ASE logo The Astronomical Society of Edinburgh


No 53 - July 2007


After the last ASE lecture (on erroneous astronomical observations) I mentioned a real event when flying in featureless conditions at night involving the unexpected appearance of the rising Moon edge directly ahead. It took several seconds for this to manifest itself in its recognisable form, and had we entered full cloud at this time both my co-pilot and I would still believe we had seen an unidentified flying object.

This was a long time ago, and I have just done some calculations on it, as much to verify my memory of it, as to draw attention to the possibility of confusing this phenomenon with a dangerous situation.

figure 1
Figure 1.

Even seeing another plane in flight away from airfields is pretty rare. In controlled airspace Air Traffic Control is mandatory, and outside it an Advisory Service is available to all, and will normally keep aircraft miles apart, where they will usually subtend less than a degree or so. But this is all too little if they are on a collision course.

First consider the rising Moon, taking the simplest case at a time and latitude where it rises perpendicularly over the horizon to go overhead. The arc appears suddenly and expands rapidly as shown in Fig. 1 (ignoring the resolution jumps). At other latitudes the rise will involve a multiplying cosine component (due account being taken of the earth axis tilt, and if necessary the 5° or so that the plane of the Moon motion differs from the ecliptic. There will also be a sine component giving a translation along the horizon, but unless one aligns a telescope on it, (or there is a reference object in view), this will not be very obvious.

The expansion in Fig. 1 is very rapid (infinitely rapid on first appearance) but how does it compare with an aeroplane object? The visual acuity of normal eyes is about 1 minute of arc. This means that at least in principle, you should be able to see a 10 m span aeroplane against a contrasting background at a range of 3600 x 10, or 36 km. Unfortunately this only applies a) when focussed at infinity, and b) if you are looking in exactly the right direction. It is well known when there is a featureless scene before you, you may be focussed much closer that you think, especially if you have just looked up from the instrument panel. If you are not looking directly at the distant object, peripheral vision comes into play, which is nowhere near as discriminating. You just have to scan around to pick up such a distant object, and by the time you see it, it will probably be down to a quarter of this, so subtending 4 minutes of arc at 9 km.

figure 2
Figure 2.

If the closing speed is Mach 1 (entirely possible if you are seeing a military jet, or are one yourself) you have just under 30 seconds to collision, (half that if you are both doing it); the yellow curve in Fig. 2 shows that the subtended-angle expansion is almost at right angles to the Moon curve (in white) at the start, and at least half the Moon has appeared before the plane's expansion begins. As a pilot you have 24 seconds to spot it before it comes within 1 km, at which time there are only 3 more seconds to take avoiding action if required. This is why the appearance of the Moon arc in a similarly short time can be disturbing, unless or until you recognise it as just the beginning of its 2 min march to full.

There is nothing to stop you going out and looking for this effect at moonrise on the right night, without having to be in an aeroplane. After all, relative to the Moon you are still travelling at a good fraction of Mach 1, modified only slightly by the Moon's 29 times slower velocity, but with a star background and illuminated foreground it will hardly be the same. The Sun too of course, being almost same size, produces the same effect every day, but with an illuminating sky and landscape, not to speak of the visual dangers, it is by no means recommended.

Graham Clarke


Cover page

Solar observing

More on cooling the Earth

Minor planet (7170) Livesey

Recent observations


Two BAA meetings in Scotland

Glen Lyon weekend 16-18 March 2007

Forthcoming events

About the ASE Journal

This journal as a single web page

This journal as PDF file (690 kByte)

Valid XHTML 1.0 Strict Valid CSS!