IAO 2010, Практически тур, Групи α и β — Задача 6. ZHR

Practical round. Problems 6 and 7 · 16 октомври 2010 г.

Внимание: Бележка към темата

В дневника към задача 6 има 425 записа: между №159 и №161 е отпечатано №150, а №239 и №240 липсват. Номерата и неследващите по време записи са запазени. В официалния отговор към задача 7 са запазени и отпечатаните числови несъответствия: Mg_min = 5.825 (1.23) и ε = (0.058−0.056)/0.056 = 0.028.

Бележка

Translation of your solution of practical round is not proposed. The only formulae, graphs, numerical values, standard defined symbols of objects (like ♎, α UMa, M31, 5m5^{\rm m}), etc. but not words and explanations (in any language including English) will be taken into account. Units (kg, pc, nm...) should be written in Latin or Cyrillic.

Условие

The visual observations of meteors are necessary to monitor the meteor showers of the high and intermediate activity. Despite the fact that the accuracy of the visual observations is much lower than that of the photometrical ones, the large number of observations have large significance for the statistical results.

You are provided by supplement papers: the log of the observations and the map of the gnomonic projection with listed meteor events.

1.

Observations were organized in Sudak, the local time (LT) used. Please, write in Table 1 the time of the beginning (TbT_b) and the end (TeT_e) of observations using Universal time (UT).

2.1.

The meteors that belong to the same shower (S) have one radiant. The name of the shower coincides with the name of the constellation where the radiant is situated.

Indicate the place on the map where the radiant is situated (for Perseids). List in Table 2 the numbers of meteors (No) that are showed on the map that belong to this stream (see the supplement).

2.2.

Determine and list in Table 2 the equatorial coordinates of the radiant (α,δ\alpha,\delta).

3.

Write in Table 2 the date of the maximum of the meteor shower Perseids (in DD.MM format). Estimate (roughly with an accuracy 1h) the beginning (TbT_b) and the end (TeT_e) of the shower visibility during the night of the maximum.

4.

The calculation of the hour number of meteors (ZHR) for the Perseid shower.

ZHR is a measure of the shower activity. It can be defined as a number of meteors that are seen by observer during one hour of observations with the favourable conditions and with a radiant situated in zenith. The corresponding formula is:

ZHR=K6.5−lmNFTeffsin⁡hrZHR=\frac{K^{6.5-lm}NF}{T_{\rm eff}\sin h_r}

KK – coefficient of the luminosity function that is equal to 2.5,

lmlm – limiting stellar magnitude (each observer determines this value individually taking the most faint star he or she can observe),

NN – observed number of meteors,

FF – coefficient correcting the cloudiness of the sky,

TeffT_{\rm eff} – effective time of observations in hours,

hrh_r – the angular altitude of the radiant above the horizon.

4.1.

Calculate the mean value of the limiting stellar magnitude (lm) for each interval. Write your results in Table 3.

4.2.

Calculate effective time of observations (TeffT_{\rm eff}) for each interval. Write your results in Table 3.

ZHR corresponds to the ideal sky condition. If there is a haze in the sky, some clouds or some extra light (Moon, artificial light, twilights), the visual number of meteors will be decreased, because faint meteors can not be observed.

4.3.

Calculate the correction for the cloudiness for each interval (FF).

F=11−kF=\frac1{1-k}

Where kk is percentage of the cloudiness, tt is corresponding time interval in minutes, and ttotalt_{\rm total} is the total time of observation in a given interval.

k=∑i=1nkiti100⋅ttotalk=\frac{\sum_{i=1}^{n}k_i t_i}{100\cdot t_{\rm total}}

Write your results in Table 3.

4.4.

Calculate zenith hour number (ZHR) of the meteors for Perseids shower for each interval. Write your results in Table 3.

