As a young teenager, I acquired an old brass astronomical telescope (a 3-in. refractor, see Fig. 1) to enable me to pursue my newfound passion for astronomy. Both the telescope and its owner are now somewhat the worse for wear …

Fig. 1.

The column editor’s telescope.

Fig. 1.

The column editor’s telescope.

Close modal

While still a teenager (and aspiring astronomer), I became interested in the subject of UFOs (more appropriately named UAPs—see Ref. 1). The region in which I lived (50 km west of London) was in the local news because of a UFO “flap”: several sightings of objects exhibiting strange and erratic behavior (e.g., sudden changes of direction in the sky) over a period of a month. One particular observation was of a tiny object, low on the horizon, moving back and forth, seemingly in a straight-line segment. Fortunately, one cloudy night, I was able to see this object in the distance, and I trained my telescope on it. What I saw were lights from a distant airplane, presumably flying in a circular holding pattern, but so low on the horizon for me that to the naked eye, its apparent path appeared to be a line segment (AB, say). It was a long time ago, but at the time I estimated the angular diameter of AB (θ) to be about 2° of arc (i.e., 4 full-moon widths). This was very subjective, however, because on that cloudy night, there was no obvious reference point. Upon later reflection, I realized that I could have compared it with the angular diameter of a nearby house or tree.

Question 1:

  • Suppose that the observed “period of oscillation” is 1 min, and the speed of the aircraft is 200 km/h. Estimate the diameter d of the aircraft path (assuming that it is circular).

  • Estimate the banking angle of the aircraft at this speed.

Question 2: Assuming θ ≈ 2° = π/90 rad, estimate the distance R to the aircraft. Assume that Rd.

1.
J. A.
Hynek
, “
Unusual aerial phenomena
,”
J. Opt. Soc. Am.
43
,
311
314
(
1953
).

Fermi Questions are brief questions with answers and back-of-the-envelope estimation techniques. To submit ideas, please email John Adam (jadam@odu.edu).