Adam Hibberd

Let’s say we eject a spacecraft with a small velocity decrement in the opposite direction to Earth’s own velocity around the Sun, what will happen to it exactly? It will stay around Earth’s heliocentric orbit since its velocity is close to Earth’s, however we shall assume that the spacecraft flies outside of Earth’s theoretical gravitational sphere of Influence (SoI) and also that it is only affected by the Sun’s gravitational field.

Well the first thing to observe is that the body will gradually drift IN ADVANCE of Earth’s orbit around the Sun. That may seem counter-intuitive but look at it this way. By having a lower velocity relative to the Sun than Earth, that means it will reach a perihelion (closest point to the Sun) slightly lower than Earth’s circular orbit and so the time period, T_C of the craft will be shorter than the time period of Earth’s orbit, T_E (1 year). Since the time-period of the spacecraft’s orbit is shorter, then that means it will gradually get ahead of Earth. The reasoning is that for every 1 period the spacecraft takes, the Earth will be slightly behind it since its period is longer.

So let’s assume that the time period of the spacecraft is indeed lower than that of Earth’s and allow the spacecraft to creep ahead of Earth until it reaches the so-called Sun/Earth L₄ point. For the uninitiated, that sits at exactly 60° (π/3 radians) in advance of the Earth along Earth’s orbit around the Sun. How long would that take exactly?

The answer to this turns out to depend on the velocity with which the object leaves the Earth’s SoI, which we shall equate here to the object’s hyperbolic excess speed relative to Earth.

I have done precisely this research and I generated the following two plots.

In these plots, the red-dashed line represents the 2-body problem we are addressing in this blog post, and for information the dark blue solid line indicates the 3-body model, with the Earth included.

When you look at the 2-body model in the first of these plots you can observe some ridges which are even more evident in the second plot. These turn out to be harmonics. They are also present to a lesser extent in the 3-body simulation.

Let’s look at what is happening a little more deeply.

The synodic period between the craft and Earth,T_S, is given by the following expression:

If we wish to reach a point at θ in advance of the Earth in time t, then it follows that approximately:

Let us say we wish to reach the S/E L4 point, thus θ=π/3 , and so:

Furthermore we wish elapsed time to be some integer multiple, n, of the craft’s time period T_C, whence:

Inserting this into (1) we get:

Now rearranging to get T_C , we find:

Thus:

From (3) & (4), this leads to a time required to reach L₄ as:

Let us now determine the theoretical hyperbolic excess speed, V_∞, needed at Earth to allow a passage to the L₄. We know the time-period of the orbit of the spacecraft, T_C, how does that translate to, V_∞ ?

First we find from Kepler’s third law that, given the ratio T_C/T_E, then the ratio of semi-major axes, a_c/a_E , is given by:

The heliocentric velocity, V_C , of the spacecraft when it returns to 1 au is described in the following equation from the well-known orbital energy relationship:

The hyperbolic excess needed at Earth is then:

Using equation (8) and with the identity, T =2 π √(a³/μ) , then we can restate equation (10) in terms of time periods as follows:

The L₅ Point.

For this we note that the RHS of (1) & (5) must be changed in sign, like so:

We then follow a similar line of reasoning to arrive at:

Also note that equation (10) now changes to:

From which we eventually obtain:

Adam Hibberd

For various reasons to do with research, I had to recompute the launch ascent trajectory for the New Horizons mission.

New Horizons was a probe sent to Pluto and took various outstanding images and measurements of this very distant dwarf planet.

But it had to be launched into space in the first place, so how did NASA manage that precisely?

Since Pluto is far away, to get there in any reasonable and practical span of time, required a LOT of speed, which translates to a very powerful launch vehicle, which in turn translates to lots of booster stages.

New Horzions was launched on an ATLAS V launch platform as the first stage, equipped with a full 5 solid strap-on boosters.

Once out of the atmosphere it fired a powerful (high specific impulse) liquid cryogenic booster stage known as a ‘Centaur’.

