Number 22: 30/10/2003 A scientific publication by SGF and NEODyS

Eclipses, Transits and Impacts
by Duncan Steel - Vice-President of the Spaceguard Foundation

One of the major ongoing problems faced by those of us who take the chance of an NEO impact upon the Earth seriously, and want to persuade others likewise so that governments will be prompted to take appropriate action, is the communication of such things as terrestrial collision frequencies in understandable terms. One point I often make to people is that saying that a particular energy level impact has a one in 100,000 probability of occurring per annum sounds quite different to describing that such events occur once every 100,000 years on average.
Moving beyond such considerations, a matter that needs to be made clear to all and sundry - the media, politicians and the public - is that what we need to do, ultimately, is to leave probabilities aside. That is, we (humankind) must put ourselves in the position of not leaving things to chance, and instead assure our future. Mathematically, we must change a probabilistic assessment into a deterministic one.

What I mean here is that, if we assume that our current assessment of the population, sizes and orbits of near-Earth asteroids results in an expectation that a 200-metre asteroid strikes our planet once every 4,000 years on average, then there is a one-in-40 chance that such a collision will occur within the next century. That is a probabilistic value based on the assumption that we know the orbits of only a minor fraction of such objects. Once we have found 50 percent of them, and shown that all that number have zero chance of striking Earth within the next hundred years, then we will have reduced the hazard assessment to a half (one-in-80) of what it was previously. At such time as all those asteroids (larger than 200 metres) are found and their orbits mapped, we will have a deterministic assessment: either we will have shown that all will miss the planet during the period of interest (we will have reduced the probability, and hence hazard, to zero for such sizes) or else we will have found one (or more!) that is due to hit home.

The above is a fairly straightforward matter, and yet it is still misunderstood, even by scientists working within the field. An analogous way to describe things, also astronomical, is to think of eclipses and transits.
The ancients knew that eclipses occurred, and had some ideas about what caused them. Knowing various things about the periodicities of the solar year and the lunar month, it was possible for them to make predictions about when eclipses might occur, for example using the Metonic cycle.
An accurate prediction of not only the occurrence of a solar eclipse but also the path of the track of totality across the face of the Earth was not possible until far greater knowledge of the orbits of the Sun and the Moon was available, and necessary mathematical techniques were developed. The name of the person who made this first precise eclipse prediction is well-known in the NEO field: it was Edmond Halley, in the early 18th century. (Two decades before then he had suggested that the comet that bears his name, and others like it, could strike the Earth with calamitous consequences.)

In fact it is quite simple to make an evaluation of about how often eclipses occur. For example, a random location on the surface of the globe may be expected to be traversed by the lunar shadow in a total solar eclipse about once every 400 years. That is not of much use to an eclipse-chaser, though, who wants to position herself in the totality track for a specific eclipse. The point here is that we do have the capability to make the relevant calculations, with great precision.
In terms of estimating the frequency of events, transits of Venus (or Mercury) across the face of the Sun are somewhat simpler than lunar or solar eclipses. A rough evaluation can be derived by using the known inclination of Venus's orbit (3.39 degrees), and the angular speeds around the Sun for Venus and the Earth, in order to calculate the apparent angle that Venus makes as it crosses the ecliptic. Knowing the solar diameter, and requiring that Venus's path must at least shave the edge of the Sun as it passes, one can find a range of longitudes along the ecliptic within which Venus must have its node if it is to perform a transit as seen from Earth. Finally, factoring in the Venusian synodic period (584 days) tells us how often we might be in the right place at the right time.

The result of such back-of-the-envelope calculations shows that a transit of Venus might be expected between once every 50 and once every 100 years, on average. In fact, at present Venus exhibits transits with spacings of 105.5, 8, 121.5 and 8 years, so that there are four transits every 243 years, or one every 60 years on average. This pattern does not persist for more than a few millennia, though, and the longer-term average is near once every 75 years.
Of course, no-one is going to spend a whole lifetime watching the Sun in the hope of seeing a Venusian transit (and in any case there would be a 50:50 chance of occurrence at night), but my point is that the simple probabilistic assessment above can be changed into a deterministic one. We know - indeed Edmond Halley knew - that there will be a transit of Venus in June next year. We can now calculate precisely what you will be able to see, second by second, depending on where you are on 8th June 2004. If you miss that one for some reason, then we can say where to be for the next on 6th June 2012.

Now, we are dead sure about this: eclipses and transits are predictable with phenomenal accuracy because we have been observing the relevant celestial objects for so long, and we have the necessary mathematical and physical knowledge.
It is also feasible for us to do much the same thing for asteroids: provided that we observe each of them for long enough and accurately enough we can predict their future paths, and whether they will intercept our planetary home. And for those we certainly need to be dead sure, or else we might be dead.