Spreadsheet: 9c15c365-5028-4462-b518-c933b31cbadd
Sheet: RoT V3.0 Beta

[NAME] of Thumb Model for estimating the required aperture for splitting unequal and faint doubles for small telescopes V3.0 Beta 2013-02-18 rA = required Aperture in mm = rA1+rA2+rA3+rA4+rA5 with a split probability of 50% and standard deviation of 14% rA1 = modified Dawes criterion = 116/1,2213*(0,0950502775050452+(1,12627632206642)/((1+(CO/0,302756091410027)^2,26536793426585)^0,152776210790626))/Sep with Sep = separation in arcseconds and CO = Central Obstruction between zero and 0.99 rA2 = f(dM) = function of delta magnitudes including CO = 5,91232283796472*dM'*(M2-M1)/Sep^0,600317738509086*(1+CO)^0,808139120750434 with dM' = switch for delta-M < 1, M1 = magnitude primary and M2 = magnitude secondary rA3 = f(M1) = function of M1 = 1,04237828050238*M1'*(M1+2,34973310685883)/(M1''*Sep^-0,304107132838227+(1-M1'')*(14-M1)^-0,304107132838227) with M1' = switch for M1 <= 6 and M1'' = switch for sep <= 14-M1 rA4 = f(M2) = function of M2 = 13,[PHONE]*M2'*(M2-9) with [NAME]' = switch for M2 <= 9 rA5 = f(NEML) = function of Naked Eye Magnitude Limit for a given location = 2,[PHONE]*m2'*(6.5-NEML). rA' = required aperture after check against the for light pollution adapted telescope magnitude limit. This is done for all doubles in several steps in an approximation process but is usually only relevant  for doubles with companions fainter than +10mag. First is calculated dNEML as base value for the TML change as LN((6,5/NEML)^2,512). Next step is the calculation of TML_M2 depending on [NAME], dNEML and NEML as 0,952988428558035*M2+(M2/13)^1,21758761926721*dNEML*3,49701599950785-6,17437592197594+NEML*1,04875246413893. As the resulting value is a numerical approximation a further check is needed by calculating the accordingly dTML as (TML_M2/13)^2,512*dNEML and then checking if TML_M2 minus dTML gives a value larger or at least equal to [NAME] as this is obviously necessary to be able to resolve M2. Any negative value in the field Check is used to calculate a new larger TML_M2' value and this value is then recalculated with 10^((TML_M2'-2,7)/5) into a corresponding aperture TML_M2' Ap and then the greater vaulue of rA or [NAME]' Ap is choosen for the final rA' value. Required input: Global input central obstruction for specific scope and naked eye magnitude limit for specific location. Per double star sep, m1, m2 and WDS ID. Name, RA, Dec for convinience only (yellow marked columns below) Error conditions (not checked): separation > 0, magnitude of primary > magnitude of secondary, 1>CO<0, 6.5<NEML<1 Planned enhancements: Enlarge the data set of limit observations for better statistical significance, smoother transition of the different components of the model when crossing the defined thesholds
CO 0.00-0.99 | 0
NEML 1-6.5 | 3.5
