Users Guide, Constants, and Symbols

Document Pages

Page 79

Page 80

Page 81

Program Card Format

The first input card is the program card. The format is as follows:

Column	Format	Description
1	I1	Ephemeris program desired: 1 = SGP, 2 = SGP4, 3 = SDP4, 4 = SGP8, 5 = SDP8
2—11	F10.0	Prediction start time
12—21	F10.0	Prediction stop time
22—31	F10.0	Time increment

All times are in minutes since epoch and can be positive or negative. The second and third input cards consist of either a 2-card transmission or 2-card G type element set. Either type can be used with the only condition being that the two cards must be in the correct order. For reference a format sheet for the T-card and G-card element sets follows this section.

Physical and Mathematical Constants

The values of the physical and mathematical constants used in the program are given below.

Variable Name	Definition	Value
CK2	$\frac{1}{2} J_2 {a_E}^2$	5.413080E-4
CK4	$-\frac{3}{8} J_4 {a_E}^4$	.62098875E-6
E6A	$10^{-6}$	1.0 E-6
QOMS2T	$(q_o - s)^4 \; (\text{er})^4$	1.88027916E-9
S	$s \; (\text{er})$	1.01222928
TOTHRD	$2/3$	.66666667
XJ3	$J_3$	-.253881E-5
XKE	$k_e \left(\frac{\text{er}}{\text{min}}\right)^{3/2}$	.743669161E-1
XKMPER	kilometers/Earth radii	6378.135
XMNPDA	time units/day	1440.0
AE	distance units/Earth radii	1.0
DE2RA	radians/degree	.174532925E-1
PI	$\pi$	3.14159265
PIO2	$\pi/2$	1.57079633
TWOPI	$2\pi$	6.2831853
X3PIO2	$3\pi/2$	4.71238898

where er = Earth radii. Except for the deep-space models, all ephemeris models are independent of units. Thus, units input or output as well as physical constants can be changed by making the appropriate changes in only the DRIVER program.

Symbols

Following is a list of symbols commonly used in this report.

Symbol	Definition
$n_o$	the SGP type “mean” mean motion at epoch
$e_o$	the “mean” eccentricity at epoch
$i_o$	the “mean” inclination at epoch
$M_o$	the “mean” mean anomaly at epoch
$\omega_o$	the “mean” argument of perigee at epoch
$\Omega_o$	the “mean” longitude of ascending node at epoch
$\dot{n}_o$	the time rate of change of “mean” mean motion at epoch
$\ddot{n}_o$	the second time rate of change of “mean” mean motion at epoch
$B^*$	the SGP4 type drag coefficient
$k_e$	$\sqrt{GM}$ where $G$ is Newton’s universal gravitational constant and $M$ is the mass of the Earth
$a_E$	the equatorial radius of the Earth
$J_2$	the second gravitational zonal harmonic of the Earth
$J_3$	the third gravitational zonal harmonic of the Earth
$J_4$	the fourth gravitational zonal harmonic of the Earth
$(t - t_o)$	time since epoch
$k_2$	$\frac{1}{2} J_2 {a_E}^2$
$k_4$	$-\frac{3}{8} J_4 {a_E}^4$
$A_{3,0}$	$-J_3 {a_E}^3$
$q_o$	parameter for the SGP4/SGP8 density function
$s$	parameter for the SGP4/SGP8 density function
$B$	$\frac{1}{2} C_D \frac{A}{m}$ , the ballistic coefficient for SGP8 where $C_D$ is a dimensionless drag coefficient and $A$ is the average cross-sectional area of the satellite of mass $m$