Dear Masatsugu:
As Professor Gaskell has pointed out in a recent communication:"Assuming that reflecting ice crystals are suspended horizontally, thecondition for specular reflection around local noon when Mars is inopposition is that the latitude of the reflecting region equals the meanof the declination of the sun (D(S)) and the declination of the earth(D(e)). Although this is stated correctly on p. 122 of T. Dobbins & W. Sheehan (2001, Sky & Telescope, 101, 115), their table on p. 123 is instead for the condition D(S) = D(e) around opposition. The mean of the declinations of the earth and sun in this table are +2 degrees while the crater Schiaparelli in Edom Promontorium lies at a latitude of -2 degrees. The specular reflection conditions will actually be met most closely at end of July, one half of the phase angle after each central meridian transit."
Here is my best effort at generating ephemerides, based on the following presumptions: Edom Promintorium stretches from -7 to 4 degrees in latitude and 345 to353 degrees in longitude. These values are based on Gerard de Vaucouleurs' analysis of Shiro Ebisawa's map (see Gerard de Vaucouleurs "Charting the Martian Surface" S&T, October 1965, pp. 196-201.) According to the Batson, Bridges, Inge "Atlas of Mars" (NASA, 1979), the Schiaparelli crater is centered at 343 degrees longitude, -3 degrees latitude. I have used a value of 345 degrees for Edom Promintorium for calculating the times of possible future events.
It would appear that Japanese observers may yet have an opprtunity to witness these events without leaving their native soil!
Tom Dobbins
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I.) LATITUDES
De = Declination of Earth from Mars
Ds = Declination of Sun from Mars
(De + Ds)/2 = Martian latitude of possible specular reflection
July 11 De = 7.0 Ds = -5.7 (De+Ds)/2 = 0.65 July 12 De = 7.0 Ds = -5.9 (De+Ds)/2 = 0.55 July 13 De = 7.1 Ds = -6.2 (De+Ds)/2 = 0.45 July 14 De = 7.1 Ds = -6.4 (De+Ds)/2 = 0.30 July 15 De = 7.2 Ds = -6.7 (De+Ds)/2 = 0.25 July 16 De = 7.2 Ds = -6.9 (De+Ds)/2 = 0.15 July 17 De = 7.2 Ds = -7.1 (De+Ds)/2 = 0.05 July 18 De = 7.2 Ds = -7.4 (De+Ds)/2 = -0.10 July 19 De = 7.2 Ds = -7.6 (De+Ds)/2 = -0.20 July 20 De = 7.2 Ds = -7.8 (De+Ds)/2 = -0.30 July 21 De = 7.2 Ds = -8.1 (De+Ds)/2 = -0.45 July 22 De = 7.2 Ds = -8.3 (De+Ds)/2 = -0.55 July 23 De = 7.2 Ds = -8.5 (De+Ds)/2 = -0.65 July 24 De = 7.2 Ds = -8.8 (De+Ds)/2 = -0.80 July 25 De = 7.1 Ds = -9.0 (De+Ds)/2 = -1.05 July 26 De = 7.1 Ds = -9.3 (De+Ds)/2 = -1.10 July 27 De = 7.0 Ds = -9.5 (De+Ds)/2 = -1.25 July 28 De = 7.0 Ds = -9.7 (De+Ds)/2 = -1.35 July 29 De = 6.9 Ds = -10.0 (De+Ds)/2 = -1.55 July 30 De = 6.8 Ds = -10.2 (De+Ds)/2 = -1.70 July 31 De = 6.7 Ds = -10.5 (De+Ds)/2 = -1.90 Aug 01 De = 6.7 Ds = -10.7 (De+Ds)/2 = -2.00 Aug 02 De = 6.6 Ds = -10.9 (De+Ds)/2 = -2.15 Aug 03 De = 6.5 Ds = -11.0 (De+Ds)/2 = -2.25 Aug 04 De = 6.4 Ds = -11.2 (De+Ds)/2 = -2.40 Aug 05 De = 6.3 Ds = -11.5 (De+Ds)/2 = -2.60 Aug 06 De = 6.2 Ds = -11.7 (De+Ds)/2 = -2.75 Aug 07 De = 6.1 Ds = -11.9 (De+Ds)/2 = -2.90 Aug 08 De = 6.0 Ds = -12.1 (De+Ds)/2 = -3.05 Aug 09 De = 5.9 Ds = -12.4 (De+Ds)/2 = -3.25 Aug 10 De = 5.7 Ds = -12.6 (De+Ds)/2 = -3.45
July 11 Phase i = 22.9 degrees (Phase i)/2 = 11.4 Longitude Offset =356.4 Time = 04:28 July 12 Phase i = 23.6 degrees (Phase i)/2 = 11.8 Longitude Offset =356.8 Time = 05:05 July 13 Phase i = 24.3 degrees (Phase i)/2 = 12.2 Longitude Offset =357.2 Time = 05:46 July 14 Phase i = 24.9 degrees (Phase i)/2 = 12.4 Longitude Offset =357.4 Time = 06:23 July 15 Phase i = 25.6 degrees (Phase i)/2 = 12.8 Longitude Offset =357.8 Time = 07:01 July 16 Phase i = 26.2 degrees (Phase i)/2 = 13.1 Longitude Offset =358.1 Time = 07:42 July 17 Phase i = 26.9 degrees (Phase i)/2 = 13.5 Longitude Offset =358.5 Time = 08:19 July 18 Phase i = 