SpaceX Falcon 9 : GPS III SV01 : SLC-40 : Dec. 23, 2018 - DISCUSSION

[Shanuson]

Is this the GPS sat?

1 43873U 18109A   18357.69183462  .00000088  00000-0  00000+0 0  9992
2 43873  55.0049 198.4368 5566277 269.9967  91.9277  3.89174632    03

55.0deg 1199km x 20205km

The final Orbit should be circular at 20200km, so only perigre raising needed. (How much deltaV is needed?) Also was this the planed insertion?

[gongora]

Lockheed

"This is the Air Force's first GPS III, so we are excited to begin on-orbit test and demonstrate its capabilities," Caldwell said. "By this time next year, we expect to also have a second GPS III on orbit and users should be receiving signals from this first satellite."

[GWR64]

perigee at 1200 km and argument of perigee 270 deg !
Not easy with only 2 ignitions, i think.
They did it, congratulations!

RAAN 198.4 deg fits to GPS plane F

[Lar]

With the final orbits in, it seems a recoverable F9 could have done the job easily.  Let's compare the delta V from LEO:

 +158 m/s for 55 degree inclination
 +278 m/s to go from 175x175 to 175x1200 (8081 m/s - 7803 m/s)
+2064 m/s to go from 175x1200 to 1200x20181  (9052 m/s - 6988 m/s)
 +156 m/s to dispose of second stage (1200x20181 to 100x20181, 2581 m/s - 2425 m/s)
-----
2656 m/s total
The final number will be slightly less since the disposal burn does not need to decelerate the satellite, and hence will be about twice as efficient.   So maybe 2600 m/s total.

F9 recoverable can put about 5500 kg to GTO (about 2450 m/s from LEO).  Reducing the payload to 3900 kg provides 490 m/s more, or about 2940 m/s total.  Even assuming an over-fueled (4400 kg) GPS like the current one, there's an extra 327 m/s for a total of 2777 m/s.  In any case it has more performance than needed.

I always appreciate your analysis, Lou.

But does this leave enough margin (as defined by the Air Force)?  I can see most commercial customers saying fine, use some of the margin for recovery?

(a tiny bit of margin has to be given back for the weight of the legs and fins too)

Also ISTR USAF saying they would consider "recovering some margin" in future launches to allow recovery.

[Alexphysics]

With the final orbits in, it seems a recoverable F9 could have done the job easily.  Let's compare the delta V from LEO:

 +158 m/s for 55 degree inclination
 +278 m/s to go from 175x175 to 175x1200 (8081 m/s - 7803 m/s)
+2064 m/s to go from 175x1200 to 1200x20181  (9052 m/s - 6988 m/s)
 +156 m/s to dispose of second stage (1200x20181 to 100x20181, 2581 m/s - 2425 m/s)
-----
2656 m/s total
The final number will be slightly less since the disposal burn does not need to decelerate the satellite, and hence will be about twice as efficient.   So maybe 2600 m/s total.

F9 recoverable can put about 5500 kg to GTO (about 2450 m/s from LEO).  Reducing the payload to 3900 kg provides 490 m/s more, or about 2940 m/s total.  Even assuming an over-fueled (4400 kg) GPS like the current one, there's an extra 327 m/s for a total of 2777 m/s.  In any case it has more performance than needed.

Just 100m/s of margin. I can understand why USAF wanted all the performance from F9.

[soltasto]

New cataloged object of this mission:

2018-109A  2018-12-23 15:32 UTC - 1193/20200km/55.01°

Made a table with the requirements and the actual result:

Parameter	Target Requirement	Accuracy Requirement	Actual Target	Actual Accuracy
Apogee Altitude (km)	20,181 km	± 100 km	20,200 km	+19 km (81% margin, 0.09% error)
Perigee Altitude (km)	≥1,000 km	±25km	1,193 km	+193 km (19.3% over requirement)
Inclination (deg)	55 deg	±0.1 deg	55.01 deg	+0.01 deg  (90% margin, 0.02% error)

[Alexphysics]

Would this be the de-orbit burn?

https://twitter.com/unitambo/status/1076943678533296128

"Possible SpaceX second stage booster over S.E Australia. Sighting also reported from Tasmania, seen in http://Nth.sky . Pic below taken overhead from Bairnsdale in East Vic. Sighted SSW of Omeo, travelling N.Easterly. @elonmusk @SpaceX #SpaceX"

If you read the whole thread, the timing of the frist tweet would correspond with the second burn which actually was south of Australia. Deorbit burn was much later, at the time of the first tweet the satellite was still attached to the second stage (around 15:30 UTC).

