Adam Hibberd
I have been considering the feasibility of a mission to 1I/’Oumuamua (under the banner of Project Lyra of course) in the context of a SpaceX Starship launch vehicle.
The word ‘Starship’ here is a contraction – as it is often used to express the combination of Super-Heavy first stage, with Starship second stage.
To be precise, I assume Starship Block 3, which (according to wiki at least) will have its maiden flight next year, and is distinguished from the Blocks 1 & 2 by the use of upgraded Raptor 3 engines (amongst other things) as opposed to the existing Raptor 2, to significantly enhance the overall performance of the launch vehicle.
The nub of the issue for Project Lyra, is what should the demands on the launch vehicle be? In other words, what orbit should the Starship target precisely?
The answer to this question is a minefield for any mission designer; it is not simply a matter of choosing the interplanetary trajectory with minimum overall ΔV (in other words minimum velocity increment from the onboard propulsion system), but actually there is a complex interplay between the launcher specification, its capabilities, the exact nature of any additional stages, and the overall aim of the mission – in this case to catch ‘Oumuamua.
However there is one fundamental, inescapable requirement of any Project Lyra mission powered by chemical rockets, and that is the spacecraft MUST encounter Jupiter, whether that be a powered gravitational assist (GA) – where the thrust is applied at perijove (otherwise known as a ‘Jupiter Oberth Manoeuvre’, JOM) – or a passive Jupiter encounter which is just a straight forward GA, without any rocket thrust.
With this in mind, the first port-of-call for any investigation requires answering the question ‘can Starship inject a payload into an escape mission to Jupiter?’
Unfortunately the Super-Heavy/Starship combination was not optimized with injection directly into an Earth escape orbit (or ‘hyperbolic’ orbit) in mind. Its methalox combination (i.e. methane and liquid oxygen), is designed perfectly to carry hugely massive payloads into LEO (Low Earth Orbit) with ease and reliability. It is from this LEO that refuelling of the Starship can take place, from which the rejuvenated upper stage can inject into any escape orbit with ease, to virtually any destination in the Solar System actually, and this is where Elon Musk’s Mars colonization plans enter the stage.
The cost of this plan is financial. There would have to be on the order of 10 Starship tankers loaded with propellant launched into LEO, before only one single Starship could carry the required propellant mass.
Now with all this in mind, is the Starship indeed capable of a launch to Jupiter? The characteristic energy C3, a measure of the energy required of the launch vehicle, would have to be at least around 100 km2s-2 for a mission to Jupiter. That turns out to be very difficult for the Starship, even with additional rocket stages attached to the spacecraft inside the cargo bay.
There is however an old trick for a mission designer which comes in very handy when the problem is reaching a distant target (like Jupiter in this case) whilst using a much smaller C3 than that for a direct flight to Jupiter. This is known as a ‘V∞ Leveraging Manoeuvre’ (VLM).
A VLM reframes the target needed by the launch vehicle and moves it from the planet in question, in other words Jupiter, around ~ 5.2 au from the Sun, to a point in deep space not quite so far away, hence the reduction in C3. A Deep Space Manoeuvre (DSM) is then conducted, followed by a return to Earth where an encounter takes place, and having significantly increased its energy as a result of this encounter, then the spacecraft flies towards Jupiter without much difficulty.
There are 4 different types of VLM, and these are shown in Table 1.
The first is a return to Earth after 1 year, i.e. with n=1, requiring the least C3, then comes n=2 with a much higher C3 , then n=3, and finally the n=4 option which requires the highest C3 of all. Trajectories n=2,3, & 4 are summarized for you in Figure 1, where they are all depicted in their entirety, though in practice it is likely that only one would be used per mission. The n=1 option would obliterate the view of Earth’s orbit so is not shown in this Figure 1.
Having carried out some preliminary analysis into which VLM from Table 1 would be optimal for Project Lyra and Starship, I have found that probably the best option is the first, i.e. the 1 year resonance, since any C3 higher than 0 km2s-2, is extremely challenging for a direct mission by a Starship Block 3.
My remit when I performed this research was to ignore the option of in-orbit refuelling, even though it has a huge potential. Thus it would seem it is to the least challenging of those options in Table 1 we must refer, if we are to achieve any kind of payload to ‘Oumuamua. The next question is ‘which combination of extra rocket stages do we attach to the Project Lyra payload in order to achieve a C3 = 0 km2s-2?’
