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, go here. 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.

This is how I'd explain my paper to a mate in a pub:

"The Solar System is comprised of lots of different objects (like planets, asteroids and comets) which go around the central Sun, in huge ellipses. You may say the Earth’s path is circular, that’s true, but in fact all circles are just special sorts of ellipses.

So if you observe a new object and its path (or ‘orbit’) is elliptical, then you know it belongs to OUR Solar System, right?

However when astronomers looked at the path of one particular object, later given the name 3I/ATLAS, it turned out NOT to be elliptically shaped, but instead it was hyperbolic. A hyperbola is just a particular sort of shape which starts off at a humongous distance from the Sun, and so we know this object came from somewhere OUTSIDE our Solar System. In fact it belongs to some other Solar System – with a different central star - in the massive Galaxy, the Milky Way, which our Solar System is a part of. Thus we call 3I/ATLAS an ‘interstellar object’.

Now by sending a spacecraft to intercept 3I/ATLAS, we can discover all sorts of things about the System to which it belongs – and by so-doing it saves us the very difficult task of having to travel light years and light years to explore the nearest stars – this object is here already, IT has done all the travelling!  

There is a problem though. 3I/ATLAS is now heading out of our Solar System at a huge speed – more than 60 km/s, so any probe we send will have to go even faster than this to catch it up.

The problem was solved using some software I developed. (I called this software ‘Optimum Interplanetary Trajectory Software’ – OITS.) It turns out there IS a way of generating a speed greater than 60 km/s. The probe must first launch in 2035, travel to Jupiter where it can slow down – since Jupiter’s incredible mass can do this – and fall in towards the Sun.

Because the Sun has a very strong attractive force due to its huge gravitational field – it is after all the most massive thing in our Solar System - the probe accelerates and accelerates, faster and faster as it approaches the Sun. By the time it reaches perihelion, so in other words when it is at the closest point to the Sun, it is travelling at 346 km/s. That speed is way faster than any spacecraft ever made, 80% faster even than the fastest of all time, Parker Solar Probe which reached 191 km/s.

The ‘Oberth Effect’ says that the faster you are moving in a gravitational field – like the Sun’s – the greater the increase in energy due to any thrust your rocket engines may generate. Thus, reaching low perihelion with a high speed, is ideal for exploiting the most from the Oberth Effect, as it is most effective use of the onboard propellant.

So my software discovered that if this rocket thrust can apply a change in velocity of only 8 km/s or so, the spacecraft can get to the target 3I/ATLAS after an overall flight time of 35-50 years.

That may seem long, but clearly far quicker than going to the nearest stars. Also notice the Voyager 1 and 2 probes were launched in 1977, 49 years ago, and they are still sending useful data back to Earth up to this very day."

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 can be found here:

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.

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 and Andreas Hein 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.

On the request of a colleague, I have solved the problem of exploiting the powerful SpaceX Starship (in fact the yet to be launched Block 3 variant) to lift a spacecraft so that it can catch up with 1I/'Oumuamua, the now rapidly receding 'interstellar object'.

This object sped through the inner group of Solar System planets in 2017, and then headed away again, back into interstellar space.

It left a mountain of questions in its wake, which a spacecraft flyby mission could answer, returning tremendous scientific data in the process.

I used the currently in production Centaur V cryogenic liquid propellant stage and also the STAR 48B solid propellant booster, in addition to the Starship upper stage.

To do this research I needed to optimize both the geocentric launcher-ascent-to-orbit trajectory (i.e. the trajectory which maximises the mass-to-Earth-escape) and the subsequent heliocentric interplanetary trajectory designed to chase 'Oumuamua down, and into which the Starship inserts the Lyra spacecraft.

The geocentric and heliocentric trajectories are shown in the plots below. The first three show the Starship ascent directly to an Earth escape orbit, and the fourth shows the interplanetary trajectory to catch 'Oumuamua after 40 years.

My software 'Optimum Interplanetary Trajectory Software' (OITS) was used in the process of conducting this research.

I have had many queries concerning the calculation of the likelihood of 3I/ATLAS's orbital plane lying within 5^° of that of the ecliptic of the Solar System.

This calculation appears in the paper 'Is the Interstellar Object 3I/ATLAS Alien Technology?' which can be found here.

The calculation exploits a simple equation based on the ratio of two areas on a spherical surface.

