For early planning purposes we assume a flight altityude of 37,000 feet above mean sea level (AMSL) - though an alternate (higher) altitude may later be implemented.  If so, the detailed "local" circumstances of the eclipse geometry and key flight milestones spoken to here would change by very small, but then a priori  very well known amounts.

To THE MAX

Point of max eclipse on the ground: 64d 25' 56.6"N, 06d 38' 45.2" W.
UTC = 09h 45m 38.6s
Altitude of Sun: 18.5 deg
Azimuth of Sun: 135.0 deg

Assume FL 370 = 11,278 meters
At FL370 the point of maximum eclipse will shift 33.706 km toward the solar azimuth
Point of max eclipse at 37.000 ft: 64d 13.0664' N, 06d 09.2988'W (64d 13' 04.0"N, 06d 09' 18.0"W)
UTC = 09h 45m 38.6s
Altitude of Sun: 18.8 deg
Azimuth of Sun: 135.4 deg
Duration of Totality (Limb Corrected): 2m 46.8s

Assume aircraft ground 470 nm/hr
Aircraft Heading = 135.4 deg – 90 deg == 45.4 deg

C2: Back off 15 nm in direction toward 225.4  are we in totality?
Test coordinate:  64:2.5342 6:33.5899 (64 02  32.05 N, 06 33 35.39 W)
Aircraft will be there –1.9149 minutes earlier than max eclipse @ UTC == 09h 43m 43.7s
C2 is at 09h 43m 41.7s
NB: c2 occured 2 seconds earlier, so backoff distance should be appx 15.26 nm  TRY AGAIN

C2: Back off 15.26 nm in direction toward 225.4  are we in totality?
Test coordinate:  64:2.3511  6:34.0082 (64 02 21.07 N, 06 34 0.49 W)
Aircraft will be there –1.948085 minutes earlier than max eclipse @ UTC == 09h 43m 41.7s
C2 is at 09h 43h 41.2s
WITHIN 1/2 SECOND OF C2 (need SLIGHTLY longer backoff)

C2 backoff to 15.33 nm in direction toward 225.4  are we in totality?
Test coordinate:  64:2.3017  6:34.1209  (64 02 18.10 N, 06 34 07.25 W)
Aircraft will be there –1.957021277 minutes earlier than max eclipse @ UTC == 09h 43m 41.2s
C2 is at 09h 43m 41.1s
CLOSE ENOUGH!!!


C3  go forward 15.33 nm in direction toward 45.4  are we in totality?
Test coordinate:  64:23.7596  5:44.1543 (64 23 45.58 N, 05 44 09.26W)
Aircraft will be there +1.957021277 minutes later than max eclipse @ UTC == 09h 47m 36.0s
C3 is at 09h 47m 31.8s
c3 occurred 4.2 s before aircraft got there (difference due to limb profile) -- need shorter distance

C3  go forward 15.00 nm in direction toward 45.4  are we in totality?
Test coordinate:  64:23.5302 5:44.6990 (64 23 31.81 N, 05 44 41.94 W)
Aircraft will be there +1.914893617 minutes later than max eclipse @ UTC == 09h 47m 33.50s
C3 is at 09h 47m 31.2s
c3 occurred 2.3 s aircraft got there (difference due to limb profile) -- need shorter distance

C3  go forward 14.82 nm in direction toward 45.4  are we in totality?
Test coordinate: 64:23.4050 5:44.9961 (64 23 24.30 N, 05 44 59.77 W)
Aircraft will be there +1.891914894 minutes later than max eclipse @ UTC == 09h 47m 32.1s
C3 is at 09h 47m 30.8s
c3 occurred 1.3 s aircraft got there (difference due to limb profile) -- need shorter distance

C3  go forward 14.59 nm in direction toward 45.4  are we in totality?
Test coordinate: 64:23.2451 5:45.3755 (64 23 14.71 N, 05 45 22.53 W)
Aircraft will be there +1.862553191 minutes later than max eclipse @ UTC == 09h 47m 30.35s
C3 is at 09h 47m 30.3s
AOK!!!

Duration of totality = 3m 51.8s


AND NOW... THE NORTH POLE!!!!