[gongora]

New cataloged object of this mission:

2018-109A  2018-12-23 15:32 UTC - 1193/20200km/55.01°

Made a table with the requirements and the actual result:

Parameter	Target Requirement	Accuracy Requirement	Actual Target	Actual Accuracy
Apogee Altitude (km)	20,181 km	± 100 km	20,200 km	+19 km (81% margin, 0.09% error)
Perigee Altitude (km)	≥1,000 km	±25km	1,193 km	+193 km (19.3% over requirement)
Inclination (deg)	55 deg	±0.1 deg	55.01 deg	+0.01 deg  (90% margin, 0.02% error)

In a post above LouSheffer mentioned finding a requirement at a different spot in the documents that gave a 1200km target perigee:
https://forum.nasaspaceflight.com/index.php?topic=30912.msg1891767#msg1891767

[soltasto]

New cataloged object of this mission:

2018-109A  2018-12-23 15:32 UTC - 1193/20200km/55.01°

Made a table with the requirements and the actual result:

Parameter	Target Requirement	Accuracy Requirement	Actual Target	Actual Accuracy
Apogee Altitude (km)	20,181 km	± 100 km	20,200 km	+19 km (81% margin, 0.09% error)
Perigee Altitude (km)	≥1,000 km	±25km	1,193 km	+193 km (19.3% over requirement)
Inclination (deg)	55 deg	±0.1 deg	55.01 deg	+0.01 deg  (90% margin, 0.02% error)

In a post above LouSheffer mentioned finding a requirement at a different spot in the documents that gave a 1200km target perigee:
https://forum.nasaspaceflight.com/index.php?topic=30912.msg1891767#msg1891767

Used this, page 20. (PDF warning)

https://www.fbo.gov/utils/view?id=decb2651ef2e646e54aa975671de3220

This is however for another batch of launches. Also once I open that link it brings me to nowhere.

[ulm_atms]

New cataloged object of this mission:

2018-109A  2018-12-23 15:32 UTC - 1193/20200km/55.01°

Made a table with the requirements and the actual result:

Parameter	Target Requirement	Accuracy Requirement	Actual Target	Actual Accuracy
Apogee Altitude (km)	20,181 km	± 100 km	20,200 km	+19 km (81% margin, 0.09% error)
Perigee Altitude (km)	≥1,000 km	±25km	1,193 km	+193 km (19.3% over requirement)
Inclination (deg)	55 deg	±0.1 deg	55.01 deg	+0.01 deg  (90% margin, 0.02% error)

In a post above LouSheffer mentioned finding a requirement at a different spot in the documents that gave a 1200km target perigee:
https://forum.nasaspaceflight.com/index.php?topic=30912.msg1891767#msg1891767

I thought it was 1200km also.

So...with that, I want to say congrats to SpaceX's GNC team(and SpaceX in general).  They put that thing right on the money.  Shows they have the characteristics of that rocket understood very well.

Any word on the de-orbit burn?

[gongora]

Used this, page 20. (PDF warning)

https://www.fbo.gov/utils/view?id=decb2651ef2e646e54aa975671de3220

This is however for another batch of launches. Also once I open that link it brings me to nowhere.

Lou linked to the draft version of the same document. In the final version they replaced 1200km with >=1000km.
(Sometimes links on that site act weird)

[ulm_atms]

Used this, page 20. (PDF warning)

https://www.fbo.gov/utils/view?id=decb2651ef2e646e54aa975671de3220

This is however for another batch of launches. Also once I open that link it brings me to nowhere.

Lou linked to the draft version of the same document. In the final version they replaced 1200km with >=1000km.
(Sometimes links on that site act weird)

If that is the case.....I guess the requirement was just get it above 1000km.

I wonder if SpaceX knew about the 1200km draft then and just targeted that since it fulfills the >=1000km requirement.  And since it was in the draft it sounded like someone wanted 1200km at first.

[gongora]

Used this, page 20. (PDF warning)

https://www.fbo.gov/utils/view?id=decb2651ef2e646e54aa975671de3220

This is however for another batch of launches. Also once I open that link it brings me to nowhere.

Lou linked to the draft version of the same document. In the final version they replaced 1200km with >=1000km.
(Sometimes links on that site act weird)

If that is the case.....I guess the requirement was just get it above 1000km.

I wonder if SpaceX knew about the 1200km draft then and just targeted that since it fulfills the >=1000km requirement.  And since it was in the draft it sounded like someone wanted 1200km at first.

I think they were targeting a particular orbit based on their contract.  The wording in the RFP is not necessarily what ends up in the actual contract.

[woods170]

What causes the chunks of ice? It seems they are coming from near the those lateral nozzles?

