Radioeho s dlitel'nymi zaderzhkami: novyi podhod k probleme
Radioeho s dlitel'nymi zaderzhkami: novyi podhod k probleme
R.T. Faizullin
Omskii Gosudarstvennyi Universitet
(Materialy konferencii "SETI-XXI")
Odnimi iz naibolee veroyatnyh kandidatov na rol' inoplanetnogo soobsheniya yavlyayutsya neodnokratno fiksirovavshiesya s samogo nachala ery radio, zaderzhki radiosignalov: tak nazyvaemyi "paradoks Shtermera", "mirovoe eho", "long delayed echoes" (LDE). Imeyutsya v vidu radioeho s ochen' dlitel'nymi zaderzhkami i anomal'no malymi poteryami energii. V otlichie ot izvestnyh eho s zaderzhkami v doli sekundy, mehanizm kotoryh davno ob'yasnen, zaderzhki radiosignalov v sekundy, v desyatki sekund i dazhe minuty ostayutsya odnoi iz samyh davnih i intriguyushih zagadok fiziki ionosfery [1]. Seichas trudno sebe predstavit', no v nachale veka lyubye zaregistrirovannye radioshumy pervym delom i s legkost'yu epohi shturma i natiska, rassmatrivalis' kak signaly vnezemnoi civilizacii:
"Otmechennye mnoi peremeny proishodili v opredelennoe vremya, i analogi mezhdu nimi i ciframi byla nastol'ko chetkoi, chto ne mog uvyazat' ih ni s odnoi izvestnoi mne prichinoi. Mne znakomy estestvennye elektricheskie pomehi voznikayushie iz-za solnca, polyarnogo sini i telluricheskih tokov, i ya byl uveren, kak tol'ko mozhno byt' uverennym v faktah, chto eti pomehi ne vyzvany ni odnoi iz obychnyh prichin... Tol'ko cherez kakoe-to vremya menya osenilo, chto nablyudaemye mnoyu pomehi mogli vozniknut' v rezul'tate soznatel'nyh deistvii. Vse sil'nee ohvatyvaet menya predchuvstvie, chto pervym uslyshal privetstvie ot odnoi planety drugoi... Nesmotrya na slabost' i nechetkost', ono dalo mne glubokuyu ubezhdennost' i veru, chto vskore vse lyudi kak odin ustremyat na nebosvod nad nami vzglyady, perepolnennye lyubov'yu i pochteniem, zahvachennye radostnoi novost'yu: Brat'ya! My poluchili soobshenie s drugoi planety, neizvestnoi i dalekoi. I zvuchalo ono: raz... dva... tri..."
Nikolai Tesla, 1900
No s LDE bylo ne tak, - ideya o tom, chto radioeho mozhet byt' iskusstvennym yavleniem, svoeobraznoi vizitnoi kartochkoi; vnezemnogo sputnika, privlekayushego nashe vnimanie, eta ideya byla vydvinuta tol'ko posle publikacii astronomom Ronal'dom Breisuellom kratkoi zametki napechatannoi v zhurnale Nature, v 1960 godu. V nachale zhe, LDE byli vosprinyaty kak svidetel'stva nalichiya v kosmicheskom prostranstve specificheskih oblakov bystro dvizhusheisya plazmy, sposobnyh ne prosto otrazhat' radiosignaly, podobno zemnoi ionosfere, no i fokusirovat' ishodnyi signal tak, chto moshnost' otrazhennogo signala prevyshaet tret' moshnosti ishodnogo! Ishodnym momentom posluzhilo pis'mo inzhenera 'orgena Halsa izvestnomu astrofiziku Karlu Shtermeru
"... At the end of the summer of 1927 I repeatedly heard signals from the Dutch short-wave transmitting station PCJJ at Eindhoven. At the same time as I heard these I also heard echoes. I heard the usual echo which goes round the Earth with an interval of about 1/7th of a second as well as a weaker echo about three seconds after the principal echo had gone. When the principal signal was especially strong, I suppose the amplitude for the last echo three seconds later, lay between 1/10 and 1/20 of the principal signal in strength. From where this echo comes I cannot say for the present, I can only confirm that I really heard it." [2]
Dlya podtverzhdeniya etih faktov astrofizik Shtermer, fizik Van-der-Pol' (znamenitoe uravnenie Van-der-Polya) i inzhener Hals organizovali seriyu eksperimentov, cel'yu kotoryh bylo: proverit' nalichie fenomena i ego chastotu proyavleniya.
V 1927 godu peredatchik, raspolozhennyi v Eindhovene nachal peredavat' impul'sy, kotorye registrirovalis' Halsom v Oslo. Pervonachal'no kazhdyi signal predstavlyal soboi posledovatel'nost' treh tochek Morze. Eti signaly Povtoryalis' kazhdye 5 sekund. V sentyabre rezhim peredatchika byl izmenen: intervaly byli uvelicheny do 20 sekund. Detali eksperimenta opisany nedostatochno podrobno, tak kak publikaciya uslovii eksperimenta proizoshla v trudah konferencii i v ogranichennom ob'eme. 11 oktyabrya 1928 goda, nakonec, byli zaregistrirovany serii radioeho, ob etom Van-der Pol' soobshaet v svoei telegramme Shtermeru i Halsu: "Proshloi noch'yu nashi signaly soprovozhdalis' eho, vremya eho var'irovalos' mezhdu 3 i 15 sekundami, polovina eho bol'she chem 8 sekund!" Hals i Shtermer v svoyu ochered' podtverdili poluchenie eti eho v Oslo. Byli polucheny neskol'ko serii eho. Registrirovavshiesya radiozaderzhki var'irovalis' ot 3 sekund, do 3.5 minut! V noyabre 1929 goda eksperiment byl zavershen.
Byli tochno zaregistrirovannye sleduyushie 5 serii radiozaderzhek [3]:
1) 15,9,4,8,13,8,12,10,9,5,8,7,6
2) 12,14,14,12,8
3) 12,5,8
4) 12,8,5,14,14,15,12,7,5,5,13,8,8,8,13,9,10,7,14,6,9,5,9
5) 8,11,15,8,13,3,8,8,8,12,15,13,8,8 (v sekundah)
V mae togo zhe 1929 goda Zh. Goll' i G. Talon proveli novoe uspeshnoe issledovanie LDE fenomena:
"... In May 1929, a French expedition was in Indo-China to study an eclipse of the Sun. J B Galle and G Talon, captain of the naval vessel L'Inconstant, had orders to study the effects of the eclipse on radio propagation, particularly long delayed echoes. They used a 500 watt transmitter with a 20 metre aerial attached to an 8 metre mast, powered by the generators of the Indo-China Hydrographic Service vessel La Perouse. The two aptly named ships sailed from Saigon on May 2nd, and on May 5th they conducted test transmissions in "la baie de Penitencier", PouloCondere, and detected long delayed echoes. Weather conditions prevented work on May 6th and 7th, but on the 8th the ships were back on station and transmitted for the first ten minutes of every half hour. On May 9th, the day of the eclipse, signals were sent for nearly six hours with one 20 minute break, and again for ten minutes in every half hour the following day. Two dots were sent every 30 seconds on 25 metres wavelength, varying in a fixed musical sequence to aid correct identification and timing of the echoes. Large numbers of echoes were heard, clearly divided into two groups: weak echoes, about 1/100 the original signal strength, and strong ones 1/3 to 1/5 the intensity of the transmitted signal, with no significant relation between strength and delay time. (These intensities are too great for natural reflection at such apparent distances, but no-one seems to have thought of that at the time.) In their preliminary report Galle and Talon said echoes stopped altogether during the totality of the eclipse, but in fact they paused 3 1/2 minutes before the eclipse became total and began again half way through it. Delay times ranged from 1 second to 30 seconds, though two 31 second echoes and of 32 seconds were heard between 15.40 and 16.00 on the day of the eclipse. 1 and 2 second echoes might seem impossible for a probe in the Moon's orbit, but for an extraordinary circumstance. At 14h 19m 29s on the day of the eclipse the operator "forgot" to send the required dots, but 5 and 10 second echoes were heard nonetheless. From this Galle and Talon concluded that some echoes might have 40 seconds delay or more: either theirmusical tone sequence let them down, or they were unable to believe evidence that the probe was anticipating their signals as it transmitted its "replies" [4, 5, 6].
V 1934 godu fenomen "zaderzhannogo radioeha" nablyudal anglichanin E.Epplton i ego dannye, oformlennye v vide gistogrammy, yavlyayutsya odnimi iz naibolee chetko oformlennyh materialov po LDE eksperimentam [1] (Ris. 1).
