# CAPSTONE mission

#### BrianJ

I've just been having a look at NASA's "CAPSTONE" mission:
• Pathfinder for Artemis
• Going to Lunar NRHO
• Launched on Rocketlab's "Electron", multiple Apogee raising burns from LEO
• Ballistic trajectory to Lunar NRHO via Earth-Sun L1 area.

Quite a navigation challenge for Orbiter!

Some CAPSTONE infos:

Electron pdf:

#### kalral

##### New member
@BrianJ That is indeed a quite challenging project, I wish you good luck. I heard someone did it using Principia in KSP, few months before, but I am not sure about the NRHO part. I am quite interested to see your methodology of using IMFD for this task.

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#### BrianJ

@BrianJ That is indeed a quite challenging project, I wish you good luck. I heard someone did it using Principia in KSP, few months before, but I am not sure about the NRHO part. I am quite interested to see your methodology of using IMFD for this task.
I hope I have the time to give it a try! The question is, as ever, "can the mission be replicated in Orbiter without NASA's sophisticated planning tools?" I wonder if GMAT might be useful? Otherwise IMFD Map and LagrangeMFD will probably be my choice of MFDs.

One thing that encourages me is that if one can get to the L1 area, then it requires only small dV to get on a useful trajectory (for Lunar intercept in this case).

Cheers,
Brian

#### kuddel

##### Donator
Donator
Thanks for bringing it up Brian!

...These are the moments I thank the universe for letting me know this forum

#### BrianJ

Hi,
I've just been making a start on simulating the CAPSTONE launch in Orbiter.
The Electron can put the Photon+Capstone into 250km LEO, but from there another ~2500 m/s dV is required to get out to the Earth-Sun L1 area.
The only info I have about "Photon" stage is "50kg wet mass".
The couple of photos and diagrams I have seen indicate 4 x 0.5m diameter spheres for propellant (Hydrazine) storage.
That equates to ~30kg propellant (being generous), so 20kg dry mass, plus 27kg for Capstone.
If I use an ISP of 3200Ns/kg for the engine, that gives ~1600m/s dV capability - a shortfall of 900m/s dV.
I have to use 35kg propellant, 15kg dry mass, ISP 4200Ns/kg, to get the required 2500m/s dV.
This seems rather optimistic to me, but hey "what do I know!" ;-)

I just wondered if anyone has any thoughts or info about Rocket Lab's "Photon" stage?
Cheers,
Brian

#### cosmonaut2040

##### Member
Hi Brian,

the "50kg wet mass" likely refers to the small "Photon LEO", as it is based on the "kick stage", which is 40 kg dry per the Payload user guide.

The "Photon interplanetary" version must be significantly heavier. Also, it is likely bipropellant.

Assuming 4 x 0.5m diameter tanks (= 0.262 m^3) and MMH+NTO propellants (ISP = 3347 m/s, average density 1190 kg/m^3 per wikipedia) one gets ~312 kg for the propellant.

The total mass is more than Electron can lift to LEO, so it will need to do more than just the 2500 m/s delta v. If I guess e.g. 1000 m/s extra to reach LEO, I get 169 kg for structure+payload which seems reasonable. It's Friday late and I'm quite tired so I don't guarantee that I didn't make some mistake in my calculation

Cheers

#### BrianJ

Ah! Thanks so much
I'm only one decimal place out on my sphere volume calculations
Those numbers make much more sense.
Cheers,
Brian

#### BrianJ

Hi,
after testing in Orbiter, it seems that 481kg is more than the Electron can lift to anywhere near orbit.
This made me take another look at the diagram of the Photon stage and reassess the propellant sphere size, which I think I over-estimated.

[Off-topic]
This led me to wonder - what is the maximum size (radius r)for 4 equal spheres packed horizontally in a cylinder of radius R, and just touching the cylinder wall? A rough sketch helped me realise: r = R * sin(45deg) / (1 + sin(45deg))
And in fact, for n spheres, it generalises to: r = R * sin(Pi/n) / (1 + sin(Pi/n))
Although it doesn't work for n = 0 or 1
I don't know why my brain likes to think about these things, really.....
[/Off-topic]

The Electron is only 1.2m diameter, and leaving a bit of room for the fairing means the Photon stage is about 1m diameter.
So the propellant spheres must be ~ 0.2m radius max.

So at the moment, I have given the Photon stage 158kg propellant , ISP 3347Ns/kg , 55kg dry mass (+27kg for Capstone), and a 500N main engine.
Thats 240kg for fully fuelled Photon+Capstone, and leaves enough dV to get to Sun-Earth L1 after LEO insertion (provided you do multiple burns around perigee to keep the burn efficiency up).

I wonder if that's anywhere near reality?
Cheers,
Brian

#### cosmonaut2040

##### Member
In the absence of actual data from Rocketlab, your numbers seem quite plausible.

And the fact that you even derived an equation for the r gives your analysis extra credibility in my opinion

Cheers

#### Sbb1413

I have planned to create Gateway scenarios with the Gateway at NRHO. However, as simulating NRHO is itself challenging, I will wait for the CAPSTONE add-on to be released. Until then, I will use the LRO orbit for the Gateway.