27.5 degrees (Phase i)/2 = 13.8 Longitude Offset =358.8 Time = 08:56 July 19 Phase i = 28.1 degrees (Phase i)/2 = 14.0 Longitude Offset =359.0 Time = 09:38 July 20 Phase i = 28.7 degrees (Phase i)/2 = 14.4 Longitude Offset =359.4 Time = 10:15 July 21 Phase i = 29.3 degrees (Phase i)/2 = 14.6 Longitude Offset =359.6 Time = 10:53 July 22 Phase i = 29.8 degrees (Phase i)/2 = 14.9 Longitude Offset =359.9 Time = 11:30 July 23 Phase i = 30.4 degrees (Phase i)/2 = 15.2 Longitude Offset =000.2 Time = 12:12 July 24 Phase i = 30.9 degrees (Phase i)/2 = 15.5 Longitude Offset =000.5 Time = 12:49 July 25 Phase i = 31.5 degrees (Phase i)/2 = 15.8 Longitude Offset =000.8 Time = 13:27 July 26 Phase i = 32.0 degrees (Phase i)/2 = 16.0 Longitude Offset =001.0 Time = 14:08 July 27 Phase i = 32.5 degrees (Phase i)/2 = 16.3 Longitude Offset =001.3 Time = 14:47 July 28 Phase i = 33.0 degrees (Phase i)/2 = 16.5 Longitude Offset =001.5 Time = 15:25 July 29 Phase i = 33.4 degrees (Phase i)/2 = 16.7 Longitude Offset =001.7 Time = 16:02 July 30 Phase i = 33.9 degrees (Phase i)/2 = 17.0 Longitude Offset =002.0 Time = 16:44 July 31 Phase i = 34.4 degrees (Phase i)/2 = 17.2 Longitude Offset =002.2 Time = 17:23 Aug 01 Phase i = 34.8 degrees (Phase i)/2 = 17.4 Longitude Offset =002.4 Time = 18:01 Aug 02 Phase i = 35.2 degrees (Phase i)/2 = 17.6 Longitude Offset =002.6 Time = 18:42 Aug 03 Phase i = 35.7 degrees (Phase i)/2 = 17.8 Longitude Offset =002.8 Time = 19:21 Aug 04 Phase i = 36.1 degrees (Phase i)/2 = 18.0 Longitude Offset =003.0 Time = 19:59 Aug 05 Phase i = 36.5 degrees (Phase i)/2 = 18.3 Longitude Offset =003.3 Time = 20:37 Aug 06 Phase i = 36.8 degrees (Phase i)/2 = 18.4 Longitude Offset =003.4 Time = 21:16 Aug 07 Phase i = 37.2 degrees (Phase i)/2 = 18.6 Longitude Offset =003.6 Time = 21:57 Aug 08 Phase i = 37.6 degrees (Phase i)/2 = 18.8 Longitude Offset =003.8 Time = 22:33 Aug 09 Phase i = 37.9 degrees (Phase i)/2 = 19.0 Longitude Offset =004.0 Time = 23:14 Aug 10 Phase i = 38.3 degrees (Phase i)/2 = 19.2 Longitude Offset =004.2 Time = 23.53
The anomalous brightenings at Edom Promintorium witnessed from the Florida Keys occured at under the conditions described below...
1.) June 7, 2001 6:40 to 7:20 U.T.
Phase i (planetocentric elongation of Mars with respect to Earth and Sun) = 5.9 degrees
(Phase i)/2 = distance in degrees of longitude from CM (in the direction of the morning limb prior to the date of opposition) of the source of specular reflection = ~3 degrees
CM at 6:40 UT was 330 degrees; CM at 7:20 was 342 degrees. This corresponds to sources at longitudes of 333 to 345 degrees, assuming a horizontal, planar reflecting surface.
De = 1.7 degrees Ds = 2.5 degrees Assuming a horizontal reflecting surface, the nominal position of the source of the reflection should be at (1.7 + 2.5)/2 = 2.1 degrees.
2.) June 8, 2001 7:00 to 7:20 UT and 7:53 to 8:24 UT
Phase i (planetocentric elongation of Mars with respect to Earth and Sun) = 5.1 degrees
(Phase i)/2 = distance in degrees of longitude from CM (in the direction of the morning limb prior to the date of opposition) of the source of specular reflection = ~2.5 degrees
CM at 7:00 UT was 326 degrees; CM at 7:20 was 331 degrees. This corresponds to sources at longitudes of 328.5 to 333.5 degrees.
CM at 7:53 UT was 339 degrees; CM at 8:24 was 347 degrees. This corresponds to sources at longitudes of approximately 342 to 349 degrees, assuming a horizontal, planar reflecting surface.
De = 1.9 degrees Ds = 2.2 degrees Assuming a horizontal reflecting surface, the nominal position of the source of the reflection should be at (1.9 + 2.2)/2 = 2.05 degrees.
It is noteworthy that despite a source latitude of 2.1 to 2.5 degrees suggested by the values of De and Ds, the apparent location of the center of the activity appeared to be several degrees to the south.