A Centaur has the advantage that its engine can be stopped at some point (for a coast arc) and then restarted later on at a more propitious moment, very handy for interplanetary missions.

In addition the New Horizons mission had a STAR 48B booster to send the probe from an elliptical Sun-bound orbit to a Sun-escape orbit, towards Jupiter in fact, whereupon a gravity assist would be conducted to arrive at Pluto even sooner.

I show attached two plots of the ground track followed by the mission, one generated by my own software – namely LVAS (Launch Vehicle Ascent Software) – and the other representing the actual ground track which I unearthed from the world wide web.

Adam Hibberd

I was using chatGPT, the smarter than smart AI conversation winner – this things knows everything under the Sun, right?

You may skip this detail as it may be completely opaque to you, but I had asked it for the hyperbolic excess of the New Horizons spacecraft mission to Pluto and it came up with an erroneous answer which only someone with a certain level of insider knowledge – like me – could call-out.

So I did!

And lo-and-behold, it dutifully, magnanimously and rather humbly corrected itself, quoting what I knew to be the right figure instead.

Who’d have thought the day would arrive when humans are actually smarter than AI?

Adam Hibberd

I have woken up at some ungodly hour and what of all things should I be obsessing about? You guessed it – that weird celestial body, to use a word employed many times by H. P. Lovecraft himself, the truly eldritch interstellar object known as ‘Oumuamua.

I occasionaly grasp for a mental image of this extrasolar visitor to our abode, but I dare not fill in the unknown aspects of this celestial body to give me a full picture, though my imagination demands it, my scientific integrity simply does NOT allow it.

All we have is its strange set of observed characteristics, one of which being its tumbling motion. That got me to thinking, what exactly sets off a chaotic tumbling state in a body such as ‘Oumuamua? Many scientists believe the likely explanation is that ‘Oumuamua was struck by an object – possibly in its planetary system of origin, indeed many asteroids in our Solar System experience the same phenomenon and with the same explanation.

But why should ‘Oumuamua have left its natal planetary system in the first place? Possibly the collision was a cause of this, but I think that would be unlikely, more likely gravitational resonances or an encounter with a massive planet in its host planetary system was the cause, after all Jupiter is known to have done exactly this to comets in our own system.

But there is a BIG problem here and I shall endeavour to explain the logic below.

What happens when Jupiter ejects a body is that the body’s so-called hyperbolic excess (its speed reached at a great distance, in other words entering into interstellar space) is very small WITH RESPECT TO OUR OWN SOLAR SYSTEM.

Look at it this way, let’s say you throw a ball gently out of a moving train. It is clearly the case that, although the ball’s velocity relative to the train is small, relative to the ground that ball has a velocity which is almost precisely the velocity of the moving train, so anyone observing that ball on the ground would get a good idea of the velocity of the train by measuring the velocity of the ball.

This should also be the case for ‘Oumuamua, by measuring its velocity in interstellar space, we should be able to get an idea of the velocity of its natal system. But therein lies a big mystery.

What we find is that ‘Oumuamua’s velocity in interstellar space was virtually zero – technically it was very close to the Local Standard of Rest (LSR), which is the mean velocity of all the stars in our vicinity as they rotate around our Galaxy’s centre. Going back to our train analogy, that means the train – or planetary system – it came from had almost zero velocity w.r.t. the LSR. What is the likelihood of that happening? My mind now is cast back to my time as a pupil at Stoke Park Comprehensive school where I impressed my chemistry teacher Dr Brooks with the following deduction.

We were studying what is known as the ‘Maxwell Distribution‘, this is what you get when you plot on the horizontal x-axis the speed of the molecules of a particular volume of gas and on the vertical axis the number of molecules in this volume which have this speed.

What one finds is that there is a peak speed, that is there is a MOST likely speed for a molecule and as the possible speeds increase, the number of molecules with these speeds reduce – in fact the graph decays and approaches zero to the right.

But what happens to the left of this peak in the curve – that is as the speed of the molecules decrease to zero?

