Page 57 - Satellite Communications, Fourth Edition

Orbits and Launching Methods 37

TABLE 2.1 Details from the NASA Bulletins (see Fig. 2.6 and App. C)
Line no. Columns Description
1 3–7 Satellite number: 25338
1 19–20 Epoch year (last two digits of the year): 00
1 21–32 Epoch day (day and fractional day of
the year): 223.79688452 (this is
discussed further in Sec. 2.9.2)
1 34–43 First time derivative of the mean motion
2
(rev/day ): 0.00000307
2 9–16 Inclination (degrees): 98.6328
2 18–25 Right ascension of the ascending node
(degrees): 251.5324
2 27–33 Eccentricity (leading decimal point assumed):
0011501
2 35–42 Argument of perigee (degrees): 113.5534
2 44–51 Mean anomaly (degrees): 246.6853
2 53–63 Mean motion (rev/day): 14.23304826
2 64–68 Revolution number at epoch (rev): 11,663

Kepler’s third law gives

1/3

a s t
2
n 0
7192.335 km

2.7 Apogee and Perigee Heights
Although not specified as orbital elements, the apogee height and perigee
height are often required. As shown in App. B, the length of the radius vec-
tors at apogee and perigee can be obtained from the geometry of the ellipse:

r a(1 e) (2.5)
a
a(1 e) (2.6)
r p
In order to find the apogee and perigee heights, the radius of the
earth must be subtracted from the radii lengths, as shown in the fol-
lowing example.

Example 2.3 Calculate the apogee and perigee heights for the orbital parameters
given in Table 2.1. Assume a mean earth radius of 6371 km.
Solution From Table 2.1: e .0011501 and from Example 2.1 a 7192.335 km.
Using Eqs. (2.5) and (2.6):

r a 7192.335(1 0.0011501)