There are several possible options from which we can choose and let me first point out that I haven’t tried ALL permutations of stages, that would entail a far more detailed analysis than I have performed here and would be worthy of a paper of itself. However, let us just take it as read for the moment that we shall use two stages, the first a cryogenic combination of liquid propellants LH2/LOX, i.e. the Centaur V rocket stage (which is in production) and also as a second stage, the STAR 48B solid propellant booster. The specification and the ΔV budget for this combination with a 500 kg payload is shown in Table 2.
It so happens I have studied the combination of Centaur and STAR 48B to get to ‘Oumuamua in this paper here, however this was exploiting a NASA SLS rocket and NOT a Starship, and also adopted an older version of the Centaur.
So if one assumes a Centaur V and a STAR 48B with a 500 kg Lyra probe on top (the same mass as the New Horizons spacecraft), then the Starship Block 3 cannot ON ITS OWN, inject this combined payload into an escape orbit with C3 = 1 km2s-2. (Note here that since the required C3 = 0 km2s-2 happens to be a PARABOLIC ESCAPE ORBIT w.r.t Earth, which introduces mathematical singularities, I decided to marginally increase the required performance to C3 = 1 km2s-2, with a perigee of 175 km altitude. This is because these orbital elements allow the target to be slightly HYPERBOLIC rather than PARABOLIC, which doesn’t alter the demands on launcher performance that much but does simplify the calculations.)
I invite you now to look at the results of the optimization process in Figures 2-4. This optimization includes the possibility of incorporating any coast arcs, though none were actually deployed.
Figure 2
Figure 3
Figure 4
Although the Starship cannot inject the payload and combination of stages itemized in Table 2 into the required escape orbit, can we still use some of the thrust from the Centaur V as well? Let us delve a little deeper into this possibility.
First of all, note in practice that for an Earth escape mission, the launcher would most likely inject into an intermediate parking orbit around the Earth, before the Centaur completed its burn to Earth escape. However bear in mind that this is a feasibility study, so a direct ascent to escape was assumed, to get a handle of what the Starship is capable of.
A Centaur V has a restartable rocket engine, meaning the thrust can be effectively turned off at any time during its burn, and more than that can be turned on again after a period of coast. This allows the Centaur V to achieve the required C3 of the target orbit after the Starship has done its best, and there will still be more of the Centaur’s LH2/LOX propellant left-over and unused. Would this spare propellant go wasted then?
If we examine Figure 2, we find that there is a remaining ΔV from the Centaur V of ~6.75 km/s. Normally a mission designer would seek to use ALL this available propellant at Earth escape since delaying would result in undesirable and very considerable boil-off and leakage of the cryogenic propellants which the Centaur exploits. But there is room for hope, go here for an investigation of how a Centaur might be restarted after a considerable elapsed time, using COLD (Cryogenic Operation for Long Duration) technologies. The authors are quite optimistic that such technology could be developed and implemented with numerous benefits for space missions.
It is at this point we turn to my ‘Optimum Interplanetary Trajectory Software’ (OITS), which can solve the over-arching problem of which interplanetary trajectory is best for catching up with ‘Oumuamua, given that the initial C3 = 1 km2s-2 at Earth.
So I proceeded with my investigations using OITS and found the trajectory in Table 3.
This is depicted in Figure 5. The plan in question requires two burns after Earth escape: the first at a Return to Earth (~6.6 km/s) and the second at the Jupiter encounter (3.6 km/s).
The encounter at Earth (an ‘Earth Oberth Manoeuvre’, EOM) exploits a ΔV equivalent to that remaining in the Centaur V after the Earth escape with ~150 m/s subtracted. This deduction is to account for 4% reduction in propellant over the course of 1 year after injection, due to boil-off and leakage, which is a low figure but apparently within the capabilities of the COLD technologies elaborated in the aforementioned paper.
This leaves the Jupiter Oberth Manoeuvre, JOM, requiring a ΔV of exactly 3.6 km/s which turns out to be precisely the amount available from the STAR 48B, allowing the 500 kg payload to be accelerated to ‘Oumuamua after 43 years from launch.
Figure 5
So is this the best plan for Project Lyra and SpaceX? It seems not necessarily.
If we reduce the Project Lyra payload to 100 kg, then there IS another way!
The alternative plan is to forget the enormous, super-powerful Starship and use a SpaceX Falcon Heavy Expendable instead. Go to a previous blog of mine, here, which shows that there is an architecture which can reach ‘Oumuamua after only 28 years.
Yet a caveat is in order here. Such is the complexity of the problem, there being SO MANY permutations of trajectories and upper stages (and launchers for that matter), I am convinced there are better alternatives available for Project Lyra, and it is my long-term aim to discover exactly what they are.
[1] Hyperbolic Excess at Earth, V∞, where C3 = V∞2