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Ris. 1. |
V 1967 godu eksperimenty po obnaruzheniyu LDE provodilis' v Stenfordskom universitete F.Kroufordom. Fenomen udalos' podtverdit', no osobo dlinnye radioeho i serii, podobnye tem, chto nablyudalis' v 20-30-h godah, ne byli obnaruzheny. Chasto vstrechalis' zaderzhki so vremenami 2 i 8 sekund, so sdvigom chastoty i szhatiem vremeni mezhdu impul'sami eho po sravneniyu so vremene mezhdu impul'sami osnovnogo signala. Opyt issledovaniya izvestnyh dannyh LDE privodit k eshe odnomu lyubopytnomu nablyudeniyu - v lyubom novom diapazone radiovoln, t.e. v tom diapazone, kotoryi tol'ko nachinaet ispol'zovat'sya, fenomen proyavlyaetsya chetko i seriino, tak zhe, kak i v 20-h godah, zatem, po proshestvii neskol'kih let eho "rasplyvayutsya" i perestayut fiksirovat'sya serii.
Angliiskii astronom Lunen [6] obratil vnimanie na to, chto eho, nablyudavshiesya v 20-h godah, byli svobodny ot vremennogo szhatiya, i ne bylo doplerovskogo sdviga chastot, i intensivnost' shtermerovskih chastot ostavalas' postoyannoi, nezavisimo ot vremeni zapazdyvaniya. Poslednii fakt ochen' trudno ob'yasnit', ostavayas' v ramkah predpolozhenii o estestvennosti signala - estestvennye radioeho s zaderzhkoi 3 sekundy i 3 minuty principial'no ne mogut byt' odnoi intensivnosti - proishodit rasseivanie signala, tak kak volna ispuskaemaya peredatchikom eto vse-taki ne kogerentnyi lazernyi impul's!
Imenno Dunkan Lunen vydvinul gipotezu o tom, chto eho shtermerovskih serii predstavlyaet soboi signal mezhzvezdnogo zonda i izmenenie vremeni zapazdyvaniya predstavlyaet soboi popytku peredachi kakoi-to informacii. Predpolagaya, chto informaciya eta o meste nahozhdenii planetnoi sistemy, s kotoroi pribyl zond, on, osnovyvayas' na analogii s kartinoi sozvezdii na zvezdnoi sfere, prishel k vyvodu, chto rodnaya zvezda otpravitelei zonda - eto epsilon Volopasa:
" ... If the data points are plotted with delay time on the y-axis (normal scientific practice, followed by all the 1920s experimenter' s who presented their results graphically), nothing significant appears. With delay time on the x-axis, however, the graph looks more like an intelligent signal . There is a vertical "barrier" at 8 seconds dividing the diagram into two parts of an equal area; on the left there is a single dot, at three seconds, which was unique in being an exact repeat of the transmitted signal, three dots, the other echoes being 2 second long dashes. On the right of the barrier the main figure has a striking but incomplete resemblance to the constellation Bootes, the Herdsman . If the 3 second dot is transplanted across the barrier to a corresponding position on the right, it occupies the position of the star Epsilon Bootis and so completes the constellation figure. ..."
Im byla rassmotrena odna iz shtermerovskih serii 1928 goda:
8, 11, 15, 8, 13, 3, 8, 8, 8, 12, 15, 13, 8, 8.
Proizvol'nost' geometricheskih postroenii Lunena byla pokazana pochti srazu zhe i ne skeptikami, a samimi entuziastami - bolgarskie lyubiteli astronomii s pomosh'yu inogo sposoba deshifrovki poluchili druguyu "rodinu" otpravitelei - zvezdu dzeta L'va, a sposob rasshifrovki A.Shpilevskogo, nakonec, pozvolil poluchit' i vsem izvestnuyu, tak vsemi ozhidaemuyu, tau Kita.
Slozhivshayasya situaciya byla ochen' pohozha na tu, kotoruyu opisal v svoem romane "Glas Gospoda" Stanislav Lem - kratkaya zametka, promel'knuvshaya v pechati i soderzhashaya namek na Kontakt byla utoplena v more psevdonauchnyh publikacii, posle kotoryh lyuboi ser'eznyi chelovek ne rassmatrival ves' massiv informacii bez predvzyatosti. Pravda v sluchae Lunena ne ponadobilos' uchastie specsluzhb, i ne ponadobilas', dezinformaciya - vse sluchivsheesya mozhno rassmatrivat', kak proceduru verifikacii, provedennuyu, kak my uzhe upominali, samimi entuziastami ... To, chto podobnye "kartinki" mozhno producirovat' bez osobogo truda pokazyvaet Ris. 3.
Na nem izobrazheny koordinaty impul'sov zaregistrirovannyh v eksperimente META i opublikovannye v Astrofizicheskom zhurnale [7]. Kazhdyi iz etih impul'sov byl podoben shiroko izvestnomu "signalu" Wow! i oni byli zaregistrirovany na toi samoi "goryachei" linii – volne dlinoi 21 sm! Chto zhe my vidim, esli soedinit' nebesnye koordinaty signalov po poryadku opredelyaemomu datami, to my poluchim "traektoriyu" nekoego kosmicheskogo korablya, kotoryi podobno samoletu, vremya ot vremeni migal nam signal'nymi ognyami (Ris. 3).
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Ris. 2. |
Kazalos' by vse - vot oni! No, k sozhaleniyu, eto vsego lish' artefakt - ustroistvo, s pomosh'yu kotorogo skanirovalos' nebo, skanirovalo lish' ochen' malen'kii interval po vertikali, i den' oto dnya interval etot podnimalsya vverh, a zatem, dostignuv maksimal'noi vertikal'noi otmetki, nachal opuskat'sya vniz. Uzhe sleduyushii risunok, na kotorom takim zhe obrazom uporyadocheny "signaly" na udvoennoi dline volny 42 sm, pokazyvaet, chto "traektoriya" poluchilas' chisto sluchaino (Ris. 4).
V chem zhe zaklyuchalas' oshibka Lunena? Esli zadana proizvol'naya konfiguraciya tochek, my pochti vsegda mozhem naiti podhodyashuyu konfiguraciyu na zvezdnom nebe. Eto utverzhdenie est' ne chto inoe, kak chastnyi sluchai tak nazyvaemoi teoremy Ramseya - to est' pri dostatochnom kolichestve tochek ili ob'ektov my mozhem naiti sredi etih tochek zaranee zadannuyu konfiguraciyu s zaranee opredelennymi svoistvami. Ideal'no tochno ona, konechno, ne poluchitsya, no, uvelichivaya moshnost' rassmatrivaemogo mnozhestva tochek (t.e. chisla tochek ili zvezd na zvezdnoi sfere) my mozhem poluchit' skol' ugodno tochnuyu kopiyu zadannoi figury.
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Ris. 3. |
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Ris. 4. |
To est' oshibka Lunena sostoyala v tom, chto on pytalsya postroit' figuru, ispol'zuya zaderzhki, kotoraya by vyglyadela KAK sozvezdie. No sozvezdii mnogo, da oni i sami yavlyayutsya kul'turnymi artefaktami - sposob gruppirovki zvezd po sozvezdiyam proizvolen i te, opredelennye sozvezdiya, chto u nas est' seichas, eto vsego lish' plod hudozhestvennogo voobrazheniya vavilonskih i grecheskih pastuhov i ne bolee togo.
Prezhde chem perehodit' k gipoteze yavlyayusheisya predmetom dannoi stat'i rassmotrim nekotorye estestvennye ogranicheniya, i ochevidnye trebovaniya, kotorym dolzhno udovletvoryat' vozmozhnoe kontaktnoe soobshenie.
Sleduet ozhidat', chto procedura peredachi, kak i samo soderzhanie, soobshenie, predstavlyaet soboi nekii ochen' horosho produmannyi i neodnokratno privodivshii k uspehu standart. Poetomu samo soobshenie dolzhno rassmatrivat'sya kak produkt vysochaishih tehnologii, produkt, proshedshii ispytaniya ne odin desyatok raz i veroyatnei vsego razrabotannyi dazhe ne toi civilizaciei, chto posylaet soobshenie v dannyi moment vremeni. Sleduet podcherknut', chto rech' idet ne tol'ko o tehnologiyah v obychnom smysle etogo slova, no i o social'nyh tehnologiyah.
Kakie otsyuda sleduyut vyvody? Vo-pervyh, sleduet ozhidat' garantirovannost' uspeha raspoznavaniya iskusstvennosti soobsheniya. Eto oznachaet, chto s vysokoi veroyatnost'yu fiksaciya soobsheniya vlechet za soboi i ego raspoznavanie. Otsyuda ochevidnym obrazom sleduet, chto soobshenie dolzhno byt' obyazatel'no zafiksirovano, to est', zaneseno v annaly nauki, religii ili drugih dolgovremennyh organizacii. Odnomomentnosti rasshifrovki, ili vernee odnomomentnosti osoznaniya ozhidat' ne sleduet, vo vsyakom sluchae, ona ochen' maloveroyatna.