#### BrianJ

I have planned to create Gateway scenarios with the Gateway at NRHO. However, as simulating NRHO is itself challenging, I will wait for the CAPSTONE add-on to be released. Until then, I will use the LRO orbit for the Gateway.
Hi,
I thought it would not be so hard to set up a NRHO orbit using ScenarioEditor and LagrangeMFD, but I have had no success so far. The characteristics of Capstone NRHO being ~ an orbit of 1500km x 70000km alt, perilune over North Pole, orbital plane roughly perpendicular to Earth-Moon line. And importantly it maintains orbital plane relative to Earth-Moon line.
Using LagrangeMFD "rotating frame" display should show this clearly, I think.
But as I said, I have had no success so far.
Cheers,
Brian

#### BrianJ

Hi,
I put my "Capstone" add-on package up on OHM:

Includes Capstone spacecraft, Photon 3rd stage for Electron, launch scenario from LC-1 Mahia, etc.

Maybe someone else will have more success setting up a NRHO in Orbiter - I have not been able to find anything that works.
The WSB transfer to the Moon from LEO is quite fun and challenging. I included a few screenshots from my last attempt in case it's useful to anyone.

Cheers,
Brian

#### Gargantua2024

##### The Desktop Orbinaut
There's now a HORIZONS trajectory for CAPSTONE available! But kind of incomplete at the moment

#### BrianJ

There's now a HORIZONS trajectory for CAPSTONE available! But kind of incomplete at the moment
Thanks! I'd really like to see the trajectory data post-LOI (13 Nov 2022?) to get a handle on the NRHO.
Cheers,
Brian

#### Gargantua2024

##### The Desktop Orbinaut
CAPSTONE's HORIZONS trajectory now extends to November 14th, a day after its scheduled lunar orbital insertion

It should be able to cover a portion of its near-rectilinear halo orbit around the Moon at this point

#### BrianJ

Hi,
Horizons data up to 14 Dec now, so I grabbed the vectors for 14 Dec - Orbiter still shows Capstone in an unstable lunar orbit ~1700x90000km, but it doesn't even make it to the next periapsis before starting to escape. So I reckon it must make another burn for "NRHO" insertion some time after 14 Dec, maybe.
Here's my scenario for 14 Dec 00:00 UTC
Code:
BEGIN_DESC

END_DESC

BEGIN_ENVIRONMENT
System Sol
Date MJD  59927
END_ENVIRONMENT

BEGIN_FOCUS
Ship CAPSTONE
END_FOCUS

BEGIN_CAMERA
TARGET CAPSTONE
MODE Extern
POS 14.540860 -81.224667 50.622992
TRACKMODE GlobalFrame
FOV 50.00
END_CAMERA

BEGIN_HUD
TYPE Orbit
REF Earth
END_HUD

BEGIN_MFD Left

END_MFD

BEGIN_MFD Right
TYPE Orbit
PROJ Frame
FRAME Ecliptic
REF Moon
END_MFD

BEGIN_SHIPS
CAPSTONE:capstone\capstone
STATUS Orbiting Moon
RPOS -35408833.1341999 -49304325.9739514  10546736.8810199
RVEL -38.6247449987071 -211.983459678939  78.1988597203457
AROT 179.506 -51.883 90.328
AFCMODE 7
PRPLEVEL 0:0.998629
NAVFREQ 0 0
SOLP 2 1.0000
AUTP 1 0
END
END_SHIPS

BEGIN_DX9ExtMFD
END

BEGIN_ExtMFD
END
A quick look at the orbit elements for 13 Nov (LOI date) show a burn at around 23:45 UTC to reduce lunar orbit eccentricity from ~0.96 to 0.93. Here's my scenario for 13 Nov 23:00 UTC.
Code:
BEGIN_DESC

END_DESC

BEGIN_ENVIRONMENT
System Sol
Date MJD  59896.958333333
END_ENVIRONMENT

BEGIN_FOCUS
Ship CAPSTONE
END_FOCUS

BEGIN_CAMERA
TARGET CAPSTONE
MODE Extern
POS 14.540860 -81.224667 50.622992
TRACKMODE GlobalFrame
FOV 50.00
END_CAMERA

BEGIN_HUD
TYPE Orbit
REF Earth
END_HUD

BEGIN_MFD Left

END_MFD

BEGIN_MFD Right
TYPE Orbit
PROJ Frame
FRAME Ecliptic
REF Moon
END_MFD

BEGIN_SHIPS
CAPSTONE:capstone\capstone
STATUS Orbiting Moon
RPOS  5883674.28252967  248931.356464805  2593534.68881761
RVEL -719.878791326623  855.51549883104 -476.155096438183
AROT 179.506 -51.883 90.328
AFCMODE 7
PRPLEVEL 0:0.998629
NAVFREQ 0 0
SOLP 2 1.0000
AUTP 1 0
END
END_SHIPS

BEGIN_DX9ExtMFD
END

BEGIN_ExtMFD
END

Cheers,
BrianJ

#### Gargantua2024

##### The Desktop Orbinaut
It makes sense since the Lunar Gateway would need weekly reboosts on this regime as well

#### Ajaja

##### Active member
Looks fine.
For example, if you try to propagate backward from 14 Dec 2022 there is the trajectory:

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