Adam Hibberd
Recently I’ve been pondering a problem of gravity.
Specifically, the gravity of a particular celestial object which has come to the world’s attention, making headline news in certain papers, I am of course talking about the potentially hazardous asteroid (PHA) designated 2024 YR4.
This object has an orbit which could – potentially – bring it to collide with Earth on 22nd December 2032, around 8 years from now.
The projected explosion – if it does collide – would be on the same order as the 1908 Tunguska meteor, though this recently discovered object, 2024 YR4, could - potentially – come down on a much more densely populated area than the Tunguska phenomenon, resulting in devastating loss of life, yet only on a local scale, certainly NOT on a global one.
As most of you will probably be aware, the energy released in an asteroid strike is dependent on the kinetic energy of the asteroid, which in turn is proportional to its mass and also the square of its impact speed relative to Earth.
The former of these, its mass, is not currently tightly constrained at all, and with a range of diameters from 40 m to 100 m, this results in a range in masses of at least ~9e7 kg to ~1.5e9 kg, yielding an uncertainty in impact energy of at least around 2 orders of magnitude.
I have recently been studying the feasibility of missions to this object, go here and here, and a natural question is ‘would we be able to determine the mass of 2024 YR4 by exploiting a simple flyby trajectory?’
One possible method would be to ascertain this mass from the influence of the object’s gravitational field on the motion of a single probe, or even better a SWARM of probes.
Some of my more avid followers will remember that I addressed just such a problem in relation to a swarm of probes encountering the nearest neighbouring star to our own, namely Proxima Centauri (at 4.2 light years distant), in a previous blog post of mine, here.
Thus I already had on my computer JUST THE RIGHT SOFTWARE to simulate an encounter of N swarm members on a mystery object of unknown mass, and this very software should enable me to determine whether this will indeed be a feasible approach.
Well I have now performed preliminary investigations using precisely this software, and have found some interesting results.
In this initial study, I assume the probes are in a ring formation of 100 m diameter as they fly past the object 2024 YR4 at a relative speed of 13.5 km/s, and the asteroid is assumed to pass through the centre of this ring during the encounter.
So what would be the consequent deflections of the swarm members if the mass of the object is, say 9e7 kg? It turns out (see plot below), that these deflections and the lateral displacements generated by the body would be on the order of 1mm over a period of 1 day. The obvious question is will this be able to determine the mass of 2024 YR4 with any degree of accuracy?
The answer to this is that it depends on the uncertainty with which we know the lateral displacements of the probes, and in addition to this, the total number of probes, N. The reason for the latter is clearly because the more probes we have available, AND therefore the more data we have, then so the accuracy to which we can calculate the mass in question must go up.
I assumed a range of N from just 2 to 100 and two possible uncertainties in the positional measurements of these probes, first of 100 micrometres and then of 1 mm. Look at the two plots provided below. These were generated using Monte Carlo simulations, thus the uncertainties are estimates from around 50 runs of my software for each value of N.
What we see is that, with uncertainties in the position of the probes of 100 micrometres, so the uncertainty of the mass calculation becomes on the order of a few %, even with only 3 members in the swarm. However where this accuracy reduces to 1 mm, so the uncertainty in mass increases to on the order of a few tens of %, depending this time critically on the value of N.
Thus whether this approach can work depends fundamentally on the means by which the required positional displacements can be determined, and our team is now, at this very moment in time, assessing the requirements of such a mission and thinking over whether there could be any sensors on board which could deliver this level of accuracy.