Sleduyushee - dolzhno li byt' soobshenie izbytochnym? Eto dovol'no tonkii vopros, chto imenno ponimat' pod izbytochnost'yu, i tak li ona polezna. Rassmotrim primer svyazannyi s znamenitym signalom "Ogo-go!" ili "Wow!". Pust' iz toi zhe tochki nebesnoi sfery, gde pervonachal'no byl poluchen etot strannyi signal, budut postupat' ego analogi, prichem vremennye intervaly mezhdu ih postupleniyami budut otnosit'sya mezhdu soboi kak prostye chisla (tak nazyvaemye pozyvnye). Budet li eto svidetel'stvom iskusstvennosti? Nesomnenno. No, est' mnogoe zavisyashee i ot poluchatelya. Budet li poluchatel' skanirovat' na protyazhenii dolgogo vremeni (stoletii) imenno etot uchastok neba, delo ne v ugasayushem nauchnom interese, delo v rutinnyh finansovyh vozmozhnostyah?
Budet li nebo poluchatelya chisto ot podobnyh radiosignalov (sputniki)? Krome togo, kto garantiruet, chto v prirode net fizicheskih processov, pri kotoryh proishodyat spontannye razryady s intervalami vremeni, otnosyashimisya drug k drugu, kak prostye chisla? Takim obrazom, izbytochnost' "signala" naoborot mozhet sluzhit' osnovaniem dlya prinyatiya resheniya ob ego estestvennom proishozhdenii.
(Poslednie issledovaniya o spontannyh scintillyaciyah v mezhzvezdnyh oblakah vodoroda stavyat pod somnenie samu vozmozhnost' podobnogo kanala svyazi, t.k. estestvennye scintillyacii sozdayut shum, prichem shum, kotoryi v silu svoei slozhnosti mozhet pohodit' na iskusstvennyi signal, t.e. opyat' proyavlyaetsya teoriya Ramseya).
Vmesto izbytochnosti sleduet ozhidat' nezavisimosti. My postepenno pereshli k obsuzhdeniyu vozmozhnogo soderzhaniya signala ili kak prinyato nazyvat' - pozyvnyh. Primery pozyvnyh uzhe est', hotya eto i primery zemnogo proishozhdeniya (Pionery 10, 11 i posleduyushie, dal'nie zondy Voyadzhery), i na osnovanii real'nyh soobshenii mozhno vpolne obosnovanno sdelat' predpolozheniya o pervonachal'noi (v istoricheskom plane) forme standartnogo soobsheniya - nemnogo o sebe, koordinaty, i chto-nibud' o Kosmose.
Izmenitsya li chto-nibud' potom?
"Kogda chelovek uznaet, chto dvizhet zvezdami, togda Sfinks zasmeetsya, i rod lyudskoi prervetsya" (Nadpis' na stenah Abu Simbela)
Skol'ko by vremeni ni proshlo, kak by ne razlichalis' urovni razvitiya civilizacii, no kontaktnoe soobshenie vsegda budet napravleno tem, kogo interesuyut zvezdy. Eto dolzhno byt' to, chto otlichaet cheloveka ot zhivotnogo, dazhe ot razumnogo zhivotnogo.
Sleduyushii nemalovazhnyi moment, opyat' privodyashii nas k zvezdam - eto interval vremeni, v kotorom kontaktnoe soobshenie budet predstavlyat' interes dlya poluchatelya. V nashem sluchae etot interval uslovno mozhno vzyat' ravnym vsemu vremeni sushestvovaniya cheloveka kak vida, t.e. eto primernoe 100 000 let!
Mozhno, konechno, zayavit', chto vse osnovnye fakty o zvezdah my uzhe znaem, no takoe utverzhdenie samo daleko ne novo ...
Vse vysheskazannoe pozvolyaet vydvinut' sleduyushuyu gipotezu i sformulirovat' trebovaniya k ee verifikacii:
- Vremena zaderzhek signala sleduet interpretirovat' kak nomera nebesnyh tel v nekotorom ob'ektivnom uporyadochenii.
- Sleduet iskat' neozhidannye geometricheskie svoistva, prisushie figuram, poluchennym na zvezdnoi sfere i v sluchae uspeha popytat'sya ustanovit' matematicheskii i fizicheskii smysl dannyh svoistv.
- Poluchennye fakty dolzhny podtverzhdat'sya dlya neskol'kih nezavisimyh serii radiozaderzhek, poluchennyh v raznoe vremya i raznymi issledovatelyami, chto pozvolit isklyuchit' proizvol'nost' interpretacii i "poddelku" dannyh.
- Poluchennye rezul'taty dolzhny proiti standartnuyu nauchnuyu aprobaciyu v vide vystuplenii na nauchnyh konferenciyah i v vide opublikovannyh nauchnyh statei (bez upominanii ili ssylok na problemu SETI), chto dolzhno podtverdit' nezavisimuyu ot gipotezy Kontakta znachimost' vyyavlennyh matematicheskih i fizicheskih faktov.
Prezhde chem perehodit' k konkretnym rezul'tatam, obsudim bolee detal'no predstavlennye punkty. Rassmotrim punkt 1, i vyyasnim, kakie nebesnye tela imeyutsya v vidu. Planety? No chast' iz nih ne mozhet byt' nablyudaema nevooruzhennym glazom i trebovanie k "demokratichnosti", t.e. trebovanie k tomu, chto poluchennoe znanie bylo by vizual'nym i dostupnym maksimal'nomu kolichestvu nablyudatelei v sluchae planet ne vypolnyaetsya. Blizhaishie k nam zvezdy? No analogichno planetam samye blizkie k nam zvezdy mogut byt' i ne vidny bez teleskopa, nastol'ko oni maly po masse i svetimosti. Krome togo, skorosti malyh zvezd nastol'ko veliki, chto ih pozicii na zvezdnoi sfere za tysyachi let izmenyayutsya ochen' sil'no i predpolagaemaya figura "rasplyvaetsya". To zhe otnositsya k galaktikam, yarkim tumannostyam i prochim slabosvetyashimsya ob'ektam. Ostayutsya naibolee yarkie zvezdy, otnositel'nye skorosti ih maly, oni nablyudaemy, oni vsegda vyzyvali interes.
Po kakim parametram ih mozhno uporyadochit'? Po rasstoyaniyam, po massam, po svetimostyam?
No ih parallaksy dazhe seichas opredeleny ne sovsem tochno, massy yavlyayutsya vtorichnymi raschetnymi velichinami, i ostayutsya svetimosti ili bolee tochno vizual'nye zvezdnye velichiny V.
Eti velichiny opredelyayutsya s vysokoi tochnost'yu fotoelektricheskim metodom, i odnovremenno ih mozhno opredelit' s pomosh'yu ekspertnoi ocenki na samoi rannei stadii civilizacii.
Nizhe privedeny koordinaty i nazvaniya pervyh pyatidesyati po vizual'noi yarkosti zvezd.
Uporyadochenie naibolee yarkih zvezd po velichine V.