Table 1 · Таблица 1

LTUT
TbT_b
TeT_e

Table 2 · Таблица 2

No
α=\alpha=δ=\delta=
DD.MM
TbT_b
TeT_e

Table 3 · Таблица 3

Nohrh_rlmNTeffT_{\rm eff}FZHR
23
29
37
47
54
63

Observation log · Sheet 1

№TSm
21:15–22:00; lm = 5.6
121:18Per2
221:18Dra3
321:20Cas3,5
421:20Cyg4
521:21Per2
k = 20%
621:22Cyg3,5
721:23Cas3
821:24Per1
921:24Her4
1021:24Lac3,5
1121:25Cas3,5
1221:26Cyg3
k = 0%
1321:26Lyr4,5
1421:27Lyr3
1521:28Cyg4
1621:29Boo2
1721:33Per1,5
1821:34Cyg2,5
1921:35Dra4
2021:36Per1
2121:37Lyr3,5
2221:37Peg2
2321:38Per2,5
2421:39Cyg3,5
2521:40Lyr4
2621:41Cam2
2721:43Cyg4
2821:44Cyg3,5
2921:44Cyg4
3021:45Per3
3121:50Per1,5
lm = 6.0
3221:50Oph1
3321:50Cep4
3421:51Per1
3521:51Per1,5
3621:52Cam2,5
3721:52Peg3
3821:53Cas3
3921:53Cas3,5
4021:54Per3
4121:54Dra3,5
4221:55Per2,5
4321:59Vul2
22:20–23:10; lm = 6.5
4422:23Per2,5
4522:25Cyg3,5
4622:25Per2,5
4722:26Dra4
4822:26Cyg4
4922:27Per1
5022:27Per1
5122:27Cas2
5222:29Vul4
5322:29Lyr4
5422:39Per2
5522:30And4,5
5622:31Per2,5
5722:31Cyg4
5822:32Per2,5
5922:33Peg0
6022:34Dra4
6122:34Aql3,5
6222:35Aql2,5
6322:35Aql0
6422:36Per3
6522:42Cyg2
6622:42Per2,5
6722:44Cas3
6822:45Per-1
6922:46Cyg3,5
7022:47Per3
7122:49Cas3
7222:50Her3
7322:51Per3
7422:51And5
7522:53Per2
7622:53Per1,5
7722:54Peg1
7822:56Peg-1
7923:00Per2,5
8023:04Per3
8123:04Cyg4
8223:05Cyg4
8323:05Per3,5
8423:06Aql3
8523:08Per0
8623:09Per1
23:30–00:20; lm = 6.5
8723:31Peg3
8823:32Per2
8923:32Peg4
9023:33Aql3
9123:34Per2,5
9223:34Cyg3
9323:34Per1
9423:35And3
9523:35Cep3,5
9623:36Per1
9723:37Cyg4
9823:37Peg3,5
9923:37Per0
10023:38Per0
10123:38Per3
10223:39Lac3,5

Observation log · Sheet 2

№TSm
10323:39Spor0
10423:40Per-1
10523:41Per1
10623:41Per2
10723:42Per2,5
10823:42Cyg3
10923:43Per2
11023:43Per1
11123:44Per1
11223:45Per3
11323:46Per2,5
11423:47Cas2
11523:47Cas3,5
11623:48Cyg3
11723:49Per3,5
11823:49And3,5
11923:49Per0,5
12023:50Per2
12123:51Peg3
12223:51Peg3
12323:52Cyg1,5
12423:53Cep1
12523:53Per1,5
12623:53Per0
12723:54Cep1
12823:54Per1
12923:55Lac3,5
13023:55Lac4
13123:56Cas0
13223:58Per0
13323:58Cas2,5
13423:58Per0
13523:58Per2,5
13623:59Lac3
13723:59Cas3
13800:00Peg2
13900:00Per3
14000:02Peg3
14100:02And5
14200:04Per2
14300:05Per0
14400:06Cyg3,5
14500:05Peg0
14600:06Per0
14700:08Per3
14800:09Per0
14900:10Per2
15000:10Per1
15100:10Peg0
15200:11Per2
15300:11Peg3
15400:12Spor1
15500:12Cep4
15600:12Per1,5
15700:13Aqr2
15800:14Per0,5
15900:16Per0
15000:17Per0
16100:18Cep3
16200:18Per1
16300:19Per2
00:40–01:30; lm = 6.5
16400:43Per1
16500:44Per1
16600:44Per2
16700:45Per3
16800:45Aqr2
16900:47Per0
17000:47Cyg3,5
17100:50Per2
17200:50Per2
17300:51Per1,5
17400:52Peg4,5
17500:52Per2
17600:53Per2
17700:53Per2
17800:54Peg1,5
17900:55Per2
18000:56Per0
18100:56Per1,5
18200:56Tri3,5
18300:56Per3
18400:57Peg4
18500:57Peg2,5
18600:57Per1,5
k = 10%
18700:58Cas5
18800:59Per3
18900:59Cyg3
19001:00Cyg2,5
19101:00Per2
19201:01Per2,5
19301:01Per2
19401:02Cep4,5
19501:04Per1,5
19601:06Cep3,5
19701:07Per3
19801:07Aqr2
19901:08Umi3
20001:08Peg3
20101:08Per2
20201:09Peg1,5
20301:09Cyg1
20401:09Cas2
20501:09Per1,5
20601:09Peg4
20701:10Per2
20801:11Per2
20901:11Per0
21001:11Per0
21101:12Per2
21201:13Per1,5

