Tuesday, December 18, 2018

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Launch into an LEO x 4000 km orbit (about 2 hour period). Takes LEO + 830 m/s.

Wait one hour until apogee, then go 4000 x 20000 km (6.9 hour orbit) . Takes 1960 m/s. Release satellite.

Second stage coasts to apogee (3.45 more hours). Then a retrograde burn at -480 m/s to a 100 x 20000 orbit (5.8 hour period). Wait 2.9 hours and re-enter.

Total delta-V is about LEO+3270 m/s, as predicted. Re-entry at launch + 6.5 hours, as stated. Satellite needs about 970 m/s to circularize.
"""
4000x35000 is a pretty standard second stage graveyard orbit for centaur, so if the deorbit burn is what pushed this expendable, it seems a bit wasteful...
"""
Also note that the 55 deg orbit inclination requires more delta-v just to get to LEO than a 28.5 deg GTO type inclination. Something like 240 m/s extra, maybe?
"""
I get 148 m/s more is needed compared to a GTO launch. Here is my thinking (this is the first time I've tried this particular calculation, so mistakes are possible):

A 55 degree orbit passes over the cape (lat 28.5o) at an azimuth of 40.74o, from azimuth = sin-1(cos(55o)/cos(28.5o)). We need about 7800 m/s for an LEO, at this angle (in an inertial frame).

Now the North-South component of this is 5910 m/s. The East-West component is 5090 m/s, but the Earth rotation provides 409 m/s of this at latitude 28.5o. That leaves 4681 m/s to be provided by the rocket. So the rocket needs to provide sqrt(5910^2+4681^2) = 7539 m/s. So the Earth's rotation here saves 7800-7539 = 261 m/s. Compared to the 409 m/s savings of a due-East GTO launch, that's 148 m/s more that the rocket needs to provide.

As a side effect, we can find the launch azimuth in the Earth-rotating frame as 90o-tan-1(5910/4681) = 38.38o.

Also, the last (de-orbit) burn has no payload mass. So if the final mass of stage-2 plus residuals is 5000 kg,and the burn is 480 m/s at an ISP of 348, then the stage starts with 5000*exp(480/348/9.8) = 5750 kg. If the 3900 kg payload was still attached, they would get only 348*9.8*ln((5750+3900)/(5000+3900)) = 276 m/s. So they are getting about 204 m/s that they can use for de-orbit, but could not use for the payload.
"""
https://forum.nasaspaceflight.com/index.php?topic=30912.msg1888982#msg1888982
https://forum.nasaspaceflight.com/index.php?topic=30912.msg1888982#msg1888982

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