What we find is that there is a similar decrease on the left side of the peak until the curve actually touches the horizontal axis, AT THE ORIGIN. Another way of looking at this is that the number of molecules with zero speed is actually zero. This is in line with the observation that the only way a gas could have ANY molecules with no speed is at minimum energy or ABSOLUTE ZERO, which is impossible, right?

Now let’s apply this to ‘Oumuamua’s system of origin which, as we have seen, had almost zero speed w.r.t. the LSR, and make the anaolgy of the speed of stars in the galaxy with the speed of molecules in a gas. A zero speed w.r.t the LSR for a star should actually be exceedingly unlikely, in precisely the way it is for molecules in a gas.

It seems the more you think about ‘Oumuamua the stranger – and more eldritch – it gets.

Adam Hibberd

I am back to dark comets (DCs), mysterious bodies showing signs of an anomalous force upon them but which don’t at all exhibit any signs of outgassing of water or carbon dioxide, since they have no coma or tail to indicate that they could actually be comets.

So they are not asteroids NOR comets, what on Earth could they be?

Well I’m pleased to announce I have ‘bagged’ another of these weird objects as NOT being natural at all, but in fact a NASA probe.

This particular object was observed briefly then disappeared altogether, never to be seen by anyone since.

I think I have the answer to this mystery in that the NASA probe in question was probably applying a thrust to change its orbit whilst and soon after it was being observed by astronomers, who incorrectly ascribed to it an anomalous force, but which was in fact deltaV from the probe’s rockets.

Thus since its orbit changed dramatically, any predictions of where this dark comet (actually NASA probe) would be in the future would be entirely erroneous!

Adam Hibberd

The object known as 2024 YR4 has laid down the gauntlet on humanity. ‘See me outside, or take the consequences!’

The consequences however would not be eternal dishonour and ignominy, but a complacent denial of the existential threat posed by Near Earth Asteroids (NEAs) such as this.

True, a few weeks after its discovery in December 2024, 2024 YR4 was determined to have a zero probability of impacting the Earth in December 2032, yet subsequent to this, it was calculated to have a >4% probability of colliding with the Moon.

With further observations recently by the JWST, any collision of the Moon around this timeline can be totally discounted. Thus this finding has been accompanied by much relief since such an impact would have sent huge quantities of debris up into cislunar space, a fair proportion of this debris showering down upon the Moon’s surface and creating a serious hazard for any astronauts or taikonauts on the Moon at the time.

Even worse, had the impact occurred on a particular region of the Moon (which it quite possibly could have done), this debris would have headed rapidly towards the Earth, possibly stimulating the catastrophic ‘Kessler Syndrome’ if the debris had impacted any artificial satellites. The Kessler Syndrome is a cascade effect where when one satellite is struck, more space debris is generated striking other satellites and so on. Needless to say the consequences to humanity would be dire now we are so reliant on satellite technology.

So it seems humanity can now put this dreadful outcome aside and instead we can legitimately ask what we could do about sending a rendezvous mission to arrive at the asteroid, collect a sample and then return it to Earth?

Indeed a flyby mission is high on the 2022 Planetary Decadal Survey list of priorities:

“The highest priority planetary defense demonstration mission…should be a rapid-response, flyby reconnaissance mission targeted to a challenging NEO, representative of the population (∼ 50–100 m in diameter) of objects posing the highest probability of a destructive Earth impact”

Yet alternatively, a sample collection mission, of the kind conducted by OSIRIS-REx would involve an even higher scientific return and is eminently worth considering.

OSIRIS-REx had a launch mass of 2,110 kg, is there anyway such a mass could be inserted by a launch vehicle into an eventual rendezvous mission to perform similar feats of analysis on 2024 YR4 as OSIRIS-REx did on Bennu?

My software, OITS (Optimum Interplanetary Trajectory Software) has found two possible trajectories which would allow a rendezvous mission to be realised with a launch on a SpaceX Falcon Heavy Expendable vehicle.

A friend Justin Wing Chung Hui, lead singer of the Coventry group, the Duck Thieves, is also a software engineer, and on my request has created animations of a trajectory solved by OITS with 2 Deep Space Manoeuvres (DSMs) and another with 2 Earth Gravity Assists.

