# A method of estimating pre-launch elements

From: Ted Molczan (molczan@rogers.com)
Date: Mon Jun 24 2002 - 09:27:33 PDT

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```This post is for the benefit of SeeSat-L readers who might wish to
estimate pre-launch elements of satellites, or at least understand how
it can be done.

I describe a method which takes advantage of the fact that new satellite
launches often are the latest in s series of similar launches. Knowledge
of the circumstances and initial elements of the past launches in the
series provides the basis to accurately estimate the initial elements of
new launches.

I break the process into 10 easy steps, using today's scheduled NOAA 17
launch as an example. How easy? All of the computations to produce the
estimates elements can be performed using the arithmetic functions of a
pocket calculator.

Familiarity with orbital elements in general, and the 2-line elements in
particular, is helpful, but not an absolute requirement. For the former,
I suggest the SeeSat-L faq:

http://satobs.org/faq/Chapter-05.txt

http://celestrak.com/columns/v04n03/

1. Select a suitable proxy satellite.

For many years, the standard NOAA orbit has been sun-synchronous, with
an initial mean-motion of about 14.1 rev/d. NOAA 16, the latest in the
NOAA series, is a typical example, as shown in these recent elements:

1 26536U 00055A   02173.90461296  .00000445  00000-0  26839-3 0  8759
2 26536  98.8696 119.4446 0009698 266.0641  93.9439 14.11707074 90194

When selecting a proxy elset, make certain that the object's launch site
was the same as that of the new launch. All NOAA satellites have been
launched from the Vandenberg AFB, so we can safely use the same
elements.

Beware of changes in launch vehicle. Recent NOAAs have been launched on
Titan 2 rockets; older ones were launched on Atlas rockets. For best
results, try to use a proxy that was launched using the same vehicle as
the new launch.

2. Obtain the proxy satellite's initial orbital elements.

We assume that NOAA 17's initial orbit will have the same relationship
to the circumstances of its launch as NOAA 16 did relative to its
launch. Therefore, we need to obtain an elset of NOAA 16 soon after its
launch.

Jonathan McDowell's archive is a convenient source of such data:

http://www.planet4589.org/space/elements/26500/S26536

I selected the third elset in the list, mainly because its mean motion
was in close agreement with subsequent elsets:

1 26536U 00055A   00265.76707352 -.00020078  00000-0 -11203-1 0    13
2 26536  98.7886 210.5136 0009705 275.1802 115.0094 14.10880075    42

3. Obtain the date and time of the proxy satellite's launch:

Jonathan McDowell provides a convenient record of all launches,
including the time of launch:

http://www.planet4589.org/space/log/launch.html

NOAA 16 was launched on 2000 Sep 21 at 10:22 UTC

4. Compute epoch of the proxy satellite's launch.

The 2-line elements express the epoch in days since the start of the
year, as yyddd.dddddddd, where yy is the year of launch, and the
ddd.dddddddd is the number of days since the start of the year.

Sep 21 was day 265 of year 2000 (make sure to take into account leap
year).

Expressing 10:22 UTC as the fraction of a day yields:

(10 h * 60 min/h + 22 min) / 1440 min/d = 0.43194444 d

So the epoch of launch was 00265.43194444

5. Compute the difference between the epoch of the proxy elset and the
launch time.

00265.76707352 - 00265.43194444 = 0.33512908 d

6. Compute the epoch of new satellite's launch.

The launch is scheduled for 2002 Jun 24 at 18:22 UTC.

Using the procedure described in Step 4, I obtain the launch epoch,
02175.765277778

7. Compute the epoch of the estimated elset of the upcoming launch.

Simply add the results of Steps 5 and 6:

02175.765277778 + 0.33512908 = 02176.10040685

8. Compute the RAAN of the estimated elset of the upcoming launch.

The RAAN (right ascension of the ascending node) states the location of
the orbital plane at the epoch. It is an angle expressed in degrees.

