Space-Track confirms presence of 4 secret payloads on Globalstar Falcon 9 launch

Author Topic: SpaceX F9 : USA 328-331 / Globalstar FM15 : SLC-40 : 19 June 2022 (04:27 UTC)  (Read 44567 times)

Quote from: jcm on 06/19/2022 06:06 pm

This is interesting but I really wish people would do some error estimates.
What is the uncertainty on the "54 degrees" measured from the launch info?  Plus or minus 0.1 deg? or plus or minus 1 deg? or what?

A reasonable request, but tough.  For practice, I tried to guess the inclination of a GPS launch from the barge position.  In this case we know the real answer, so we can check.

From the FCC notice, the locations are:
Cape 28 29 11N, 80 32 51W
ASDS 32 49 43N, 75 59  8W

Using the spherical geometry website: https://www.movable-type.co.uk/scripts/latlong.html
We find the initial bearing is 40.95 from North and hence 49.05 from equator

Assuming an instantaneous dV, and an orbit of 533 km (7598 m/s), we find the components in the launch frame:
X = 7598 * cos(49.05 degrees) = 4980 m/s
Y = 7598 * sin(49.05 degrees) = 5739 m/s

Next, we need to correct for Earth rotation, which will add to the X component, giving
X = 4980 + 40000000/(24*3600)*cos(28.5 degrees) = 5387 m/s

Then we re-find the azimuth
atan(5739/5387) = 46.81 degrees from equator and hence azimuth = 43.19

Next, an orbit's azimuth depends on its latitude.  The usual equation is:
azimuth = asin(cos(inc)/cos(lat))

We instead solve for inclination:
sin(azimuth) = cos(inc)/cos(lat))
cos(inc) = sin(azimuth)*cos(lat)
inc = acos(sin(azimuth)*cos(lat))

So we get:
inc = acos(sin(43.19 degrees)*cos(28.5 degrees)) = 53.02 degrees

But this GPS launch was known to be 55.0 degrees.  So we seem to be about 2 degrees off.  Either I made a mistake (entirely possible) or perhaps the extended nature of the launch maneuver causes the difference.

Probably more accurate is differential, which is what I think the original poster did, comparing it to previous launches, their barge location, and their inclination.   If you go through the same exercise with the GlobalStar launch (see below), you get about 0.16 degrees less inclination.  This makes sense since the landing locations were very similar.  This would say the mystery orbit inclination would be about 54.84 degrees.  But the error margin is hard to say.

Second stage burns are even guess-ier.  The duration is hard to estimate from the camera, the startup and shutdown transients are a big part of the dV, and we don't know what throttle settings are used.

---- Same calcs for GlobalStar:

Step 1 : get long, lat of ASDS and Cape from notice
https://apps.fcc.gov/oetcf/els/reports/STA_Print.cfm?mode=current&application_seq=115185&RequestTimeout=100Connection
   Cape: 28 29 11N, 80 32 51W
  ASDS: 32 52 26N, 75 53 58W

Step 2 : find bearing, get 41.16 from north = 48.84 from equator

Step 3 : Consider launch as a single impulse.  V for a 533 km orbit is 7598

Step 4: Find components
X = 7598 * cos(48.84) = 5001
Y = 7598 * sin(48.84) = 5720

Step 5: Add Earth rotation:
X = 5001 + 40000000/(24*3600)*cos(28.5) = 5408
Inertial inclination = atan(5720/5408) = 46.61 degrees; azimuth=43.39

Step 6: Convert azimuth at a latitude to inclination
azimuth = asin(cos(inc)/cos(lat))
sin(azimuth) = cos(inc)/cos(lat))
cos(inc) = sin(azimuth)*cos(lat)
inc = acos(sin(azimuth)*cos(lat))
inc = acos(sin(43.39 degrees)*cos(28.5 degrees)) = 52.86 degrees

Well, we can simplify the request to 'what is the uncertainty on the launch azimuth'.   The FCC position is given to 1" of lat/lon corresponding
to 31 metres, but I am skeptical the droneship is held to that degree of accuracy. Let's say it's good to 100m. Taking that and 655 km from the pad gives 0.01 degree uncertainty on the azimuth, which is pretty good.  But it's clear (e.g. from Raul's LHA maps) that there
was something of a dogleg, and that introduces a larger uncertainty.  Usuing the droneship hazard area only, we can get perhaps about a 0.1 degree confidence on its alignment, giving an uncertainty in the intended trajectory. I'm not sure though what the
added uncertainty is for slop from intended to actual. It does look a lot better determined than I would have guessed before doing the math.
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