(Revised January 21st 1999; a shorter preliminary version was at this URL from 9 September 1998)

Researchers interested in studying the large number of photographs taken by witnesses to the assassination of President John F. Kennedy have often expressed the wish to take their own photographs in order to test various theories that depend on precise shadow measurements or observations. The best date and time to attempt to duplicate the shadows created by the Sun in Dealey Plaza is usually stated (correctly) to be 12:30 CST (Central Standard Time, the time zone appropriate to Dallas, Texas) on November 22nd each year. However, due to the inexact relationship between the length of the astronomical year and the calendar year, an equally good date is now as likely to be November 21st. Furthermore, there is an equally good alternative date and time which can be used (weather permitting) to avoid interfering with memorial ceremonies: January 20th at 12:55 CST. To avoid errors of more than half a degree in the Sun's position, dates of observation may be at most one day from these dates and the times must be within two minutes of those given. There are no other dates or times during the year when the angles of the Sun may be so closely duplicated. Precise calculations may be done for each year, reducing the errors to less than 0.15 degrees by choosing optimal dates, and times within a few seconds of the best value. Predictions for years 1999 through 2007 are given.

Tom Geletka asked me a question by e-mail: could I help photographers interested in comparing the assassination photographic record with photographs of Dealey Plaza taken more than a third of a century later? These photographers wished to duplicate the shadows and sun angle at the moment of the assassination of President John F. Kennedy.

To do this requires determining the precise altitude and azimuth of the Sun at 12.30 CST on November 22nd, 1963 in Dealey Plaza, Dallas, TX, and the dates and times each year when the Sun angle would be within some acceptable tolerance of the correct value.

I used the American Ephemeris and Nautical Almanac, 1963 (Nautical Almanac Office, U.S. Naval Observatory, Washington DC) to obtain the apparent right ascension and declination of the Sun at 18:30:35 Ephemeris Time (equal to precisely 18:30:00 Universal Time) on November 22nd, 1963:

RA 15h 50m 04s,

Dec -20 degrees 05 minutes 48 seconds.

I then used standard formulae based on spherical trigonometry and calculated Local Sidereal Time for the coordinates Tom supplied (Lat +32.77825 degrees, Long W 96.80923 degrees) to obtain the altitude and azimuth of the Sun. The accuracy was no better than a few arcseconds because I used linear interpolation. No allowance for refraction was made, which introduces an absolute error of about 1 or 2 arcminutes and a relative error of only a few arcseconds (small compared to the other errors involved--see below):

Altitude: 36.973 degrees

Azimuth: 184.896 degrees (i.e., just under 5 degrees West of the meridian).

The declination of the Sun changes rapidly at this time of year, so conditions for duplicating the Sun angle to within, say, 0.25 degrees will only last for a couple of days each November. The best date for duplicating the circumstances from year to year will vary by as much as ± half a day. By comparison, the apparent diameter of the solar disk is 0.5 degrees. Since the refraction would be virtually the same for all configurations approximating the time of the assassination, further calculations can be done neglecting refraction, by making a direct comparison to these figures with no loss of accuracy.

The Astronomical Almanac 1999 (Nautical Almanac Office, US Naval Observatory) was used to obtain data for the inverse calculation. I find that, on November 22nd, 1999, the closest time for duplicating the assassination Sun angle will be exactly 12:30:00 CST when the difference will be about 3 arcminutes in declination. This is one of two best times and dates every year. The Sun angle is generally as close or even closer on November 21st in about two out of three years, but the best date, when the declination shortly after mid-day is precisely the value at the moment of the assassination, will range over as much at one day. Some years will provide much more precise fits than others.

To match the shadows seen at the moment of the assassination, the only requirements are that the Sun's declination should be the same and that the Sun's hour angle should be the same. There is one other date when the Sun's declination is close to that on November 21st -22nd; this date is usually January 20th. But observations on that date at 12:30 CST would be very greatly in error!

There is a relationship in astronomy called the Equation of Time (tabulated in the Almanac) which gives the time difference between the True Sun and the Mean Sun (an imaginary Sun that moves along the celestial equator at a uniform rate). On November 21st, 1999, the True Sun is 14 minutes 7 seconds ahead of the Mean Sun; On January 20th it is 11 min 4 sec behind. Taking this into account, the correct time to make observations (weather permitting) on January 20th would be 12:55:11 CST.

(The Equation of Time arises from the combined effects of the tilt of the Earth's equator to the plane of the Ecliptic, or orbital plane, and the eccentricity of the Earth's orbit. More detailed explanations and formulae can be found in textbooks that cover positional astronomy in some detail.)

It is possible to calculate the best dates for observation for several years to come. In all cases, taking Dealey Plaza photographs of buildings and other features at the instant of CST specified for November 21st or 22nd (12:30pm) or January 20th (12:55:11pm) would be necessary for best accuracy. The table below gives predictions for the next few years, and it may be worth noting that in some years, better pictures could be taken on November 21st without causing disturbances to memorial ceremonies that take place on November 22nd. Researchers attending conferences in Dallas may find this knowledge particularly useful. Where two consecutive dates are given for an entry, they are equally good. Dates marked with an asterisk (*) provide very good matches to the precise solar altitude and azimuth corresponding to the Kennedy assassination.

Table 1. Dates when solar altitude and azimuth at the moment of President Kennedy's assassination are best reproduced in Dealey Plaza, Dallas, so that shadows of permanent features should be duplicated. An asterix (*) denotes a date when the solar position will be particularly close to the 1963 circumstances.

The errors in altitude for entries in Table 1 are no greater than about 8 minutes of arc. Errors in azimuth will be about 1 minute of arc for every 4 seconds error in timing of a photograph. If a looser but still acceptable tolerance of 0.5 degrees (30 minutes of arc) were chosen, using the specified CST on the days before and after the entries in the table would give accuracies within this tolerance. To achieve a similar azimuth error tolerance, the time would have to be within 4 minutes of the exact times given above.

21 January 1999

Mike Dworetsky, Department of Physics and Astronomy,

University College London, London WC1E 6BT

mmd@star.ucl.ac.uk