So should we act on this discovery and send a sample return mission?

That is not for the likes of Justin and me to decide.

Adam Hibberd

‘Oumuamua is inexorably receding from the sun, travelling farther and farther away as time goes by, it is now well beyond the orbit of Neptune, and even beyond the Kuiper Belt.

The opportunity is ebbing with every tick of the clock.

I, and others of the i4is team, are trying to stimulate interest in a mission to ‘Oumuamua, but however you care to look at the prospect, it throws up loads of problems and difficulties which are, though challenging, not insurmountable.

Q: ‘Oumuamua is travelling at speeds of 26.3km/s, how can we possibly catch it?

A: We can catch up using gravitational assists and slingshots of the Sun and Jupiter.

Q: ‘Oumuamua was only visible in telescopes for less than three months and because of limited observations we don’t have an accurate fix on where it will be at intercept distances needed by Project Lyra.

A: With the same sort of LORRI telescope used on-board the New Horizons s/c encountering Pluto, we would be able to detect ‘Oumuamua at the expected distances of intercept. Also using more than one probe would help, in fact various mission architectures exist.

Q: The s/c will be travelling in excess of 20km/s w.r.t ‘Oumuamua, will we be able to image anything?

A: The Earth travels at 30km/s w.r.t. sun, does this prevent us from viewing celestial bodies in our own solar system?

The above are just three questions but there are many, many more associated with Project Lyra. Answering them is a matter of science and engineering, and also creativity and imagination. With all humanity aboard, there would be NO STOPPING US, what is it exactly that is holding us back?

The monsters of the Id?

Adam Hibberd

A fair few people of my age and older will remember the American actor Doug McClure and his popularity in the UK as the personification of the brave, handsome and daring adventurer into distant lands inhabited by dinosaurs and other strange creatures, in a fairly long list of British action adventure films made largely in the ’70s.

What can I say? I remember them with a great deal of fondness, but I remind you at the time I was a young and impressionable child with a wild imagination and these films were just up my street. Compared to today the special effects were distinctly low-key and primitive, but that left a lot to the imagination and I was always willing to forgive their crudeness and fill in the deficiencies with creations of my own mind. A man in a monster suit, for instance, was never, ever a man in a monster suit but a monster which happened to look like a man in a monster suit.

The film I show you below, I watched at the ABC cinema on Hertford Street, Coventry, with my good friend Ravinder Bains. I’ve mentioned Ravinder before he was well ahead of me in intelligence at this age and he immediately saw through to the tragic ridiculousness of this film and came out of the cinema trying desperately to stop himself laughing – for me – bless him – for I had taken the film so seriously I was rather indignant at his mocking attitude.

My father who had reluctantly taken us and had patiently watched it as well, actually sided with Ravinder on this and of course looking back at this film with the benefit of hindsight; this truly was a pretty crap, risible, attempt at an action-adventure movie.

Never mind, I still love it for heaven’s sake!

Adam Hibberd

Let me put people to rights if they have some idea that what I do is unimportant and even irrelevant. Some even make a comparison with art and culture and try to emphasize how art can transcend the material, that these pursuits have inherent worth and validity as they communicate what can’t be in any other way.

That maybe a point, but in my view it seriously misses THE point.

What I like to do is ask the question, ‘what would we do if we discovered an asteroid will collide with Earth and wipe out humanity?’

Knowledge of STEM would be crucial here in designing a spacecraft, a trajectory, a kinetic impactor to throw the asteroid off course at the calculated optimal time and save humanity.

But what good would art be in comparison? An example course-of-action might be to bring different people together and ask individuals to imagine and paint the asteroid impacting the Earth as a kind of cathartic exercise to make us FEEL better.

There is a stark difference, one is actionable and physically useful, the other is socially and psychologically comforting. One saves the Earth, the other lubricates communication.

They each have a place, and we should do our best to realise that – instead that is of succumbing to the ignorance of ridiculous accusations of uselessness.