(Kulikovskii [8], 1985)
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l | b | |
| 1. Sirius | 6h 43m | -16 35 | 227 | -9 |
| 2. Kanopus | 6h 23m | -52 40 | 261 | -25 |
| 3. Arktur | 14h 13m | +19 27 | 15 | +69 |
| 4. Vega | 18h 35m | +38 44 | 67 | +19 |
| 5. Toliman | 14h 36m | -60 38 | 316 | +1 |
| 6. Kapella | 5h 13m | +45 57 | 163 | +5 |
| 7. Rigel' | 5h 12m | -08 15 | 209 | -25 |
| 8. Procion | 7h 37m | +05 21 | 219 | +13 |
| 9. Betel'geize | 5 52 | +07 24 | 200 | -9 |
| 10. Ahernar | 1 36 | -57 29 | 291 | -59 |
| 11. Hadar | 14 00 | -60 08 | 314 | .0 |
| 12. Al'tair | 19 48 | +08 44 | 48 | -9 |
| 13. Akruks | 12 24 | -62 49 | 300 | 0 |
| 14 Al'debaran | 4 33 | +16 25 | 181 | -20 |
| 15. Antares | 16 26 | -26 19 | 352 | +15 |
| 16. Spika | 13 23 | -10 54 | 316 | +51 |
| 17. Polluks | 7 42 | +28 09 | 192 | +23 |
| 18. Fomal'gaut | 22 55 | -29 53 | 20 | -65 |
| 19. Mimoza | 12 45 | -59 09 | 302 | +3 |
| 20. Deneb | 20 40 | +45 06 | 84 | +2 |
| 21. Regul | 10 06 | +12 13 | ||
| 22. Adara | 6 57 | -28 54 | ||
| 23. Kastor | 7 31 | +32 00 | ||
| 24. Shaula | 17 30 | -37 04 | ||
| 25. Bellatriks | 5 22 | +06 18 | ||
| 26. Gakruks | 12 28 | -56 50 | ||
| 27. El'-Nat | 5 23 | +28 34 | ||
| 28. Miaplacidus | 9 13 | -69 31 | ||
| 29. Alnilam | 5 34 | -01 14 | ||
| 30. Al' Nair | 22 05 | -47 12 | ||
| 31. Aliot | 12 52 | +56 14 | ||
| 32. Alnitak | 5 38 | -01 58 | ||
| 33. Dubhe | 11 01 | +62 01 | ||
| 34. Mirfak | 3 21 | +49 41 | ||
| 35. Gamma Par | 8 08 | -47 12 | ||
| 36. Kaus Aust | 18 21 | -34 25 | ||
| 37. Vezen | 7 06 | -26 19 | ||
| 38. Benetnash | 13 46 | +49 34 | ||
| 39. Avior | 8 22 | -59 21 | ||
| 40. Teta Sk | 17 34 | -42 58 | ||
| 41. Menkalinan | 5 56 | +44 57 | ||
| 42. Al'hena | 6 35 | +16 27 | ||
| 43. Metalah | 16 43 | -68 56 | ||
| 44. Del'ta Par | 8 43 | -54 31 | ||
| 45. Pikok | 20 22 | -56 54 | ||
| 46. Mirzam | 6 20 | -17 56 | ||
| 47. Al'fard | 9 25 | -08 26 | ||
| 48. Mira | 2 17 | -03 12 | ||
| 49. Hamal' | 2 04 | +23 14 | ||
| 50. Polyarnaya | 1 49 | +89 02 |
(Gipparh pervyi uporyadochil zvezdy po zvezdnoi velichine sobrav neskol'ko chelovek, slavivshihsya isklyuchitel'no ostrym zreniem, on predlozhil im ocenit' po poryadku yarkosti zvezdy. Usredniv rezul'taty, on poluchil svoyu shkalu. Eto bylo ne chto inoe, kak pervoe nauchnoe primenenie tak nazyvaemogo metoda ekspertnoi ocenki. Zametim, chto uporyadochenie Gipparha neskol'ko otlichaetsya ot uporyadocheniya po fotoelektricheskoi velichine)
Vtoroi punkt, kakie figury sleduet iskat'? Opyt neudachi Lunena demonstriruet, chto poisk antropomorfnyh simvolov, skoree vsego obrechen na neudachu i poisk sleduet napravit' na matematicheskie figury, ne sluchainye po svoei suti i yavlyayushiesya otrazheniem zakonov zvezdnoi dinamiki. No kakoe otnoshenie imeet zvezdnaya velichina k dinamike? Izvestno, chto polnaya svetimost' zvezdy L yavlyaetsya funkciei ot ee massy, bolee tochno ona proporcional'na masse v kube, plyus nekaya mala velichina, a vizual'na zvezdnaya velichina, ochevidno proporcional'na L/R2. To est', zvezdnaya velichina yavlyaetsya avtomodel'nym parametrom, odnovremenno harakterizuyushim i massu i rasstoyanie.
Tretii punkt est' ne chto inoe, kak obychnoe trebovanie k eksperimentu - povtoryaemost' isklyuchaet sluchainost'. To zhe otnositsya i k chetvertomu punktu, mozhno predstavit' sebe, chto sluchainym obrazom my poluchili nechto strannoe i "pohozhee" na matematicheskuyu figuru, no sam fakt publikacii sluzhit dokazatel'stvom znachimosti rezul'tata. Publikacii predpolagayut ne tol'ko opisanie fenomena, no i nekotoroe razvitie, naprimer, podtverzhdenie predlozhennoi fizicheskoi modeli chislennymi eksperimentami, sozdanie novyh algoritmov, na osnove nablyudaemyh fenomenov i t.p. Takzhe - kakova veroyatnost' togo, chto, osnovyvayas' na sluchainom nabore chisel mozhno poluchit' nauchnyi fakt?
Pereidem k neposredstvennomu rassmotreniyu faktov i vydvizheniyu gipotezy.
Rassmotrim tak nazyvaemuyu pervuyu seriyu Shtermera:
15, 9, 4, 8, 13, 8, 12, 10, 9, 5, 8, 7, 6.
Estestvenno ozhidat', chto eta seriya, esli, konechno, ona yavlyaetsya iskusstvennym poslaniem, soderzhit "pozyvnye" - nekotoryi geometricheskii fakt, illyustraciyu, podobnuyu toi, chto byla predlozhena Gaussom (teorema Pifagora illyustrirovannaya vyrubkami v sibirskih lesah ili kanalami s goryashei neft'yu v Sahare).
Chto osobennogo v predstavlenii etih zvezd? Esli rassmatrivat' ih v obychnyh dekartovyh koordinatah v prostranstve ili na zvezdnoi sfere, to kazalos' by nichego neobychnogo net, no davaite pereidem v sfericheskuyu sistemu koordinat.
Kak ona stroitsya? Rassmotrim zvezdnuyu sferu s radiusom edinica, to est' predstavim, chto my kak nablyudateli nahodimsya na Zemle, a nas okruzhaet ochen' bol'shaya sfera. Pust' zvezdy, nahodyashiesya snaruzhi sfery, proektiruyutsya na etu sferu i my, prenebregaya rasstoyaniyami do nih, vidim tol'ko yarkie tochki na sfere. Kazhdaya takaya tochka lezhit na peresechenii linii so sferoi, linii provedennoi cherez centr sfery i real'nym mestopolozheniem zvezdy. Togda zvezde mozhno sopostavit' uglovye koordinaty (l,b).
Cherez centr sfery prohodit ploskost', vybrav nekii luch na etoi ploskosti, prohodyashii cherez centr, mozhno otschityvat' ugol otnositel'no lucha- eto odna koordinata l. Druga poluchaetsya kak ugol b mezhdu ploskost'yu i luchom, napravlennym iz centra sfery na tochku sfery, kotoraya ne lezhit na dannoi ploskosti.
Ochevidno, chto ugol l menyaetsya ot nulya do 360 gradusov, a b var'iruetsya ot -90 do +90 gradusov. Togda esli rassmotret' sistemu koordinat, gde v kachestve osi OX vystupaet OL, a v kachestve osi OY os' OB, to my poluchim predstavlenie vseh zvezd v pryamougol'nike [0,360]x[-90,90]. Kazalos' by, raznica zaklyuchaetsya lish' v udobstve predstavleniya dannyh, no ne vse tak prosto. Naprimer, v kachestve sekushei zvezdnuyu sferu ploskosti mozhno vybrat' proizvol'nuyu ploskost', no mozhno vybrat' i ploskost' vrasheniya sistemy nablyudatelya! T.e. vybrat' dinamicheski vydelennuyu sistemu koordinat svyazannuyu s momentom vrasheniya. Tak pod (l,b) ponimaetsya galakticheskaya sistema koordinat, gde ploskost' secheniya zvezdnoi sfery sovpadaet s ploskost'yu Galaktiki, l = 0 vybrano, konechno, proizvol'no, no mozhet byt' i ne sovsem proizvol'no, tak kak l = 0 otvechaet napravleniyu na centr Galaktiki.
Drugaya sistema koordinat sootnesena s ploskost' ekliptiki i otvechaet ploskosti vrasheniya ili sootvetstvuet momentu Solnechnoi sistemy i tret'ya sfericheskaya sistema koordinat, eto ekvatorial'naya, zdes' sekushaya ploskost' perpendikulyarna osi vrasheniya Zemli.
Otmetim, chto v silu proizvol'nosti vybora nachala l = 0 i periodichnosti, my imeem dlya predstavleniya zvezd ne pryamougol'nik, a cilindr, vosstanovlennye perpendikulyary nad l = 0 i l = 360 zadayut odni i te zhe pryamye.
Na pervyi vzglyad, dannaya sistema koordinat kazhetsya nadumannoi i neudobnoi, no na samom dele neudobno imenno dekartovo predstavlenie, sfericheskie zhe sistemy koordinat, pozvolyayut izobrazhat' vsyu zvezdnuyu sferu na ogranichennom kuske ploskosti i yavlyayutsya estestvennymi, v silu lokal'noi sfericheskoi simmetrii, v silu izotropnosti prostranstva, i v silu estestvennoi svyazi l-koordinaty s momentom vrasheniya sistemy.
Togda v galakticheskoi sisteme koordinat my poluchaem deistvitel'no udivitel'nuyu figuru, figuru, kotoraya vpolne mozhet vypolnyat' rol' "pozyvnyh" (Ris. 5).
