OK, here's an analysis of the launch windows of SZ-9, using the longitude of the ascending node of TG-1 during the launch of SZ-8 (which should have more or less the same launch profile) and project it to the case of SZ-9. (

thanks to 9ifly member darklighter)

These three equations are useful for the calculations:

Due to the oblate shape of the Earth, the LAN of an object in orbit actually moves around. The rate of change of the LAN can be estimated by this equation:

ΔΩ = -9.964 * (Re / a)^3.5 * (1 - e^2)^0.5 * cos(i)

** (Eq. *)**

Re = Earth radius (6,378,138 m)

a = orbit's semi-major axis

e = eccentricity

i = equatorial inclination

Then we can get the LAN of TG-1 at any time: Ωt(t) = Ωt0 + ΔΩt * (t - Tt0) + 360 * n1

**(Eq. 1)** (n1 is an integer such that Ωt(t) is between 0 and 360)

To get the relationship of the LAN of the chasing spacecraft (SZ-9 in this case) at orbit insertion and the launch time, we can use a similar launch and compare the LAN with its launch time, and project it to this launch. Here the reference launch is SZ-8.

Ω0(t) = (t - T0h) * ωe + Ω0h + 360 * n2

**(Eq. 2)**t = launch time

ωe = Earth's angular rotation speed (= 360.9856 deg./day)

n2 is an integer such that Ωt(t) is between 0 and 360

Combining the last two equations, we have

T = (ωe * T0 - ΔΩ * T1 + Ω1 - Ω0 + 360 * n)) / (ωe - ΔΩ)

**(Eq. 3)**T0 is the launch time of the spacecraft of our reference launch. In this case it's the launch time of SZ-8, 2011-10-31 21:58:10 UTC (40847.915394 days since 1900-01-01 00:00:00 UTC).

Ω0 is the LAN of TG-1 during our reference launch. From NORAD data, it's about 359.762 deg.

T1 is the epoch time of the target spacecraft (TG-1) for a certain TLE. Here we use the TLE data on June 2 @ 08:54 UTC (41062.371069 days since 1900-01-01 00:00:00 UTC).

Ω1 is the LAN of TG-1 at T1, which is 141.0052 deg.

ΔΩ is the rate of change of the LAN of TG-1 in the orbit as shown in the TLE at T1. Assume that TG-1 is in a 336 km circular orbit, the rate is -6.1102 deg/day.

Thus we can calculate the launch time of SZ-9 at n days after last October 31 (launch of SZ-8). So for n=224 (June 10), T = 41070.559211 (= 13:25:16 UTC on June 10). For others days, substitute a different value of n.

He calculated the launch windows of SZ-9 as follows: (Given that TG-1 can still change its orbit, the error is about 5 minutes)

UTC Beijing time

2012-06-10 13:25:16 2012-06-10 21:25:16

2012-06-11 12:57:26 2012-06-11 20:57:26

2012-06-12 12:29:36 2012-06-12 20:29:36

2012-06-13 12:01:46 2012-06-13 20:01:46

2012-06-14 11:33:56 2012-06-14 19:33:56

2012-06-15 11:06:05 2012-06-15 19:06:05

2012-06-16 10:38:15 2012-06-16 18:38:15

2012-06-17 10:10:25 2012-06-17 18:10:25

2012-06-18 09:42:35 2012-06-18 17:42:35

2012-06-19 09:14:45 2012-06-19 17:14:45

2012-06-20 08:46:55 2012-06-20 16:46:55

2012-06-21 08:19:05 2012-06-21 16:19:05

2012-06-22 07:51:15 2012-06-22 15:51:15

2012-06-23 07:23:25 2012-06-23 15:23:25

2012-06-24 06:55:35 2012-06-24 14:55:35

2012-06-25 06:27:45 2012-06-25 14:27:45

2012-06-26 05:59:55 2012-06-26 13:59:55

2012-06-27 05:32:05 2012-06-27 13:32:05

2012-06-28 05:04:15 2012-06-28 13:04:15

2012-06-29 04:36:24 2012-06-29 12:36:24

2012-06-30 04:08:34 2012-06-30 12:08:34

*Note: Apparently the current trend points to launch at around June 15 (and I heard a rumor that it might even be moving up (!)), and the Chinese television channels are now starting to play promos about upcoming coverage of the mission, so sit back and enjoy the show... *