Adam Hibberd

An article I wrote for Principium, quarterly publication of the ‘Initiative for Interstellar Studies‘, several years ago now, not long after the first interstellar object passing through our Solar System was discovered, namely, 1I/’Oumuamua.

It’s about how I solved the problem of sending a mission to catch 1I/’Oumuamua using my software, ‘Optimum Interplanetary Trajectory Software’ (OITS), which serendipitously I had already developed just before ‘Oumuamua was discovered.

Do give it a read. It is written for a lay-person though admittedly, perhaps, it doesn’t always succeed in that regard.

Here’s a mission to interstellar object 2I/Borisov from which the stills were taken at the end of the article:

Adam Hibberd

A mission to Near Earth Asteroid designated 2024 YR4 which for a while had a relatively high chance of colliding with the Earth.

This probability has dropped to zero but instead the likelihood of impact with the Moon has gone up – it is now ~ 4 %.

Such a collision would cause debris to fly all over the place and any astronauts – or taikonauts for that matter – on the Moon at the time would have to take evasive measures. Furthermore it would hurl debris into cis-lunar space, and might possibly knock out some Earth satellites, leading to onset of the ‘Kessler Syndrome’.

This animation assumes that the asteroid actually misses the Moon with an associated likelihood of ~ 96 %.

So would a sample return mission be feasible for this object?

It turns out yes, assuming 2 Deep Space Manoeuvres (DSMs) on the way and a launch Characteristic Energy (C3) of ~ 81 km2s-2.

This launch C3 would enable the Falcon Heavy Expendable to loft an OSIRIS-REx mass spacecraft to the necessary interplanetary orbit, this being a previous sample return mission to the asteroid ‘Bennu’.

This was all solved and generated by my ‘Optimum Interplanetary Trajectory Software’ (OITS).

The link to the video is here:

Adam Hibberd

I’ve been setting my software, ‘Optimum Interplanetary Trajectory Software’ (OITS) challenging tasks which take ages to solve but are uniquely solvable by my software.

I am looking at Sample Return missions atm, specifically ones which rendezvous with the target, loiter with it, then return home to Earth. The loiter phase includes a lander being dispatched by the spacecraft, picking up a sample from the asteroid’s surface, and returning to the mother craft. The mother craft then leaves the asteroid and heads home.

The key task astrodynamically speaking is how on Earth do we lower the velocity increment needed to match velocity with the asteroid?

The answer to this question is to be in an orbit as close to that of the asteroid’s as possible.

This means one may have to conduct one or more GAs (Gravity Assists) with Earth, for example, to alter the spacecraft’s orbital path to gradually manipulate it so that its orbital elements are as close as possible to that of the target’s.

This is the challenge I have set OITS, and a massive challenge at that. Results so far are inconclusive since it might well just be a matter of waiting long enough for the solution combination to fully converge.

The solutions I’m getting are tantalizingly close to being viable, I so wish and hope that ultimately there is a way!

Adam Hibberd

Life is like a box of chocolates, you sometimes over-indulge, scoff the lot and then regret you had the box of chocolates.

I know at least one ex-acquaintance who became rather wealthy, but lost it all due to his own ‘greed’ (his own word). I admire his honesty but not something you should talk about or even boast about as he seemed to be doing. Mind you it proves my point doesn’t it? But the following is a better example.

I made the huge mistake of buying 2 cylindrical containers (excuse the scientific pedantry here) of tubular biscuits from Amazon yesterday, and to be frank they are probably the most delicious biscuits I’ve ever tasted.

They were intended to accompany the orange mousse I have made for my neighbours both sides when they come over tomorrow for roast lunch. I attach the menu for you to peruse.

Unfortunately, I decided to try one. It is at this point the concerned and altruistic reader may wish to discontinue reading this update, as I have no rational explanation for what happened to me next.

These things are outrageously moreish, I would call them dangerously addictive in fact, probably on the same level of heroin or cocaine.

I managed to scoff them all in matter of hours, with now only a few bits at the bottom which I had promised myself I would save for my dear guests arriving tomorrow.