My poluchili 8 pryamyh iz kotoryh, sleduya poryadku postupleniya signalov mozhno obrazovat' dve troiki parallel'nyh pryamyh i eshe odnu paru vzaimno parallel'nyh (Ris. 6, Ris. 7).
Otmetim, chto proizvol'naya vyborka iz nomerov, otvechayushih pervoi serii Shtermera, uzhe ne daet podobnoi simmetrii i bolee togo, veroyatnost' sluchainoi i nastol'ko polnoi illyustracii svoistva parallel'nosti, pri sluchainom obhode zadannyh tochek, ravna chislu poryadka 1/(12!). ( Kod, esli eto kod, legko poddaetsya rasshifrovke - soedinyaya pervye 5 tochek v poryadke 15, 9, 4, 8, 13 my poluchaem dve parallel'nye pryamye i dalee stanovitsya sovershenno ochevidnym, chto neobhodimo provesti pryamye 13, 8, 12, chtoby poluchit' otrezki (8, 12), (12, 10) i.t.d., zdes', navernoe, stoit vspomnit' ideyu o kodah maksimal'no prostyh dlya rasshifrovki i o uzhe sushestvuyushih kodah s ispravleniem oshibok).
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Ris. 5. |
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Ris. 6. |
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Ris. 7. |
Okazyvaetsya, chto i chetvertaya seriya Shtermera yavlyaetsya illyustraciei svoistva parallel'nosti. Naprimer, obhod tochki na ploskosti (l,b), v poryadke 12 8 5 14 14 15 12 7 5 5 13 8 8 8 13 9 10 7 14 6 9 5 9 my poluchaem analogichnuyu figuru (Ris. 8). Svoistvo parallel'nosti proillyustrirovano na sleduyushih risunkah 9-12
Zametim, chto zdes' my zamenili 11 po schetu otmetku (ili 11-i eho-signal) ravnuyu 13 na 14, principial'no eto ne menyaet kartinu, no dobavlyaet paru "parallel'nyh" pryamyh.
Vozmozhno, pri registracii radioeha byla dopushena oshibka, no kak my vidim, ona ne vliyaet na deshifrovku v celom! Dalee, eti bol'shie po ob'emu serii, budem schitat' "obertkoi" pis'ma vypolnyayushie odnovremenno funkciyu "soderzhaniya" i popytaemsya naiti nekotoroe ob'ektivnoe ob'yasnenie tomu, chto dlya kazalos' by sovershenno sluchaino raspredelennyh tochek na ploskosti udaetsya postroit' stol'ko pochti parallel'nyh pryamyh. Neposredstvennaya proverka pokazyvaet, chto esli vzyat', k primeru, koordinaty blizhaishih 50 zvezd, to podobnoi bogatoi "parallel'nosti" ne nablyudaetsya, takzhe ee ne nablyudaetsya v sluchae esli my rassmatrivaem sluchainye nabory tochek.
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Ris. 8. |
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Ris. 9. |
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Ris. 10. |
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Ris. 11. |
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Ris. 12. |
Budem dalee schitat', chto galakticheskaya sistema koordinat eto to pole ili "doska", na kotoroi v dal'neishem budet predstavlena informaciya i rassmotrim 3 seriyu zaregistrirovannuyu Shtermerom, Halsom i Van-der-Polem - zaderzhki ravnye 12,5, 8.
Snova rassmatrivaya uporyadochenie po zvezdnym velichinam, izmerennym fotoelektricheskim sposobom (dannye vzyaty iz monografii Kulikovskogo), my poluchim sleduyushie, sootvetstvuyushie nomeram zvezdy, 5- al'fa Centavra (araby nazyvayut ee Toliman), 8 - Procion, 12 - Al'tair. Okazyvaetsya, chto eti tri zvezdy lezhat na odnoi linii, prichem tochka 5 lezhit na "perekrest'e" dvuh linii (esli rassmatrivat' cilindr). Obratimsya ko vtoroi serii Shtermera 12, 14, 14, 12, 8, zdes' k ukazannym trem zvezdam dobavlyaetsya Al'debaran.
Opyat' tri zvezdy 14, 12, 8 lezhat primerno na odnoi linii, kotoraya, kstati, soderzhit i tochku 5. Poidem dal'she i sdelaem dopushenie, chto znachimy ne tol'ko sami zaderzhki - eho, no i ih dopolneniya do 20, my uchityvaem konkretnye usloviya eksperimenta Shtermera i, schitaya, chto signaly imeyut iskusstvennyi harakter, my mozhem rassmatrivat' kak ravnopravnye dannye i zaderzhki i ih dopolneniya (Ris. 13).
Dobavlyayutsya vsego dve novyh zvezdy 6 - Kapella i 15 - Antares, no kartina priobretaet zavershennyi i isklyuchitel'no simmetrichnyi vid. Mozhet byt' eto sluchainoe sovpadenie? Pust' dazhe i perehod v drugie sfericheskie sistemy koordinat, v eklipticheskuyu (Ris. 14), i v ekvatorial'nuyu (Ris. 15), sohranyaet simmetriyu, no vse-taki mozhet byt' otlichie ot ideal'nyh pryamyh delaet podobnye svoistva ochen' veroyatnymi?
Obratim vnimanie na to, chto chislo 20, ili, inache govorya, interval mezhdu signalami poslannymi s Zemli, "zavyazano" v predstavlennyh kartinah
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Ris. 13. |
Naprimer, v galakticheskom predstavlenii tochki s nomerami 5 i 6 lezhat na perekrestii linii, soedinyayushih tochki s nomerami v summe dayushimi chislo 20. V ekvatorial'noi zhe sisteme koordinat linii, peresekayushiesya nakrest, ogranichivayutsya tochkami, nomera, kotoryh vzaimno dopolnitel'ny do 20. Esli rassmatrivat' dopolneniya do 20, dlya pervoi serii Shtermera, to my opyat' poluchim illyustraciyu parallel'nosti, t.e. esli soedinit' tochki s nomerami 5 11 16 12 7 12 8 10 11 15 12 13 14, yavlyayushimisya dopolnitel'nymi k nomeram 15 9 4 8 13 8 12 10 9 5 8 7 6, to poluchennyi "negativ" prosto porazhaet svoei simmetriei! (Ris. 16) i opyat' my poluchaem illyustraciyu svoistva parallel'nosti.
Provedennye chislennye eksperimenty pokazyvayut, chto podobnye simmetrii poluchit' dovol'no trudno, no bolee vsego dokazatel'no rassmotrenie nezavisimyh dannyh - obrabotka rezul'tatov eksperimenta Eppltona 1934 goda.
Okazyvaetsya, chto uzhe dlya 50 tochek ( pozicii 50 zvezd) my mozhem vydelit' invariantnuyu konfiguraciyu "setka": v ekvatorial'nom (Ris. 17) predstavlenii, v eklipticheskom (Ris. 18) i v galakticheskom (Ris. 19). Zdes' takzhe, kazhdoi zaderzhke otvechaet zvezda, s sootvetstvuyushim nomerom i proveryaetsya svoistva "lezhat' na odnoi pryamoi". Obratim vnimanie na to, chto "setka" stroitsya s pomosh'yu dvuh obrazuyushih cilindra.
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Ris. 14. |
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Ris. 15. |
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Ris. 16. |
Legko proverit' invariantnost' i po prostranstvu, to est' to, chto Solnechnaya sistema ne est' nekotoraya vydelennaya sistema koordinat. Naprimer, esli v kachestve nachala koordinat rassmatrivat' mestopolozhenie zvezdy al'fa Centavra i pereschitat' vizual'nye yarkosti 50 zvezd, samyh yarkih v novoi sisteme otscheta (naprimer, minus al'fa Centavra, plyus Solnce i nekotorye drugie zvezdy), to my poluchim polnyi analog uzhe imeyushimsya kartinam (Ris. 20).
To zhe samoe poluchaetsya v sluchae perenosa nachal koordinat na mesto Prociona (Ris. 21).
V kachestve sistemy koordinat vybrana galakticheskaya sistema, i my zdes' ogranichilis' predstavleniem dlya dvuh blizhaishih sosedei Solnca- rasstoyanie do al'fy Centavra 4 svetovyh goda, a do Prociona 11 svetovyh let.
Perehod k bolee udalennym zvezdam, naprimer, k Al'tairu (Ris. 22) takzhe vozmozhen, no trebuetsya ochen' akkuratnyi pereschet parallaksov i vizual'nyh yarkostei dlya bolee chem sta blizhaishih zvezd.
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Ris. 17. |
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Ris. 18. |
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Ris. 19. |
No chto eto oznachaet? Kakoi smysl (poka eshe dinamicheskii, konechno) kroetsya za naidennymi figurami?
