Technical Notes for HPOP

HPOP uses a numerical integration method to propagate the satellite state in the J2000 reference frame. Available integration techniques are the Runge-Kutta-Fehlberg method of order 7-8, the Burlirsch-Stoer method, and the Gauss-Jackson method of order 12.

HPOP uses the following values for various physical constants:

Symbol Constant Value Units
mu sub E Gravitational Constant of Earth gravity file m3/sec2
RE Equatorial Radius of Earth gravity file m
fE Flattening Coefficient of Earth 0.00335281 (dimensionless)
c Speed of Light 299792.458 km/sec
LS Luminosity of Sun 3.828e26 W

HPOP uses the following values for the differences among various astronomical time systems:

Time System Difference Unit
TAI-UTC Tabulated based on leap seconds seconds
UTC-UT1 Tabulated based on Earth Orientation Parameter file seconds
TAI-TDT -32.184 seconds

The models for atmospheric drag and solar radiation pressure use the following default values:

Coefficient Default Value
cD (coeff of drag) 2.0
cR (coeff of solar radiation pressure) 1.0

These coefficients are defined by the following expressions for the accelerations due to drag and solar radiation pressure.

Acceleration caused by drag is:

    drag acceleration equation

Acceleration caused by solar radiation is:

solar radiation acceleration equation

where:

CR = coefficient for solar radiation = 1 + , where is the surface reflectivity (approx. 0.95 for aluminum)

CD = coefficient for drag

AD = satellite cross-sectional area along velocity vector

AR = satellite cross-sectional area presented to the Sun

M = satellite mass

= atmosphere density

V = satellite speed relative to the atmosphere

K = fraction of the solar disk visible at satellite location

LS = luminosity of the Sun

c = speed of light

r = distance of satellite from Sun