If you imagine the plane of 3I/ATLAS's orbit has a vector perpendicular to it, and the inclination of its orbit therefore is the angle between this vector (more precisely known as the 'angular momentum' vector) and the axis representing the ecliptic north pole.

The probability therefore that the inclination of the orbit lies within 5^° of this ecliptic north pole, is the area, A, of a circular cap surrounding this North pole (extending 5 degrees either side of this pole) divided by the total area of the sphere, S.

Now by Archimedes 'Hat Box' theorem we have A=2πr²( 1 - cos(5^°)), and we have the total area of a sphere, S = 4πr². The ratio A/S =( 1 - cos(5^°))/2 = 2e-3 or ~ 0.2 %. This latter figure is quoted in the paper. In fact to be exact we need to multiply this by 2, since we might be within 5^° of the south polar axis also.

There is an alternative logic, however, which has been put to me which comes up with a much higher probability. This I believe to have a flawed logic. I shall elaborate below.

The counter-argument goes like this. Let's say we represent the ISOs as darts and assume they arrive, isotropically (meaning from all directions with equal likelihood) at the Solar System which is represented again as a perfect sphere.

The idea is that the number of darts, L, arriving within 5^° latitude of the ecliptic plane should then be divided by the total number of darts, N, and thus the probability of the plane having an inclination < 5^° is simply the ratio of these two numbers, i.e. L/N.

What one find when one does this calculation is that you get a MUCH HIGHER PROBABILITY, than that derived in the paper. In other words L/N >> A/S.

So why the disagreement?

The reason is because there is a fallacy in the argument of the latter scenario. Let's say that a dart arrives at 4^° latitude above the ecliptic, does it necessarily follow that the inclination of its orbit is also exactly 4^°?

It turns out: not at all! If the velocity when it hits the sphere is vertical (so parallel to the ecliptic north) then, its inclination will be exactly 90^°, even though it strikes the sphere at only 4^° latitude!

Thus by adding up all the darts arriving at less than 5^° latitude we shall arrive at a spurious answer since we shall be unwittingly including in our calculations, darts that have a much higher orbital inclination than 5^°.

Please also refer to my personal blog, which has the same post.

Yesterday I was trying to gauge the measure of the SpaceX Starship in terms of its ability to launch the Project Lyra spacecraft on its way to its destination.

BTW Project Lyra is the initiative to send a mission to catch-up with very quickly receding interstellar object 1I/'Oumuamua. So exactly how do we get a probe to intercept this object?

Well I discovered ages ago that whatever mission plan we might adopt; a visit to the planet Jupiter, either as a means-to-an-end, or alternatively to exploit it directly by delivering a Jupiter Oberth Manoeuvre would be vital in achieving the mission goal: 1I/'Oumuamua.

So how does the Starship fare as far as lofting a payload that will eventually reach Jupiter is concerned?

The unfortunate answer is not very well. This answer is important because this super-heavy launch vehicle is designed as a part of Elon Musk's initiative to colonise the planet Mars, which involves an Earth escape (hyperbolic) orbit just like Project Lyra's - though obviously the former escape is to Mars and the latter is to Jupiter.

So what's holding it back?

The straight-forward answer is the choice of Starship's propellants which are methane and oxygen as opposed to the likes of alternatives like NASA's Space Launch System (SLS) which employs the much more powerful, and efficient, LOX and LH2 combination of cryogenic propellants.

It seems that Starship's methane/LOX combination is ideal for inserting a payload into LEO (Low Earth Orbit), from which the Starship can then be refuelled and sent off to any destination within the Solar System without much difficulty, but absolutely pants at injecting a payload directly into an escape orbit from launch.

To be fair, Elon Musk has made it quite clear that Starship was designed with this refuelling strategy in mind, but there is a cost, which one would expect for any decision along these lines.

The cost is indeed financial - it would take on the order of 10 Starship tankers filled with the requisite methane+LOX in the cargo bay to fully refuel ONE Starship located in LEO - the logistics and economics are a tough reality check for anyone who has bought into the glib Mars colonisation rhetoric spouted by Elon.

So where does this leave Project Lyra? Well I shall continue my research into using a Starship launch vehicle, and I shall have to add two or even three extra stages to the Project Lyra craft payload itself.

If you are slightly concerned by this profligate use of rocket stages, have no fear, there is plenty of space in the Starship's huge cargo bays for these rocket stages + the Lyra craft.