Vo-pervyh, chto my mozhem skazat' o risunkah bolee tochnym yazykom - yazykom matematiki? Chto mozhno naiti pohozhego v arsenale geometrii?
Okazyvaetsya, est' matematicheskie ob'ekty v nekotorom rode "pohozhie" na vyyavlennye geometricheskie prirodnye sootnosheniya. Eto tak nazyvaemye konfiguracii [9], prosteishim primerom mozhet sluzhit' konfiguraciya Brianshona - Paskalya (Ris. 23).
Dannye 9 tochek udovletvoryayut sleduyushim usloviyam: cherez kazhduyu tochku prohodit po tri pryamye, na kazhdoi pryamoi lezhit po tri tochki. Poetomu formal'noe oboznachenie etogo ob'ekta (9)_3
Zametim, chto sovpadenie svoistv ili "pohozhest'" proyavlyaetsya pri podobnyh operaciyah postroeniya, konfiguracii eto matematicheskie ob'ekty, bazovye dlya proektivnoi geometrii
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Ris. 20. |
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Ris. 21. |
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Ris. 22. |
Dlya togo chtoby isklyuchit' element sluchainosti obratimsya k predstavleniyam blizhaishih gigantskih i sverhgigantskih galaktik, naibolee yarkim galaktikam.
My rassmatrivaem galaktiki sravnimye po masse, naprimer, tumannost' Andromedy, nasha Galaktika, Dvingelo 1, Treugol'nik - eto gigantskie galaktiki, a karlikovye galaktiki po masse v tysyachi i desyatki tysyach raz men'she gigantskih.
Pri postroenii analogichnom tomu, kakoe my provodili dlya sluchaya yarchaishih zvezd v ekvatorial'noi sisteme koordinat my poluchim analog konfiguracii Paskalya (Ris. 24). Otmetim tol'ko, chto uporyadochennost' po yarkosti zdes' ne predstavlena.
Tochno takzhe kak i v sluchae blizhaishih zvezd, uporyadochennost' imeetsya i v drugih sistemah koordinat eklipticheskoi (Ris. 25), galakticheskoi (Ris. 26) i dobavlyaetsya predstavlenie v tak nazyvaemoi cupergalakticheskoi (Ris. 27) sisteme koordinat, koordinaty galaktik vzyaty iz bazy dannyh vnegalakticheskih ob'ektov NED: http://nedwww.ipac.caltech.edu/index.html
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Ris. 23. |
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Ris. 24. |
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Ris. 25. |
Vypolnenie svoistv, vyyavlennyh snachala dlya raspolozheniya zvezd, i dlya galaktik neskol'ko proyasnyaet situaciyu. Galaktiki prakticheski pokoyatsya otnositel'no drug druga, - skorosti ih prenebrezhimo maly po sravneniyu s harakternymi lineinymi razmerami galaktik i rasstoyaniyami mezhdu nimi, to est' polnaya energiya sistemy pochti sovpadaet s potencial'noi energiei. No eto oznachaet, chto potencial'naya energiya sistema dostigaet svoego maksimal'nogo znacheniya.
Mozhet byt', konfiguracionnye svoistva i est' sledstvie ekstremal'nosti sostoyaniya sistemy?
Chto togda mozhno skazat' otnositel'no sistemy blizhaishih yarkih i massivnyh zvezd? Blizhaishee okruzhenie Solnca nahoditsya v tak nazyvaemom korotacionnom uzle [14], gde skorost' vrasheniya Galaktiki i skorost' vrasheniya spiral'nyh vetvei sovpadayut. Eto oznachaet, chto uzhe neskol'ko milliardov let okruzhenie Solnca dvizhetsya vne zon, gde proishodyat nestacionarnye processy i poetomu mozhno ozhidat', chto za eto vremya proizoshlo stacionirovanie raspredeleniya mass, svyazannyh seichas v zvezdy bol'shoi svetimosti i massy.
Eto privodit nas k rassmotreniyu izvestnoi matematicheskoi problemy, nosyashei nazvanie zadachi Shteinera:
- zadany N tochek ili na ploskosti ili v prostranstve, neobhodimo soedinit' ih otrezkami pryamyh tak, chto summa dlin etih otrezkov budet minimal'na. Sleduet uchest', chto mozhno vvodit' dopolnitel'nye tochki, krome teh kotorye imeyutsya.
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Ris. 26. |
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Ris. 27. |
V obshei, matematicheskoi postanovke zadacha byla sformulirovana v stat'e Milosha Kesslera i Voiceha Yarnika opublikovannoi v 1934 godu, no izvestnost' k zadache prishla posle znamenitoi knigi Kuranta i Robbinsa "Chto takoe matematika?" [11]. Kurant i Robbins ukazali na svyaz' obshei postanovki zadachi s problemoi Shteinera - poisku odnoi tochki, summa rasstoyanii, ot kotoroi do vseh tochek zadannogo mnozhestva byla by minimal'na (Yakov Shteiner krupnyi nemeckii geometr 19 veka). Dal'neishie sledy uvodyat v glub' vekov, eshe Evandzhelista Torrichelli i Bonaventura Kaval'eri zanimalis' interesnym chastnym sluchaem zadachi: naiti tochku R, summa rasstoyanii ot kotoroi do kazhdoi iz treh zadannyh minimal'na. Oni dokazali, chto summa rasstoyanii minimal'na, kogda vse sopryazhennye ugly bol'she ili ravny 120 gradusam. Krome togo, oni predlozhili i algoritm resheniya zadachi.
Chtoby proillyustrirovat' skazannoe vyshe privedem geometricheskie figury yavlyayushiesya resheniyami zadachi Shteinera (derev'ya Shteinera) dlya malogo chisla tochek. Dlya sluchaya treh tochek, raspolozhennyh v vershinah pravil'nogo treugol'nika: reshenie i priblizheniya privedeny na risunke 28.
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Ris. 28. |
Dlya sluchaya 4 tochek, raspolozhennyh v vershinah pryamougol'nika, reshenie i sravneniya privedeny na sleduyushem risunke 29.
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Ris. 29. |
Nas bol'she interesuyut mehanicheskie analogii, kogda minimum dliny interpretiruetsya kak nekii ekstremal'nyi energeticheskii princip dlya mehanicheskoi sistemy. Naprimer, Kurant i Robbins (KR) [11] ukazali, chto esli vershiny dereva Shteinera rassmatrivat' kak soedinennye uprugoi nit'yu uzly, to minimum dliny otvechaet minimumu summarnoi potencial'noi energii natyazheniya.
Sleduya dannoi analogii, oni postroili ostroumnoe ustroistvo pozvolyayushee nahodit' priblizhennye resheniya zadachi. KR ispol'zovali v kachestve modeli myl'nuyu plenku, natyanutuyu mezhdu dvumya parallel'nymi steklami, soedinennymi mezhdu soboi sterzhnyami v polozheniyah zadannyh tochek. Pripodnimaya odno steklo nad drugim, KR poluchali nekotoruyu plenku, soedinyayushuyu strezhni. V silu ekstremal'nogo energeticheskogo principa polozhenie plenki davalo odno iz reshenii zadachi. K sozhaleniyu, poluchit' tochnoe reshenie takim sposobom ne vsegda predstavlyaetsya vozmozhnym, i my poluchaem tak nazyvaemye otnositel'no minimal'nye derev'ya Shteinera. No okazyvaetsya, to takie derev'ya mozhno poluchat' ne tol'ko s pomosh'yu mehanicheskogo ustroistva KR.
Obratim vnimanie na tot fakt, chto v dereve Shteinera net vershiny, imeyushei bolee treh reber i krome togo, kazhdaya tochka Shteinera, t.e. dopolnitel'naya k zadannym tochka imeet shodyashiesya k nei rebra, pod uglami 120 gradusov. Predstavim sebe, chto zadannye tochki dereva fiksirovany, a tochki Shteinera "ishut" polozhenie staticheskogo ravnovesiya, tak, chtoby itogovaya konfiguraciya udovletvoryala principu maksimuma potencial'noi gravitacionnoi energii (massy tochek schitayutsya ravnymi, a potencial'na gravitacionnaya energiya otricatel'na).
Togda mozhno legko pokazat', chto lyuboe maloe otklonenie ot podobnoi konfiguracii privodit k tomu, chto summarnaya dlina reber dereva Shteinera vozrastaet i bolee togo, mozhno ranzhirovat' otnositel'no minimal'nye derev'ya Shteinera po "sile" otvechayushei zadannomu vozmusheniyu.