To obtain the RAAN of the orbit of the new launch, we must adjust the
RAAN of the proxy elset for the Earth's rotation that has occurred in
the interim. The formula is:

New elset RAAN = [ Proxy elset RAAN + (New elset epoch - Proxy elset
epoch) * Earth Rotation Rate ] mod 360

Substituting the previously obtained data, yields:

= [ 210.5136 + ( 02176.10040685 - 00265.76707352) * 360.985647362 deg/d
) ] mod 360

Note that the difference between the two epochs must be in days. If the
above two epochs were in the same year, then we could simply subtract
them, but since they span more than one year (years 2000 to 2002), we
must modify the calculation to take into account the number of days in
each of the three years:

year 2002: 176.10040685 days

year 2001: 365 days

year 2000: 366 - 265.76707352 days

Substituting this into the formula yields:

= [ 210.5136 + ( 176.10040685 + 365 + 366 - 265.76707352) *
360.985647362 deg/d ) ] mod 360

= [ 210.5136 + 641.33333333 d * 360.985647362 deg/d ) ] mod 360

= 231722.6462107 mod 360

= 242.6421 deg

9. Insert new epoch and RAAN into proxy elset.

Our proxy NOAA 16 elset, from Step 2, was:

1 26536U 00055A   00265.76707352 -.00020078  00000-0 -11203-1 0    13
2 26536  98.7886 210.5136 0009705 275.1802 115.0094 14.10880075    42

To create the elset for the corresponding elset of the new launch, we
need only substitute the new epoch computed at Step 7, and the new RAAN,
computed at Step 8.

To avoid confusion with NOAA 16 or any other launches, we should also
change the catalogue number and international designator to fall outside
their normal range of values:

1 70000U          02176.10040685 -.00020078  00000-0 -11203-1 0    18
2 70000  98.7886 242.6421 0009705 275.1802 115.0094 14.10880075    40

My preference is to use a pseudo-catalogue number between 70000 and
79999, because that is far above the highest official catalogue entries
to-date. I avoid using values between 80000 and 89999, because U.S.
Space Command's analyst elements use much of that range. For reasons
unknown, unclassified analyst elements are not normally made public,
though many seem to have leaked out over the years. I also avoid using
values between 90000 and 99999, because some hobbyists use portions of
that range for unidentified satellites and other purposes.

Even if I could know with absolute certainty the actual catalogue number
and international designation ahead of launch, I would not use them for
the estimated elements, in order to avoid the possibility of
contaminating the eventual archives of elements. Archivists may employ
automated methods to extract 2-line elements from e-mail messages,
SeeSat-L posts and anywhere else they may be found, so my naming method
avoids their mistaking an estimated pre-launch elset for an official
elset.

The above elset is sufficient for the purpose of finding the object
during at least the first 24 hours after launch, until an official elset
becomes available. No two launched are ever identical, so a prediction
time uncertainty of a few minutes is to be expected.

The negative rate of decay inherited from the proxy elset is
unrealistic, but its effect on predictions is likely to be smaller than
the uncertainty resulting from the other estimated elsets. I find the
negative decay rate irritating, so I substituted more reasonable values:

1 70000U          02176.10040685  .00000200  00000-0  11164-3 0    19
2 70000  98.7886 242.6421 0009705 275.1802 115.0094 14.10880075    40

Note that the final digit of each line is a checksum, which is computed
from the preceding digits on the line. Some ephemeris generators may
reject elsets that do not have a proper checksum. If you have this
problem, then you will need to compute the checksum. An explanation is
found in Dr. T.S. Kelso's aforementioned article:

http://celestrak.com/columns/v04n03/

10. Check the results.

The above process is simple, but it is easy to make an error, so it is
always a good idea to check the result. I do this by computing and
comparing ephemerides for the proxy launch and the new launch, as seen
from the launch site near the launch time.