WDS ID | Name | RA | Dec | Sep | M1 | M2 | rA' | rA | Dawes rA1 | f(dM) rA2 | f(m1) rA3 | f(m2) rA4 | f(NELM) rA5 | dM' | M1' | M2' | M1'' | dNEML | TML_M2 | dTML | Check | TML M2' | TML_M2' Ap
WDS03543-0257 | STF470, IDS03493-0315, BDS1939, ADS2850, BD-03 00631 | 03h 54m 17s | -02°57,2' | 6.6 | 4.8 | 5.89
WDS04352-0944 | STF570, IDS04305-0957, [NAME], BD-10 00959 | 04h 35m 14s | -09°44,1' | 12.7 | 6.71 | 7.64
WDS04380-1302 | [NAME], IDS04334-1314, BDS2294, ADS3355, [NAME] | 04h 38m [NAME] | -13°01,7' | 12.4 | 7.33 | 7.85
WDS04436-0848 | STF590, IDS04388-0859, BDS2330, ADS3409, BD-09 00970 | 04h 43m 35s | -08°47,7' | 8.8 | 6.74 | 6.78
WDS04144-1015 | STF516, IDS04096-1030, BDS2102, ADS3079, BD-10 00867 | 04h 14m 24s | -10°15,3' | 6.7 | 5.03 | 8.53
WDS03323-0705 | STF411, IDS03274-0726, [NAME], ADS2596, BD-07 00618 | 03h 32m 15s | -07°05,4' | 18.8 | 7.36 | 9.19
WDS05007-1330 | STF631, IDS04561-1339, BDS2475, ADS3606, BD-13 01047 | 05h 00m 41s | -13°30,2' | 5.9 | 7.49 | 8.77
WDS04233-0500 | [NAME], IDS04183-0514, [NAME], ADS3176, BD-05 00895 | 04h 23m 15s | -05°00,3' | 17.2 | 7.76 | 9.58
WDS04380-1302 | ENO10, ADS3355 | 04h 38m [NAME] | -13°01,7' | 9.9 | 7.33 | 9.36
WDS05030-0840 | STF636, IDS04582-0848, BDS2494, ADS3640, BD-08 01013 | 05h 03m 02s | -08°39,7' | 3.6 | 7.11 | 8.52
WDS04009-1027 | STF487, IDS03562-1044, BDS1997, ADS2933, BD-10 00813 | 04h 00m 55s | -10°27,0' | 12 | 9.47 | 9.98
WDS04459-1157 | STF596, ADS3428 | 04h 45m 51s | -11°57,0' | 10 | 8.31 | 10.02
WDS04207-1413 | STF532, IDS04161-1428, [NAME], BD-14 00875 | 04h 20m 44s | -14°13,3' | 19.1 | 9.05 | 10.4
WDS03030-0205 | STF341, IDS02580-0229, BDS1550, ADS2316, BD-02 00538 | 03h 03m 02s | -02°05,1' | 8.9 | 7.57 | 9.97
WDS04009-1027 | STF487, IDS03562-1044, BDS1997, ADS2933 | 04h 00m 55s | -10°27,0' | 19.9 | 9.47 | 10.51
WDS03464-0810 | HDS478, ADS2752, BD-08 00723 | 03h 46m 23s | -08°10,1' | 7.2 | 8.57 | 10.03
WDS03532-0200 | STF466, IDS03482-0218, BDS1930, ADS2838, BD-02 00747 | 03h 53m 12s | -01°59,8' | 8.4 | 8.41 | 10.3
WDS04247-0845 | STF544, IDS04199-0859, BDS2188, ADS3197, BD-09 00892 | 04h 24m 42s | -08°45,1' | 3.3 | 8.59 | 9.51
WDS04221-0957 | STF537, IDS04173-1011, BDS2158, ADS3164, BD-10 00902 | 04h 22m 04s | -09°57,1' | 18.8 | 8.36 | 10.79
WDS04331-1208 | STF564, IDS04284-1221, [NAME], ADS3299, BD-12 00922 | 04h 33m 06s | -12°08,2' | 3.4 | 9.39 | 9.53
WDS02471-0142 | BAL18, IDS02421-0207, BD-02 00486 | 02h 47m 08s | -01°41,7' | 9.2 | 9.5 | 10.5
WDS04322-0936 | GAL141, IDS04275-0949, ADS3292, BD-09 00921 | 04h 32m 14s | -09°36,3' | 6.9 | 9.9 | 10.44
WDS04360-0337 | STF571, IDS04310-0349, BDS2277, ADS3328, BD-03 00830 | 04h 36m 02s | -03°36,6' | 17.7 | 6.33 | 10.72
WDS03545-1243 | HLD67, IDS03498-1301, [NAME], ADS2860, BD-13 00770 | 03h 54m 32s | -12°43,3' | 2.8 | 8.4 | 9.5
WDS04190-0725 | STF527, IDS04142-0740, BDS2135, ADS3127, BD-07 00792 | 04h 19m 03s | -07°25,3' | 6.6 | 8.16 | 10.38