I suggest you stop using the word “chunk”. It implies heavy solid ice. But it is not. This is gaseous stuff turning into ice. It is therefore extremely fluffy ice.

[Wolfram66]

What causes the chunks of ice? It seems they are coming from near the those lateral nozzles?

I suggest you stop using the word “chunk”. It implies heavy solid ice. But it is not. This is gaseous stuff turning into ice. It is therefore extremely fluffy ice.

Merlin Space boogers

[smoliarm]

What causes the chunks of ice? It seems they are coming from near the those lateral nozzles?

I suggest you stop using the word “chunk”. It implies heavy solid ice. But it is not. This is gaseous stuff turning into ice. It is therefore extremely fluffy ice.

From my side (as a chemist) I'd suggest to stop using the word "ice".
Just because it is not

[Tommyboy]

What causes the chunks of ice? It seems they are coming from near the those lateral nozzles?

I suggest you stop using the word “chunk”. It implies heavy solid ice. But it is not. This is gaseous stuff turning into ice. It is therefore extremely fluffy ice.

More commonly called snow

[ZachF]

Is this the GPS sat?

1 43873U 18109A   18357.69183462  .00000088  00000-0  00000+0 0  9992
2 43873  55.0049 198.4368 5566277 269.9967  91.9277  3.89174632    03

55.0deg 1199km x 20205km

The final Orbit should be circular at 20200km, so only perigre raising needed. (How much deltaV is needed?) Also was this the planed insertion?

It'll need about 1,300m/s to circularize

[niwax]

Is this the GPS sat?

1 43873U 18109A   18357.69183462  .00000088  00000-0  00000+0 0  9992
2 43873  55.0049 198.4368 5566277 269.9967  91.9277  3.89174632    03

55.0deg 1199km x 20205km

Assuming the target was 55.0x1200x20200, that is impressively accurate.

Have we heard about the deorbit burn? It just occured to me that the transfer orbit also crosses near Iridium and future Starlink...

[LouScheffer]

31,424 km/hr at 1,200 km altitude, not including the contribution of earth's rotation.

If correct, wouldn't this be underperformance?  I'll note that depending on the SpaceX velocity versus altitude numbers has seemed in the past to provide underestimates of the actual orbit.

Aha!  I think I finally tracked down why the SpaceX cutoff numbers give different apogees than tracking reveals.

We know the SpaceX numbers read 0 m/s at liftoff.   But the rocket is going east at 409 m/s at this time.   Previously we've been adding this into the SpaceX velocity to get the inertial velocity, and calculating apogee from that.   This always appears to be a little low once the real orbit is revealed.

But suppose SpaceX is actually reporting the inertial velocity in the reference frame of the rotating Earth at all times?  Since the altitude during flight is always greater than 0 (we hope), the radius at cutoff is greater, the frame is rotating faster, and hence we should be applying a larger correction.  Since we have been using the sea level correction (which is smaller) we get a lower apogee.

Since on the GPS-III mission, SECO was higher, this effect should be bigger, so let's try that.  SpaceX reported a cutoff at 31226 km/hr = 8729 m/s.   From the map, the burn happened about -45 degrees latitude.  So at that time the rocket was heading at an angle of 90-asin(cos(55)/cos(45)) = 34 degrees from East-West.  Taking the sin() and cos() components, we get 7062 m/s East-West, and 5130 m/s North-South.  By our hypothesis this is in the rotating Earth frame.

Now how much to add from Earth rotation?  Earth rotates at 465 m/s at the equator, with a radius of 6371 km.  So at 1200 km altitude, 45 degrees south, it's 465*cos(45)*((6371+1200)/6371) = 391 m/s.    So the inertial X velocity is 7062+391 = 7453 m/s.  Combine with Y to get sqrt(7453^2+5130^2) = 9047 m/s in inertial space.   Presto!  This is the perigee speed of a 1200x20181 orbit, as desired.

It appears to improve GTO prediction as well.  Take Telstar 18, for example.   Cutoff happens at 33432 km/hr = 9287 m/s.  With the old scheme we add +409 for Cape rotation, giving 9696 m/s and a 17500 km apogee, which is an underestimate.   With the new scheme, using the 27 degree inclination, we get an E-W of 8274 m/s and a N-S of 4216 m/s.  At an altitude of 267 km at the equator, rotation is 465*(6371+259)/6371 = 484 m/s E-W.  This gives a total E-W of 8758 m/s, which combined with the N-S, gives 9720 m/s, or an 18000 km apogee.  It was reported as (in 2018-069A/43611) in 259 x 18098 km x 26.93°, so the new estimate is much better.

So the trick, I think, is to do the rotating-inertial conversion *at the 3D location of the burn*.