. .

  • ORIENT = PLANET (or 0): the vehicle coordinate system is planet oriented. Its X axis points towards the center of the planet. Its Z axis is in the Northern half–space or in the plane of the equator. Its Y axis lies in the orbit plane.
  • ORIENT = SUN (or 1): the vehicle coordinate system is sun oriented. Its X axis points towards the sun. Its Z axis lies in the plane formed by the Sun vector and the North vector, such that it is positive Northward. Its Y axis completes the right–handed set.
  • ORIENT = SURFACE (or 2): the vehicle coordinate system is attached to the surface of the planet, and rotates with it. Its X axis points towards the center of the planet. Its Z axis points North and its Y axis points West. Only solar vectors are computed for this option; planet view factors are not computed.
  • ORIENT = STAR (or 3): the vehicle coordinate system is star oriented. Its X axis points towards a star. Its Z axis lies in the Sun–North plane, positive Northward. Its Y axis completes the right–handed set. The star’s coordinates are defined on the ORBSADD Card.

ALB

ALB is the albedo value, e.g. .35. If ALB = 0, solar view factors with eclipse will be calculated without Earth or albedo factors. ALB is ignored for ORIENT=SURFACE.

NINT

NINT is the number of equally spaced subintervals into which the Card 6l orbit interval STARTANGLE to ENDANGLE is divided. The number of orbital positions is NINT + 1 + twice the number of eclipse points. Two calculations are performed for each eclipse point, one on each side of it, separated by a 0.1 degree interval.

SUNDECL

SUNDECL is the sun's declination angle in degrees. SUNDECL is the angle between the sun vector, which points towards the sun, and the equatorial plane. SUNDECL is > 0 in the Northern and < 0 in the Southern hemispheres. For Earth, –23.44 ≤ SUNDECL ≤ 23.44, and is = 0 at equinox.

ORBINCL

ORBINCL is the orbit inclination angle in degrees, i.e. the angle between the orbit plane and the equatorial plane. ORBINCL is positive counterclockwise when looking towards the planet's center from the orbit ascending node. ORBINCL equals the latitude for ORIENT=SURFACE.

E

E is the orbit eccentricity, 0 ≤ E ≤ 1.

E = 0 is a circular orbit.

E is ignored for ORIENT = SURFACE.

SMAR

SMAR is the orbit semi major axis ratio, i.e. the ratio of the length of the orbit's semi major axis to the planet's radius. Earth's radius is 3441 nautical miles = 3963 miles = 6378 kilometers.

SMAR is ignored for ORIENT = SURFACE.

OMEGA

OMEGA is the angle between the reference line, which is the projection of the sun vector onto the equatorial plane (local noon), and the orbit ascending node, in degrees, measured in the equatorial plane. (This is not the same as the Right Ascension of Ascending Node, which is the angle measured from the Vernal Equinox, nor the Geographic Longitude of Ascending Node, which is the angle measured from the Prime Meridian.)

OMEGA is positive when the equatorial plane is viewed from the North Pole (measured "East" from the reference line).

OMEGA is ignored for ORIENT = SURFACE.

ANGPER

ANGPER is the periapsis angle in degrees, i.e. the angle between the ascending node and the perigee, measured in the orbit plane. Periapsis is the point in the orbit closest to the planet.

ANGPER is positive in the direction of the spacecraft's motion.

ANGPER is ignored for ORIENT = SURFACE.

PER

PER is the period of the orbit in appropriate time units.

PER is the length of a day for ORIENT = SURFACE.

N1

N1 is the element (or elements if N1 is a group name) for which the calculations are performed.

N1 must be blank for the ORBSALL and ORBNALL options.

Code example

In this example, the spacecraft is in a geosynchronous (SMAR = 6.625, PER = 24) equatorial (ORBINCL = 0) orbit, during equinox (SUNDECL = 0). Solar eclipse calculations with shadowing (L = ORBSALL), but no Earth view factor or albedo factor calculations (ALB = 0) are performed every 2 hours (NINT = 12), plus just before and just after entering and exiting eclipse. The vehicle coordinate system's X axis points towards the Earth, its Z axis North, and its Y axis West (ORIENT = PLANET).


 ORBSALL PLANET 0 12 0 0 0 6.625 180 0 24.0

The vehicle coordinate system is anchored to Earth at latitude of 45.5 degrees (Montreal).


 ORBSALL SURFACE 0 12 -23.5 45.55 0 0 0 0 24

Notes

If a planet's radius RP and acceleration of gravity at its surface G (6378 km and 9.81 m/sec2 for Earth) are known, then the orbital period can be calculated:

The maximum and minimum altitudes above the center of the planet are:

at periapsis

at apoapsis