Observation log · Sheet 3

№TSm
k = 0%
21301:13Per2
21401:14Per3
21501:14Per4,5
21601:15Per4
21701:16Peg3
21801:16Cas4
21901:17Per3
22001:18Per3
22101:18Aqr3
22201:18Per2
22301:19Per0
22401:21Per0
22501:22Per1
22601:22Cas4
22701:22Cas2,5
22801:23Per3
22901:23Per2
23001:24Per0
23101:24Per1,5
23201:25Per0
23301:25Peg5
23401:26And3
23501:27Cep3
23601:28Per0,5
23701:29Per2
23801:30Per1
01:50–02:40; lm = 6.5
24101:51Per1,5
24201:53Per2
24301:53Per2,5
24401:55Peg-2
24501:56Peg-1
24601:57Per0
24701:57And4
24801:58Tri2
24901:58Cyg3,5
25001:59Per1
25102:00Per2
25202:03Tau3
25302:03Per2,5
25402:03Per1,5
25502:04Per1
25602:06Per2,5
25702:06Ari3,5
25802:06Lac4
25902:07Per1,5
26002:08Per1
26102:08Per1
26202:08Per2
26302:08Per0,5
26402:08Peg2
26502:11Per3
26602:11Cas3
26702:11Per0
26802:12Aql2
26902:12Per0
27002:13Dra3
27102:13Per3
27202:13And5
27302:14Per2
27402:14Per2,5
27502:14Cas4,5
27602:15Per2,5
27702:15Per3
27802:15Per1
27902:15Per0,5
28002:15Per3
28102:16Per2
28202:17Cas3
28302:18Per-3
28402:19Per2
28502:20Per3
28602:20Per3
28702:21Cas5
28802:21Per0
28902:21Per1
29002:22Peg4
29102:23Peg3
29202:24Per4
29302:25Per1
29402:25Per1
29502:25Per-1
29602:26Per1
29702:26Per4
29802:27Per2,5
29902:27Per2
30002:28Per1
30102:28Per3
30202:28Per3
30302:28Per2
30402:29Peg2
30502:30Per1
30602:30Per1
30702:30Per1
30802:30Per4
30902:30Per2
31002:31Per2
31102:31Per1
31202:31Per1,5
31302:32Per-1
31402:33Per1
31502:33Tau3
31602:33Per2,5
31702:35Cyg2
31802:36Per2
31902:37Per1
32002:38Per1
32102:38Per1
32202:38Per1,5
32302:38Peg2
32402:39Per1

Observation log · Sheet 4

№TSm
32502:39Per2
32602:39Per1
32702:40Per2
03:00–04:00; lm = 6.5
32803:03Cas2
32903:03Per3
33003:04Per2
33103:04Cyg3
33203:04Psc3
33303:05Peg3
33403:05And4,5
33503:06Lac2,5
33603:07Per2
33703:07Per1,5
33803:07Per2
33903:08And1
34003:08Per3
34103:08Per3
34203:08Per3
34303:09Per2
34403:09Dra2
34503:10Per2
34603:11Per2
34703:11Per2
34803:11Per0
34903:12Per-1
35003:13Spor0
35103:14Per3
35203:15Per0
35303:15Per2
35403:16Per2
35503:16Per1
35603:16Per0
35703:17Peg3,5
35803:17Peg3
35903:18Per2
36003:19And3
36103:20Peg4
36203:21Cet2
36303:22Per2,5
36403:22Per3
36503:22Per3
36603:22Tri4
36703:23Per0,5
36803:23Per0
36903:24Aqr2
37003:25Per-3
lm = 6.0
37103:28Cas2,5
37203:28Per3
37303:28Per3
37403:29Per1,5
37503:29Peg3
37603:29Lac3
37703:30Per2
37803:31Cas2
37903:32Per3
38003:33Per3
38103:33Cas3
38203:33Peg2
38303:34Spor1
38403:35Per2,5
38503:35Cas3,5
38603:35Cas3
38703:36Per2,5
38803:36Per3
38903:37Per0,5
39003:38Boo3
39103:39Psc4
39203:38Per3
39303:38Per3
39403:40Per3
39503:40Per2,5
39603:40Per3
39703:41Per2
39803:42Per2
39903:42Per2
40003:42Per0
40103:42And4
40203:43Per1,5
40303:44Per1
40403:45Per3
40503:45Per3,5
40603:46Per3
40703:48Psc3
40803:48Per2,5
40903:48Cyg3
41003:49Per2
41103:49Per1
41203:50Per3
41303:51Per1,5
41403:51Per3
41503:51Per3
41603:51Boo4,5
41703:52Per2
41803:53Per3
41903:53Per3
42003:54Aqr3
42103:54Cas2,5
42203:55Per2
42303:55Peg1,5
42403:55Per3
42503:56Per3
42603:59Per1
42703:59Per-0,5

Gnomonic map

Original gnomonic map with meteor numbers and observed tracks.
Original gnomonic map with meteor numbers and observed tracks.

Supplementary star map

Original polar star map accompanying the practical packet, with equatorial coordinates and calendar scale.
Original polar star map accompanying the practical packet, with equatorial coordinates and calendar scale.

Решение


Оригинал в Архива: pract1.jpg · официални решения: practsol1.jpg · допълнителни данни: pract2.jpg · допълнителни данни: pract3.jpg · допълнителни данни: pract4.jpg · допълнителни данни: pract5.jpg · допълнителни данни: pract6.jpg · допълнителни данни: pract7.jpg · допълнителни данни: pract8.jpg · допълнителни данни: pract9.jpg · допълнителни данни: pract10.jpg · допълнителни данни: practsol2.jpg · допълнителни данни: practsol3.jpg