Early Morning School Work.

I was standing by my bathroom window in the early hours of this morning regarding the third quarter moon hanging bright in the clear eastern sky. I saw the winking wing lights of a commercial aircraft encroaching into my view from the right, evidently outbound from East Midlands Airport and flying north-west, probably to Belfast. The plane approached the moon, crossed it, and then continued its flight to Northern Ireland.

My first thought was that the passengers would have watched the moon coming towards them until it was alongside, and then slipping away behind as the plane continued its journey. I quickly realised that I was wrong; the moon would have appeared more or less perpendicular to their view through the window all the way from the airport to their destination. So then I set about working out why, and realised that it’s a simple matter of the function of arc.

The distance between East Midlands Airport and Belfast is a tiny fraction of the distance between the moon and the plane, which means that the arc described on the line of travel would be extremely slim. The angle between the two, therefore, would hardly change in such a short distance, and so the moon would appear to the passengers to be in more or less the same place. It’s simply a matter of geometrical relativity.

And so having demonstrated to myself that my mind still functions moderately well after two double scotches and in a state of fatigue, I continued to bed with an almost satisfied air.