Needless to say this will be simply insufficient to go with the orange mousse, but hold on I just remembered I have another cylindrical container of these morsels of delight, but in a different flavour.

I must now try one to see what they are like……

Adam Hibberd

I live now powerless in the depressing context of a planet occupied by what I once would have called an ‘intelligent race’ and watching helplessly as humanity suffers and slides into an abyss of eternal darkness, never to be remembered, without any lasting legacy, having made little or no enduring impression on the universe. 

This despite the likes of incredible superhuman minds through the centuries which seemingly transcended human limitations, Newton, Einstein, da Vinci, and I would include those further afield, Beethoven, van Gogh, Shakespeare, etc. The incredible impact all these geniuses have made will have lasted only fleetingly in this magnificent cosmos, their continuing flame will be snuffed out, unceremoniously extinguished in the face of a new and more powerful force: our huge stupidity.

The human race has elected leaders, and in particular a leader, with an infantile and truly embarrassing ignorance of how to comport themselves, let alone their respective nations. Upon reflection, in the face of this new force of moral emptiness and visionary vapidity, how could these geniuses, and for that matter the whole of humanity, possibly have stood any chance whatsoever?

I do still feel passionately however that there is something really important that I personally could have done to end this debacle, and this is the simple yet obvious notion of formulating a vision for humanity’s future. Not a manifesto full of promises to be approved and held to account on, and not a vision to line my own pockets as quickly as possible, but instead one with real long term foresight for all of us, no matter what our race, beliefs, income. A passage onward through stormy and treacherous waters, a way forward though the largely self-inflicted wounds we have suffered ourselves, as a species, and those inflicted on our only, fragile yet precious life support, the planet Earth.

Adam Hibberd

I was recently asked by a US colleague to do a little research using ‘OITS’.

For those of you unaware by now, ‘OITS’ stands for ‘Optimum Interplanetary Trajectory Software’ and is a powerful tool I developed single-handedly for studying the problem of sending spacecraft on heliocentric trajectories to a planet or for that matter any other celestial body in our Solar System.

What makes it so powerful is that it can accommodate multiple gravitational assists (GAs) on the way which can result in a lower propellant mass needed by the spacecraft to get to the target in question. This mass is a very important metric in determining the feasibility of a mission, since as you probably know, mass must be driven down to as low as possible, since mass-to-orbit has a significant launch cost.

Anyway my colleague suggested I do some analysis into the feasibility of missions to a selection of Near Earth Objects (NEOs) which will come very close to Earth in the near future.

The requirement for OITS would be to minimize this propellant mass for the launch vehicle (actually minimize V∞) but with a further constraint imposed – that of arriving at the target NEO with a relative arrival velocity less than <= 300 m/s.

Would my software be up to this task?

It turns out yes! And you can find below a selection of successful ‘matches’ which comply with these requirements. The reader may note that some of these can be rejected due to being too challenging for any launcher, but note I have NOT included all solutions found by my software – this is not an exhaustive list.

Adam Hibberd

I am fundamentally an astrodynamicist, but I have been known to occasionally look at the wider picture. I have been thinking recently about humanity.

Human existence, and for that matter all life, has been a story of death. Obviously enough, life attempts to preserve itself by defying death.

You might say that evolution is simply an attempt by the universe to learn more about itself.

In my view death has a purpose. It is teaching life to know and understand.

Look at humanity.

People have died for generations upon generations. But understanding and technology have always advanced.

Particularly since around the time of the industrial revolution, we have begun to outwit death, our longevity has been increasing, child mortality rates have plummeted. This has largely been a consequence of deeper scientific understanding, particularly in medicine.

Death catches up with us all, has all this loss of life been futile? Has every living thing struggled in vain?

Not at all. By individuals dying, life is collectively knowing more and more.

What wonders will our successors discover? Maybe a way of defying death forever?

Perhaps even the ultimate celebration of life, a kind of unification of all life that has ever existed?

The creation of a new universe.