NP: 90d N,  any W.
UTC = 10h 17m 15.8s
Altitude of Sun: 0.0 deg
Azimuth of Sun: undefined
Duration of Totality (Limb Corrected): 1m 51s

The concept of "azimuth" is degenerate at the North Pole.  The direction to the Sun, must be referenced  to a different fiducial.  This is most intuitively expressed using the longitude of the sub-solar poinrt on the Earth.  In the case of TSE 2015 at UTC = 10h 17m 15.8s the sub-solar point is at a longude of 27.39 deg E.  Thus, to have the Sun at the North Pole "straight out" the aircraft main cabin windowa, the aircraft must approach the pole from a longitude of  62.61° W and, once crossing the pole, fly toward a longitude of 117.39° E.

When is C2?
Estimate C2 will occur when aircraft id 10.13 nm before pole crossing.
Back off  aircraft to 10.13nm  = 77.59s of flying time.
At 470 nm/hr  the aircraft will be at this position at UTC_mid - 77.59 s = 10h 15m 58.21s
The AC location at that time is 62.61 W, 89 49.87N  (62 36 36 W, 89 49 52.2N)
C2 for that location is:  10h 16m 06.8s
So... C2 occurs 8.6s AFTER the aircraft is at that position

Back off aircraft to 9.00 nm before pole crossing. = 69.94s of flying time.
At 470 nm/hr  the aircraft will be at this position at UTC_mid - 69.94s = 10h 16m 06.9s
The AC location at that time is 62.61 W, 89 51.0 N  (62 36 36 W, 89 51 00N)
C2 for that location is: 10:16:08.3
So, C2 occurs 1.4s AFTER the AC is at that position.     If aster shorten length

Backoff AC to  8.8 nm before pole crossing. = 67.40s of flying time.
At 470 nm/hr  the aircraft will be at this position at UTC_mid - 67.40s = 10h 16m 08.4s
The AC location at that time is 62.61 W, 89 51.2 N  (62 36 36 W, 89 51 12N)
C2 for that location is: 10h 16m 08.6s
WITHIN 0.2s CLOSE ENOUGH!


NOW for C3...  Assume the SAME distance to start.
Forward AC to  8.8 nm after pole crossing. = 67.40s of flying time.
At 470 nm/hr  the aircraft will be at this position at UTC_mid + 69.94s = 10h 18m 23.2s
The AC location at that time is 117.39 W, 89 51.2 N  (117 23 24 E, 89 51 12N)
C3 for that location is: 10:18:00.5
So, C3 occurs ~ 23s BEFORE the A/C is at that position.  

Try 10nm
Forward AC to  10 nm after pole crossing. = 76.60s of flying time.
At 470 nm/hr  the aircraft will be at this position at UTC_mid + 76.60s = 10h 18m 32.4s
The AC location at that time is 117.39 W, 89 50.0 N  (117 23 24 E, 89 50 00 N)
C3 for that location is:  10:17:58.9
So, C3 occurs ~ 34s BEFORE the A/C is at that position.    WRONG WAY!!!!

 (Increased diff by 11 seec wanted to shorted ny 23.  Factor 2.09.  Diff was +1.2 nm so try 8.8-1.2 * 2.09 = 6.29 nm 
Forward AC to   6.29 nm after pole crossing. = 48.18s of flying time.
At 470 nm/hr  the aircraft will be at this position at UTC_mid + 48.18s = 10h 18m 04.0s
The AC location at that time is 117.39 W, 89 53.17 N  (117 23 24 E, 89 53 42.6 N)
C3 for that location is:   10:18:03.6s
WITHIN 0.4s CLOSE ENOUGH!


NORTH POLE EFLIGHT 2015
MAX ECLIPSE INTERCEPT @ 90N
FLIGHT LEVEL 11278m (37,000 ft)
Ground Speed (no wind) 470 nm/hr

Contact 2: 10h 16m 08.6s  62 36 36 W, 89 51 12N
Max Eclipse: 10h 17m 15.8s
Mid Eclipse: 10h 17m 05.8
Contact 3: 10:18:03.6s  117 23 24 E, 89 53 42.6 N

TOTALITY DURATION = 1m 55.5s