WDS03527-0522 | HJ338, IDS03478-0540, BDS1924, ADS2832, BD-05 00769 | 03h 52m 42s | -05°21,6' | 8.3 | 5.5 | 10.35
WDS04387-0024 | STF575, IDS04336-0036, BDS2296, ADS3362, BD-00 00739 | 04h 38m 39s | -00°23,7' | 4.4 | 9.42 | 10.12
WDS04024-0700 | STF489, IDS03575-0717, BDS2010, ADS2949, BD-07 00724 | 04h 02m 23s | -07°00,3' | 3 | 9.61 | 9.68
WDS04127-0650 | STF514, IDS04078-0705, [NAME], ADS3059, BD-07 00768 | 04h 12m 40s | -06°50,0' | 8.1 | 8.94 | 10.7
WDS05099-0906 | A483, IDS05052-0914, BDS2559, ADS3741, BD-09 01086 | 05h 09m 55s | -09°06,3' | 4 | 9.74 | 10.08
WDS03581-0454 | HLD70, IDS03532-0511, BDS1970, ADS2903, BD-05 00787 | 03h 58m 09s | -04°53,9' | 3.5 | 9.2 | 10.1
WDS04510-1214 | HJ3693, IDS04463-1225, BDS2387, BD-12 01007 | 04h 51m [NAME] | -12°14,3' | 8 | 9.84 | 11.08
WDS04369-1456 | BU185, IDS04323-1508, BDS2286, ADS3340, BD-15 00819 | 04h 36m 54s | -14°55,5' | 2.7 | 8.12 | 9.86
WDS04478-1043 | HU214, IDS04431-1053, BDS2360, ADS3455, BD-10 01013 | 04h 47m 47s | -10°42,5' | 4.3 | 8.91 | 10.6
WDS04222-0441 | STF536, IDS04172-0455, [NAME], ADS3163, BD-05 00889 | 04h 22m 10s | -04°40,6' | 1.5 | 7.94 | 8.73
WDS05051-0631 | A482, IDS05002-0640, [NAME], ADS3674, BD-06 01081 | 05h 05m 06s | -06°31,4' | 4.6 | 8.7 | 10.7
WDS04246-0452 | STF543, IDS04192-0506, BDS2185, ADS3193, BD-05 00903 | 04h 24m 36s | -04°52,3' | 5 | 8.78 | 10.8
WDS03579-0708 | STF475, IDS03530-0725, [NAME], ADS2900, BD-07 00712 | 03h 57m 56s | -07°07,5' | 7.6 | 8.87 | 11.3
WDS04231-0117 | [NAME], IDS04181-0130, BDS2167, ADS3175, BD-01 00629 | 04h 23m 09s | -01°16,7' | 9.5 | 9.34 | 11.3
WDS04343-0045 | A836, IDS04292-0058, BDS13000, ADS3312, BD-01 00669 | 04h 34m 21s | -00°45,0' | 2.6 | 9.7 | 10.7
WDS03307-0416 | STF408, IDS03257-0437, BDS1743, [NAME], BD-04 00609 | 03h 30m 39s | -04°16,3' | 1.2 | 8.23 | 8.41
WDS04236-0534 | HJ2229, IDS04186-0548, [NAME], ADS3183, BD-05 00897 | 04h 23m 34s | -05°34,0' | 5.5 | 9.8 | 11.4
WDS04574-0625 | A479, IDS04526-0634, BDS2440, ADS3564, BD-06 01034 | 04h 57m 26s | -06°25,1' | 2.6 | 8.74 | 10.66
WDS03503-0131 | [NAME], IDS03452-0150, BDS1907, ADS2803, [NAME] | 03h 50m 16s | -01°31,3' | 4.2 | 6.54 | 10.51
WDS05036-0509 | HJ31, IDS04587-0517, BDS2498, BD-05 01138 | 05h 03m 38s | -05°08,7' | 13.9 | 9 | 11.43
WDS03575-0110 | BU543, IDS03524-0127, [NAME], [NAME], BD-01 00565 | 03h 57m 29s | -01°09,5' | 11 | 8.21 | 11.45
WDS02597-0232 | A209, IDS02546-0256, BDS1524, [NAME], BD-03 00476 | 02h 59m 41s | -02°32,2' | 1.8 | 9.86 | 10.31
WDS03532-0150 | BU1276, ADS2837 | 03h 53m 10s | -01°50,2' | 1.6 | 9.7 | 10
WDS03379-0739 | BU308, IDS03330-0759, BDS1795, ADS2653, BD-08 00688 | 03h 37m 55s | -07°39,0' | 1.8 | 8.93 | 10.25
WDS04075-0628 | A467, IDS04026-0644, BDS2047, ADS3003, BD-06 00823 | 04h 07m 28s | -06°28,0' | 3.6 | 9.6 | 11.4
