High Precision Orbit Propagator

The High-Precision Orbit Propagator (HPOP), developed by Microcosm, Inc. of El Segundo, CA, is a state-of-the-art orbit generator which can generate orbits for a wide variety of Earth satellites with accuracies on the order of 12 meters per orbit or better. It can handle circular, elliptical, parabolic, and hyperbolic orbits at distances ranging from the surface of the Earth to the orbit of the Moon and beyond, although orbits around the Moon itself are not currently supported.

The HPOP includes modern, ultra-high-fidelity models for all of the major perturbations affecting an Earth satellite:

  • Goddard Earth Model (GEM) 10B, an advanced 21 x 21 spherical harmonic expansion
  • Lunar-solar point-mass gravitational effects using the U.S. Naval Observatory Compressed Ephemeris to predict the positions of the Sun and Moon. This ephemeris is accurate to within one thousandth of an arc-second.
  • Atmospheric drag using the Harris-Priester atmosphere model, modified to take into account the diurnal bulge, to compute the atmospheric density. The drag model assumes single-collision specular reflection, which is appropriate for most satellites. Departures from this can be modeled by changing the area-to-mass ratio of the satellite.
  • Solar radiation pressure. This model assumes that the satellite is either a mirror sphere or a black body, which is appropriate for most satellites.

The HPOP also takes into account all of the major predictable motions of the Earth which affect the apparent position of the satellite:

  • Precession of the equinoxes
  • Nutation
  • Diurnal rotation
  • Barycentric displacement

Unpredictable Earth motions cannot be modeled at the present time, but fortunately these are small. They include polar motion, irregular variations in the Earth’s rotation rate, and continental drift. Polar motion causes the poles to wander in irregular circles in a region about 30m square, taking many years to complete each circle. Irregular variations in the Earth’s rotation rate can change the length of the day by up to 1/4 millisecond per year, but such large changes tend to cancel out over time, leaving a residual secular increase of 1.5 milliseconds per century. Continental drift occurs at rates of up to 5 centimeters per year.

The HPOP also accounts for the differences among the three major astronomical time systems:

  • Universal Time Coordinated (UTC), also known as Greenwich mean time
  • International Atomic Time (TAI)
  • Terrestrial Dynamic Time (TDT), formerly known as Ephemeris Time (ET)

For ultra-high precision, the HPOP uses the Runge-Kutta-Fehlberg method of order 7-8 to integrate the equations of motion.

The HPOP requires the following input:

  • Initial satellite position and velocity
  • Satellite area-to-mass ratio
  • Output schedule

It produces as output a set of satellite positions and velocities at equally-spaced times. Both input and output positions and velocities must be given in mean-of-J2000.0 coordinates.