Here is the ephemeris of the NOAA 16 proxy elset, on the day of its
launch, 2000 Sep 21, near the launch time of 10:22 UTC, from the vantage
point of Vandenberg AFB, located near 34.7 N, 120.6 W, zero metres above
sea-level:

21/ 9/ 2000  10:00 - 24:00 UTC  J2000.0  EL > 15  Vandenberg  AFB

TIME      %I   Mvv    AZ  EL     R.A.       DEC      FE    VANG  RANGE   ALT
--------    --  ----   ---  --   --------  ---------  ----   ----  -----  -----
10:21:50    31   8.4    12  15   12:10:19   67:25:21   6.1   0.10   2161    870
10:23:02      UMBRA     12  24   11:08:49   74:53:55   6.1   0.15   1712    869
10:23:53      UMBRA     12  33   08:49:17   79:49:21   6.1   0.20   1415    868
10:24:30      UMBRA     12  41   05:42:48   78:32:05   6.0   0.26   1220    868
10:24:59      UMBRA     11  50   04:02:01   72:34:19   6.0   0.32   1086    867
10:25:22      UMBRA     10  58   03:17:08   65:27:46   6.0   0.38    997    867
10:25:42      UMBRA      9  66   02:51:57   57:53:49   5.9   0.43    935    866
10:26:00      UMBRA      6  74   02:35:41   50:10:10   5.8   0.46    895    866
10:26:16      UMBRA    358  82   02:24:31   42:45:19   5.6   0.48    873    866
10:26:32      UMBRA    284  88   02:15:29   35:03:13   3.1   0.49    866    866
10:26:47      UMBRA    212  82   02:08:25   27:47:54  12.7   0.48    873    865
10:27:02      UMBRA    203  75   02:02:24   20:43:17  12.4   0.47    892    865
10:27:18      UMBRA    200  68   01:56:51   13:33:46  12.3   0.43    925    865
10:27:35      UMBRA    199  61   01:51:42   06:33:01  12.3   0.40    974    865
10:27:54      UMBRA    198  54   01:46:41  -00:28:23  12.3   0.35   1042    864

Note that the pass would have been from north to south, culminating
nearly overhead of the launch site about 4 min 32 s after launch. Of
course, this this pass did not actually occur, but it provides a simple
basis to check the pre-flight elements of the new launch, which yield
the following ephemeris for today's launch, 2002 Jun 24, near the launch
time of  18:22 UTC:

24/ 6/ 2002  18:00 - 24:00 UTC  J2000.0  EL > 15  Vandenberg  AFB

TIME      %I   Mvv    AZ  EL     R.A.       DEC      FE    VANG  RANGE   ALT
--------    --  ----   ---  --   --------  ---------  ----   ----  -----  -----
18:21:50    41   7.9    12  15   14:18:43   67:26:35   6.1   0.10   2160    870
18:23:02    34   7.7    12  24   13:17:05   74:55:23   6.1   0.15   1711    869
18:23:53    28   7.6    12  33   10:57:02   79:50:19   6.1   0.20   1414    868
18:24:30    22   7.7    12  41   07:50:27   78:31:12   6.0   0.26   1219    868
18:24:59    17   7.9    11  50   06:09:59   72:32:08   6.0   0.32   1085    867
18:25:22    13   8.1    10  58   05:25:17   65:24:49   6.0   0.38    996    867
18:25:42    10   8.4     9  66   05:00:11   57:50:21   5.9   0.43    935    866
18:26:00     8   8.8     6  74   04:43:58   50:06:20   5.8   0.46    895    866
18:26:16     6   9.1   358  82   04:32:50   42:41:17   5.6   0.48    873    866
18:26:32     5   9.3   282  88   04:23:49   34:59:06   3.1   0.49    866    866
18:26:47     5   9.3   211  82   04:16:47   27:43:50  12.7   0.48    873    865
18:27:02     6   9.1   203  75   04:10:46   20:39:23  12.4   0.46    892    865
18:27:18     8   8.8   200  68   04:05:14   13:30:07  12.3   0.43    925    865
18:27:35    10   8.5   199  61   04:00:06   06:29:41  12.3   0.39    974    865
18:27:54    13   8.3   198  54   03:55:06  -00:31:21  12.3   0.35   1042    864

As expected, the ephemeris time, azimuth, elevation, angular velocity
(VANG), range and altitude, all occur at the same time relative to the
launch time of their respective launches, which confirms that the
pre-flight elements were computed correctly.

Ted Molczan

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