WDS04166-1005 | BU548, IDS04118-1020, [NAME], ADS3103, BD-10 00882 | 04h 16m 36s | -10°05,1' | 6.2 | 7.5 | 11.39
WDS04518-0751 | [NAME], IDS04470-0801, BDS2392, [NAME], BD-08 00961 | 04h 51m 50s | -07°51,2' | 1.3 | 9.32 | 9.41
WDS03562-0657 | [NAME], ADS2882 | 03h 56m 13s | -06°56,6' | 1.7 | 9.23 | 10.3
WDS04016-0255 | A49, IDS03566-0311, BDS2002, ADS2942, BD-03 00661 | 04h 01m 38s | -02°54,5' | 1.9 | 9.71 | 10.78
WDS04140-1209 | [NAME], IDS04094-1224, ADS3076, BD-12 00828 | 04h 14m 02s | -12°08,8' | 1.9 | 9.97 | 10.88
WDS04429-1758 | B1940, IDS04384-1809, BD-18 00903 | 04h 42m 51s | -17°57,7' | 1.5 | 9.68 | 10.29
WDS04511-0946 | HU31, IDS04464-0956, BDS2380, [NAME], BD-10 01026 | 04h 51m 09s | -09°46,2' | 1.3 | 8.89 | 9.74
WDS04320-0243 | RST4243, IDS04270-0256, BD-03 00804 | 04h 32m [NAME] | -02°43,0' | 2.4 | 9.8 | 11.3
WDS03580-1013 | HU26, IDS03532-1030, BDS1971, [NAME], BD-10 00799 | 03h 57m 59s | -10°13,4' | 1.9 | 9.89 | 11.03
WDS05041-0602 | B9002 | 05h 04m 07s | -06°02,0' | 3.5 | 7.07 | 11
WDS04234-0007 | HO330, IDS04183-0020, [NAME], ADS3177, BD-00 00695 | 04h 23m 26s | -00°06,7' | 2.3 | 9.3 | 11.3
WDS03160-0555 | BU84, IDS03111-0617, [NAME], [NAME], BD-06 00636 | 03h 16m [NAME] | -05°55,1' | 1 | 6.38 | 7.93
WDS04399-0650 | HJ25, IDS04350-0702, BDS2306 | 04h 39m 46s | -06°49,5' | 15 | 10 | 11.7
WDS04040-1145 | HJ3617, IDS03593-1201, BDS2020, BD-12 00784 | 04h 04m 02s | -11°44,9' | 16.8 | 8.71 | 11.7
WDS04211-0851 | A472, IDS04163-0905, BDS2148, ADS3148, BD-09 00874 | 04h 21m 04s | -08°51,1' | 2.8 | 8.33 | 11.31
WDS03284-0434 | BU1180, IDS03234-0455, BDS1725, ADS2562 | 03h 28m 22s | -04°33,7' | 6.9 | 8.74 | 11.73
WDS03493-0131 | BU539, IDS03442-0149, BDS1901, ADS2792, BD-01 00538 | 03h 49m 16s | -01°30,5' | 2.5 | 8.85 | 11.43
WDS03088-0341 | STF358, IDS03037-0404, BDS1582, ADS2369, BD-04 00531 | 03h 08m 45s | -03°41,2' | 15.3 | 9 | 11.8
WDS04382-1418 | KUI18, IDS04336-1430, BD-14 00933 | 04h 38m 11s | -14°18,2' | 1.1 | 4.02 | 6.95
WDS03388-0830 | [NAME], IDS03340-0850, BDS1807, ADS2660, BD-08 00692 | 03h 38m 50s | -08°30,4' | 2.4 | 7.45 | 11.05
WDS04307-0642 | A475, IDS04259-0655, BDS2238, ADS3278, [NAME] | 04h 30m 45s | -06°41,8' | 2 | 9.37 | 11.55
WDS04103-0849 | A470, IDS04055-0904, BDS2065, ADS3037, BD-09 00833 | 04h 10m 18s | -08°48,5' | 1 | 9.72 | 9.82
WDS04459-1157 | HU104, IDS04412-1208, BDS2351, ADS3428, BD-12 00982 | 04h 45m 51s | -11°57,0' | 1.2 | 8.31 | 10.22
WDS04528-0517 | BU316, IDS04478-0527, [NAME], [NAME], BD-05 01067 | 04h 52m 46s | -05°17,1' | 0.8 | 8.45 | 8.57
WDS04209-1156 | GAL365, IDS04162-1210 | 04h 20m 59s | -11°55,5' | 18.9 | 8.9 | 11.9
WDS04339-0644 | BU881, IDS04290-0657, BDS2268, ADS3305, BD-07 00838 | 04h 33m 55s | -06°44,3' | 1.3 | 5.72 | 9.19
WDS05077-0952 | HU216, IDS05030-1000, BDS2540, ADS3719, BD-10 01101 | 05h 07m 44s | -09°51,8' | 1.9 | 8.74 | 11.47