Adam Hibberd

The 2024 YR4 of the title is an asteroid which was discovered in December of 2024 with a really cool Christmas present for humanity: the prospect of a collision with Earth only 8 years down the line (in 2032) and this with an associated high level of probability.

The result was initially a high Torino impact hazard score, which as is so often the way, initially escalated and then collapsed to zero after further more detailed observations and measurements of its orbit.

Attention has now changed from an Earth impact to a Moon impact with currently a probability of 4%, and this could potentially have dire consequences, particularly if we have men on the Moon by this time.

I have written a paper on the subject of missions to 2024 YR4 which can be found here. Its next encounter with the Earth/Moon system will be in December 2028, and this is known with an excellent level of confidence as a miss of both bodies.

Note that for a flyby mission to this asteroid on its next close approach in 2028, there are two possible arrival windows, the first in October of that year and the second in December.

It turns out that for purely astrodynamical reasons, the second arrival window (in December) yields a marignally lower Earth ‘Characteristic Energy’ for the launch vehicle when the flyby probe is launched to its destination. In other words the demands on launch vehicle performance are not so challenging, meaning a more massive probe can be accommodated and delivered by the launch vehicle to the target, which is clearly advantageous.

There is a caveat though. If one examines the ‘phase’ of 2024 YR4 as seen by the probe at the encounter (where phase is a measure of the fraction of the asteroid lit by the Sun with phase = 0 degs meaning fully lit and phase = 180 degs corresponding to completely dark), then the arrival in October 2028 would actually be preferable. Look at the Figure below which reveals all.

Referring to this plot we find that optimal routes launched in October 2027 to January 2028 arrive in October 2028 (the blue solid line and left vertical axis) and the orange dashed line (right vertical axis) shows the encounter phase of 2024 YR4 will be as low as around 20 degs. Thus 160 degs of the asteroid will be lit up by the Sun for this arrival date.

Launches subsequent to January 2028 arrive optimally in December 2028 and involve an encounter phase of around 155 degs, indicating only 25 degs of the asteroid will be lit.

To summarise all this, it means the shorter and more challenging launch window from October 2027 to January 2028 would actually be preferable to maximise science return from the probe.

Adam Hibberd

Have you noticed, 3I/ATLAS is well and truly on its way out of the Solar System? It has afterall passed through its closest approach to the Sun (perihelion) and is well on its way to a close encounter with Jupiter in mid-March – given this, it would seem to be the ideal moment to contemplate a mission to catch it up.

Many readers will immediately object at this point since hasn’t it conclusively been shown by such papers as this one, that a spacecraft mission from Earth is completely infeasible?

That may be the case but the reader will have overlooked a significant and important detail if they believe so. Most of these previous papers have assumed direct transfer to the target in question – 3I/ATLAS – and have not addressed (to any depth at least) the possibility of indirect missions.

This is where I come in with my extremely powerful software development ‘Optimum Interplanetary Trajectory Software‘ (OITS), a tool I designed to study precisely the indirect possibility – i.e. gravitational assists (or sling-shots) and/or ‘Oberth Manoeuvres’ along the way to the target – and it can handle the direct case also. What amazing software, hey?

You may well have heard of the gravity assist (GA) but what on Earth is an ‘Oberth Manoeuvre’?

This is where a spacecraft under the gravitational influence of a massive body (in this case the Sun) waits to achieve the closest approach (periapsis, or perihelion for the Sun) and then applies thrust at this most propitious point to achieve a high heliocentric speed, in this case resulting in it being shot out of the Solar System, and towards the interstellar object which will have travelled a huge distance by this time.

My research paper with Marshall Eubanks has come out on arXiv here, or alternatively feel free to visit my ResearchGate profile here.

To summarise the results, there is a way to achieve intercept using a ‘Solar Oberth’ but launch would have to be in the year 2035 to allow optimal alignment between Earth/Jupiter and 3I/ATLAS, and the flight duration would be 50 years, but this could be reduced marginally.

I provide an animation created by OITS of just such a trajectory.

Adam Hibberd Memoirs