No vmesto togo, chtoby rasschityvat' gravitacionnye sily, mozhno rasschityvat' vtorye proizvodnye ot koordinat, i vybiraya v iteracionnoi procedure dlya kazhdoi tochki Shteinera polozhenie s minimal'noi summoi vtoryh proizvodnyh, a proshe govorya, stavya ee v centr koordinat treh blizhaishih sosedei, my dovol'no bystro poluchim priblizhennoe reshenie zadachi. Naprimer, vse ranee rassmotrennye sluchai, poluchayutsya posle neskol'kih (4 - 10) iteracionnyh obhodov podvizhnyh tochek. Ochevidno, chto trehmernyi sluchai (kak i sluchai bolee vysokoi razmernosti) nichem ne otlichaetsya ot dvumernogo. Var'iruya nachal'nye priblizheniya, my poluchim neskol'ko otnositel'no minimal'nyh derev'ev, i esli kazhdoe iz nih poluchaetsya ne odin raz, to veroyatnost' togo, chto my propustili samoe minimal'noe, ochen' mala. Podobnym obrazom udaetsya poluchit' i drugie izvestnye tochnye resheniya zadachi Shteinera (ris 30)
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Ris. 30. Tochnoe reshenie zadachi Shteinera, poluchennoe metodom gravitacionnoi analogii (chernye kruzhki - tochki Shteinera). |
Vernemsya k zvezdam. Pust' v kachestve "zadannyh" ili fiksirovannyh tochek dereva Shteinera vystupayut ochen' massivnye zvezdy, a v kachestve dobavochnyh, ili tochek Shteinera figuriruyut zvezdy, massa kotoryh neskol'ko men'she. Togda polozhenie s maksimal'noi potencial'noi energiei budet otlichat'sya tem, chto zvezdy srednei massy ili "tochki Shteinera" raspolozhatsya tak, chto kazhdaya budet lezhat' v ploskosti treh svoih blizhaishih sosedei.
Chto otsyuda sleduet? V sfericheskoi sisteme koordinat, s ploskost'yu odnogo ugla l, sovpadayushei s ploskost'yu obrazovannoi trem sosedyami, vse tri zvezdy-sosedki budut lezhat' na linii l = 0. Esli zhe my nachnem povorachivat' ploskost' tak, chto odna zvezda budet ostavat'sya v ploskosti ugla l, to v silu simmetrii, v novoi sfericheskoi sisteme koordinat izobrazhenie vseh treh zvezd budet lezhat' na odnoi linii, vernee na dvuh obrazuyushih cilindra, takzhe kak i v nablyudaemyh sluchayah.
Mozhno oslabit' uslovie nepodvizhnosti samyh massivnyh zvezd i schitat' fiksirovannymi polozheniya tol'ko zvezd, lezhashih na granice nekotorogo ob'ema. Okazyvaetsya, chto i v etom sluchae simmetrii v sfericheskih sistemah koordinat sohranyayutsya.
Na sleduyushem risunke 30 priveden primer, kogda odna tochka uravnoveshivaetsya tremya.
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Ris. 31. |
Na risunke 31 priveden primer, kogda rassmatrivayutsya uzhe 5 tochek, odna iz kotoryh est' tochka obzora.
Na risunke 32 privedeny rezul'taty rascheta dlya bol'shego chisla tochek.
Kak my vidim, risunki, poluchennye v rezul'tate modelirovaniya ochen' pohozhi na te konfiguracii, kotorye nablyudayutsya na zvezdnom nebe.
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Ris. 32. |
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Ris. 33. |
Aprobaciya predstavlennyh vyshe materialov, v kotoryh, konechno, ni slovom ne upominalis', ni problema SETI, ni fenomen LDE, zaklyuchalas' ne tol'ko v publikaciyah statei i v vystupleniyah na nauchnyh konferenciyah, no i v nekotorom teste na znachimost' rezul'tatov, t.e. v nablyudenii za reakciei slushatelei, i za ih ocenkami urovnya novizny predstavlennyh geometricheskih faktov. V bol'shei mere, chem sam fakt publikacii, eto vlilo na ocenku znachimosti poluchennyh faktov samim avtorom.
T.e eto byl rastyanutyi po vremeni social'no-psihologicheskii eksperiment s obratnoi svyaz'yu.
Hronologicheski pervym bylo vystuplenie na Mezhdunarodnoi konferencii "Gruppy v geometrii i analize" Omsk 1995. Otmetim, chto Orgkomitet vozglavlyal akademik Reshetnyak Yu.G. i d. f.-m. n. Vinberg E.B., to est' konferenciya po urovnyu deistvitel'no byla znachimoi.
Byl predstavlen doklad s nazvaniem "Simmetrii v raspolozhenii yarkih zvezd i zadacha N-tel s konechnoi skorost'yu peredachi signala". Vystuplenie bylo prinyato v shtyki i vyzvalo dovol'no goryachuyu diskussiyu, v kotoroi uchastvovali professor Vinberg i professor Vodop'yanov i drugie. No tak kak avtor ne pretendoval na vydvizhenie "teorii", a prosto predstavil legko proveryaemyi eksperimental'nyi fakt invariantnosti konfiguracionnyh svoistv dlya estestvennyh ob'ektov, to fakt byl prinyat vo vnimanie (byl prinyat, nado skazat', skrepya serdce).
Sleduyushim shagom aprobacii stala diskussiya s akademikom A.T. Fomenko, v avguste 1996 goda. Ego rezyume bylov sleduyushim:
"Predstavlennye fakty, nesomnenno tayat nekotoryi global'nyi po znachimosti zakon, no na dannyi moment ya ne vizhu matematicheskih instrumentov sposobnyh opisat' ego, mozhet byt' stoit obratit' vnimanie na poisk grupp, otvechayushih dannym simmetriyam, i popytat'sya promodelirovat' podobnye struktury v ryade chislennyh eksperimentov"
V tom zhe 1996 godu byl sdelan doklad "An Approximations for Genetic Algorithms and Star Patterns" [12].
V etoi rabote, na osnove ukazannyh simmetrii, byl predlozhen algoritm optimizacii, gde znachenie celevoi funkcii rassmatrivalos', kak gravitiruyushaya massa, zavisyashaya ot mestopolozheniya probnoi tochki, a poisk ekstremuma funkcii modelirovalsya, kak fizicheskii process kollapsa neskol'kih takih tochek (v dal'neishem razrabotannyi metod gravitacionnoi analogii byl uspeshno primenen v zadache poiska traektorii elementarnyh chastic v eksperimentah fiziki vysokih energii i v chisto tehnicheskoi zadache optimizacii raboty gidravlicheskogo ustroistva.)
S drugoi storony, popytki modelirovaniya konfiguracii priveli k postroeniyu priblizhennogo algoritma resheniya zadachi Shteinera, podobnogo algoritmu Kuranta - Robbinsa, prigodnomu uzhe ne tol'ko dlya ploskosti, no i dlya prostranstva proizvol'noi razmernosti.
V 1997 godu avtorom byl predstavlen doklad na XIV Sessii Mezhdunarodnoi Shkoly po modelyam mehaniki sploshnoi sredy . "Konechnoelementnye analogii pri modelirovanii nestandartnyh sploshnyh sred" [13].
Utochnennyi i rasshirennyi variant etogo doklada byl predstavlen na 2-i Zimnei shkole po Novym Matematicheskim Metodam v Mehanike, g. Novosibirsk, Institut Gidrodinamiki im M.A.Lavrent'eva, 1998 god.
Tezisy dokladov byli opublikovany takzhe na neskol'kih nauchnyh fizicheskih i astronomicheskih konferenciyah, naprimer, na konferencii Vychislitel'naya Astrofizika- 98, Yaponiya, Tokio, 2-oi Kongress po Industrial'noi Matematike g. Novosibirsk, i.t.d.
Sleduet sdelat' vyvod o tom, chto v celom reakciya slushatelei byla blagozhelatel'noi, tak, naprimer, inogda dazhe vstrechalis' vykriki "eto otkrytie!" i ne bylo otkrovennogo skepsisa i nepriyatiya, no utverzhdat', chto novye fakty stali horosho izvestny i interesny shirokomu krugu issledovatelei poka nel'zya, no etogo na pervyh porah i ne trebuetsya.
Ostaetsya vazhnyi vopros, mozhno li poluchit', hotya by predpolozhitel'nuyu, no vse-taki informaciyu o mestonahozhdenii planety ili bazy otpravitelei zonda? Konechno, zdes' my stupaem na zybkuyu pochvu interpretacii simvolov, no nekotoryi vyvod sdelat' mozhno.