WDS04257-0214 | BU403, IDS04206-0227, [NAME], ADS3214, BD-02 00899 | 04h 25m 42s | -02°13,9' | 1 | 7.47 | 9.42
WDS04102-1454 | TDS2768 | 04h 10m 14s | -14°53,6' | 1.5 | 9.89 | 11.49
WDS05068-0439 | HUB5, IDS05018-0447, BDS2530, ADS3698, BD-04 01044 | 05h 06m 46s | -04°39,3' | 1.6 | 5.12 | 9.38
WDS04554-1309 | A2623, IDS04507-1318, ADS3532, [NAME] | 04h 55m 21s | -13°08,8' | 1.2 | 9.77 | 10.96
WDS04399-0650 | HJ25, IDS04350-0702, BDS2306 | 04h 39m 46s | -06°49,5' | 7.2 | 10 | 12
WDS03562-1040 | HO220, IDS03514-1057, BDS1954, ADS2883, BD-11 00762 | 03h 56m 12s | -10°39,5' | 1.6 | 8.28 | 11.29
WDS04485-1052 | RST3402, IDS04437-1103, BD-11 00969 | 04h 48m 28s | -10°52,2' | 1.2 | 9.5 | 11.42
WDS04431-0725 | A476, IDS04383-0736, BDS2327, [NAME], BD-07 00882 | 04h 43m 07s | -07°24,7' | 0.7 | 9.44 | 9.61
WDS04075-0657 | A468, IDS04026-0713, BDS2048, ADS3004, BD-07 00746 | 04h 07m 29s | -06°57,2' | 0.7 | 8.96 | 9.7
WDS03493-0127 | RST4760, IDS03442-0145, BD-01 00539 | 03h 49m 19s | -01°27,1' | 0.8 | 6.74 | 9.32
WDS04073-0846 | B2551, IDS04025-0902, BD-09 00815 | 04h 07m 17s | -08°46,0' | 0.6 | 9.8 | 9.85
WDS04481-0625 | A477, IDS04432-0635, BDS2361, ADS3458, BD-06 00992 | 04h 48m 06s | -06°24,6' | 0.6 | 9.99 | 10.17
WDS04061-0122 | A1295, IDS04010-0139, ADS2988, BD-01 00584 | 04h 06m 07s | -01°22,4' | 0.6 | 9.71 | 10.17
WDS03547-0755 | [NAME], BD-08 00751 | 03h 54m 43s | -07°54,6' | 0.8 | 8.53 | 10.97
WDS04517-1302 | TDS2988, ADS3474 | 04h 51m 40s | -13°02,4' | 0.6 | 9.93 | 10.39
WDS04501-1548 | HDS622, ADS3452, BD-16 00963 | 04h 50m 07s | -15°48,2' | 1.1 | 6.84 | 10.95
WDS04385-0524 | RST4249, IDS04335-0536, BD-05 00978 | 04h 38m 28s | -05°23,7' | 0.5 | 8.7 | 9.5
WDS04568-1057 | HU215, IDS04521-1106, BDS2436, ADS3555, BD-11 01011 | 04h 56m 46s | -10°56,7' | 0.5 | 9.48 | 9.82
WDS05043-0602 | A481, IDS04594-0610, BDS2508, ADS3662, BD-06 01075 | 05h 04m 18s | -06°01,8' | 0.5 | 7.07 | 8.96
WDS04407-0112 | RST4772, [NAME], BD-01 00692 | 04h 40m 41s | -01°12,0' | 0.5 | 8.93 | 9.87
WDS02584-0135 | A208, IDS02533-0159, BDS1511, ADS2250, BD-02 00529 | 02h 58m 24s | -01°34,8' | 0.5 | 9.26 | 10.07
WDS04196-1510 | HU437, IDS04150-1524, [NAME], [NAME], BD-15 00765 | 04h 19m 34s | -15°10,1' | 0.7 | 9.18 | 11.59
[NAME]-0056 | HDS606, ADS3396, BD-01 00702 | 04h 42m 23s | -00°55,7' | 0.5 | 6.95 | 9.2
WDS03567-0134 | SEE503, IDS03517-0152, ADS2886, BD-01 00561 | 03h 56m 43s | -01°34,3' | 0.7 | 8.15 | 11.52
WDS04540-1238 | RST3405, IDS04493-1248, BD-12 01019 | 04h 53m 58s | -12°38,0' | 0.5 | 9.8 | 11.5
WDS04561-0354 | HDS639, BD-04 00978 | 04h 56m 04s | -03°54,2' | 0.6 | 8.47 | 11.45
WDS04564-0510 | HDS641, ADS3540, BD-05 01091 | 04h 56m 24s | -05°10,2' | 0.6 | 5.49 | 9.64
WDS04438-1041 | HDS610, ADS3407, BD-10 00993 | 04h 43m 46s | -10°40,9' | 0.6 | 7.98 | 11.62
WDS04334-1047 | HDS592, BD-11 00900 | 04h 33m 22s | -10°47,1' | 0.5 | 6.24 | 9.98