Obratim vnimanie na to, chto bol'shaya chast' zaderzhek zaregistrirovannyh radioeho i v 20-ye gody i v eksperimentah Krouforda ravnyalas' vos'mi. Chislu vosem' u nas otvechaet zvezda Procion, dvoinaya zvezda, odna komponenta kotoroi belyi karlik, a druga eto zvezda spektral'nogo klassa F5 IV, u kotoroi s bol'shoi veroyatnost'yu net planet prigodnyh dlya zhizni. No pochemu my schitaem, chto signal dolzhen ukazyvat' nepremenno na rodnuyu planetu otpravitelei? S tochki zreniya gipotezy o tom, chto razvitaya civilizaciya uzhe davno ne zavisit ot resursov tol'ko materinskoi planety, eta zvezda odna iz naibolee podhodyashih zvezd iz blizhaishego okruzheniya Solnca, - kak vremennaya baza, zdes' vozmozhno raspolozhit' dolgovremennyi sputnik okolo vysokoenergetichnogo belogo karlika i orbita sputnika budet stabil'na.
Konechno, neobhodimy nezavisimye uliki, ukazyvayushie na Procion. Okazyvaetsya, chto oni imeyutsya. Rassmotrim pyatuyu seriyu Shtermera, tu samuyu, na osnovanii kotoroi Lunen sdelal vyvod o mestopolozhenii otpravitelei, i pokazhem, chto eta seriya mozhet soderzhat' informaciyu o mestopolozhenii.
Rassmatrivaya risunki poluchennye provedeniem linii, soedinyayushih tochki s koordinatami otvechayushim nomeram zvezd, my poluchim treugol'niki (dovol'no interesnye i ne sluchainye treugol'niki) s obshei vershinoi v tochke otvechayushei raspolozheniyu Prociona.
Esli zhe rassmotret' drugoe uporyadochenie zvezd po blesku, naprimer, vzyav za osnovu poryadok predlozhennyi Gipparhom (ili poryadok opredelyaemyi ne fotoelektricheskim, a fotograficheskim sposobom fiksacii vizual'noi yarkosti), to togda proekcii linii soedinyayushih koordinaty zvezd na ploskost' zemnogo ekvatora budut davat' v nekotorom rode "strelu", prohodyashuyu cherez centr okruzhnosti, i sohranyayushuyu svoyu formu pri perehode k eklipticheskim koordinatam i ukazyvayushuyu na Procion (Ris. 33).
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Ris. 34. |
Sleduet otmetit', chto zdes', kazalos' by, my otstupaem ot postulirovannogo ranee trebovaniya "ob'ektivnosti" simvola, no tak li uzh simvol "strela" antropomorfen? Vozmozhno, chto simvol vektora ili napravlennosti takzhe obsheprinyat, kak i strogo opredelyaemye matematicheskie figury.
No stoit otmetit' eshe odin nemalovazhnyi moment, vremya registracii signalov, eto konec dvadcatyh, nachalo tridcatyh godov... Ne byl li togda narushen nekii zapret na kontakt, s cel'yu predotvratit' gibel' desyatkov millionov lyudei? Imeya sootvetstvuyushii social'nyi opyt netrudno sprognozirovat' razvitie posledovavshih sobytii. I nam ved' eshe krupno "povezlo" - bud' atomnaya bomba sdelana ran'she na god ili dva, i obeimi storonami srazu, to, skol'ko by eshe lyudei pogiblo v itoge?
Konechno, kategorichno utverzhdat', chto predstavlennye materialy est' ne chto inoe, kak rasshifrovka "soobsheniya" slishkom rano, no kak my nadeemsya, v rabote udalos' pokazat', chto ochevidnaya gipoteza o sootnesenii nomerov zaderzhek s nomerami zvezd v estestvennom uporyadochenii privodit k netrivial'nym rezul'tatam, poluchivshim razvitie v nauchnyh publikaciyah.
Takzhe nam kazhetsya, chto sposob predstavlenii geometricheskih svoistv i figur neposredstvenno na zvezdnoi sfere, pryamo pereklikaetsya s ideei Gaussa (1826g), predlozhivshego osushestvit' gigantskie vyrubki v sibirskoi taige v vide pryamougol'nogo treugol'nika s dlinami storon otnosyashimisya kak 3, 4, 5..
Avtor vyrazhaet priznatel'nost' za pomosh' i podderzhku L.M.Gindilisu.
PS :Obsudit' rabotu mozhno po adresu: http://cmm.univer.omsk.su/gbook
(*)
Project Meta's data. There was registred 37 strong strange 'aletrts' similar famous
signal WOW! (Horowitz&Sagan ApJ, 415, 218-235, 1993).
Five year of project Meta:an all-sky narrow-band radio search for extraterrestrial signals.
1420 MHz
00.82 3.25 7735
00.87 57.5 6942
06.08 -3.5 6782
06.23 9.5 6822
11.58 31.5 6876
21.15 -21.0 6737
21.98 38.5 6894
01.70 33.5 8014
02.90 32.0 8022
03.10 58.0 7847
12.32 16.0 8160
12.73 -12.5 8364
15.55 17.0 8154
19.57 47.5 7916
23.72 8.5 8216
2840 MHz
00.82 3.25 7735
01.30 -22.00 7577
01.83 7.0 7769
05.73 6.0 7326
08.00 -8.50 7415
08.03 11.00 7301
08.08 7.00 7769
08.67 45.75 7159
08.95 -15.75 7452
10.43 -21.25 7481
11.23 58.00 7230
14.30 57.50 7228
14.65 46.50 7164
15.47 -18.00 7599
17.10 2.00 7351
18.05 23.50 7061
18.37 -19.50 7467
18.45 38.50 7127
18.67 -23.25 7493
18.68 -22.25 7565
19.18 -0.50 7699
19.67 -23.00 7560
20.03 30.75 7092
01.30 -22.00 7577
01.83 7.0 7769
05.73 6.0 7326
08.00 -8.50 7415
08.03 11.00 7301
08.08 7.00 7769
08.67 45.75 7159
08.95 -15.75 7452
10.43 -21.25 7481
11.23 58.00 7230
14.30 57.50 7228
14.65 46.50 7164
15.47 -18.00 7599
17.10 2.00 7351
18.05 23.50 7061
18.37 -19.50 7467
18.45 38.50 7127
18.67 -23.25 7493
18.68 -22.25 7565
19.18 -0.50 7699
19.67 -23.00 7560
20.03 30.75 7092
RA DEC Date
00.87 57.5 6942
06.08 -3.5 6782
06.23 9.5 6822
11.58 31.5 6876
21.15 -21.0 6737
21.98 38.5 6894
01.70 33.5 8014
02.90 32.0 8022
03.10 58.0 7847
12.32 16.0 8160
12.73 -12.5 8364
15.55 17.0 8154
19.57 47.5 7916
23.72 8.5 8216
2840 MHz
00.82 3.25 7735
01.30 -22.00 7577
01.83 7.0 7769
05.73 6.0 7326
08.00 -8.50 7415
08.03 11.00 7301
08.08 7.00 7769
08.67 45.75 7159
08.95 -15.75 7452
10.43 -21.25 7481
11.23 58.00 7230
14.30 57.50 7228
14.65 46.50 7164
15.47 -18.00 7599
17.10 2.00 7351
18.05 23.50 7061
18.37 -19.50 7467
18.45 38.50 7127
18.67 -23.25 7493
18.68 -22.25 7565
19.18 -0.50 7699
19.67 -23.00 7560
20.03 30.75 7092
Literatura
- Ya.L. Al'pert Rasprostranenie voln v ionosfere M., Nauka, 1985.
- Macvey, J.W., Whispers From Space. Chapter 13 "From What Far Star" P.193. London Abelard Schuman. 1973. ISBN 0 200 72243 3
- C. Stormer, Proceedings of the Royal Society of Edinburgh 50, Part II, no. 15 (1933)
- J B Galle, "Observations relatives a la radio-electricite et a la physique du globe", L'Onde Electrique 9 (1930), pp. 257-265
- J B Galle, G Talon and M Ferrie, "Recherches relatives a la propogation des ondes radioelectriques effectuees a l'occasion de l'eclipse du 9 mai 1929", Comptes Rendus de L'Academie des Sciences, vol. 130 (1930), pp 48-52.
- Lunan. D. INTERSTELLAR CONTACT. Chapter 12. "The News From Bootes". P.223 - 262. Henry Regnery Company: Chicago. 1975 ISBN 0 8092 8258 5 (First published in Great Britain 1974 under the title "Man and the Stars")
- P.Horowitz, C. Sagan Five Years of Project META: All-Sky Narrow-Band Radio Search for Extrateerestrial Signals The Astrophysical Journal, 451:218-235,1993 September 20.
- P.G. Kulikovskii Zvezdnaya astronomiya M., Nauka, 1985.
- Gil'bert D., Kon-Fossen S. Naglyadnaya geometriya M.: Nauka, 1981.-344 s.
- Gilbert E.N., Pollak H.O. Steiner minimal trees, SIAM Journal of Applied Mathematics, 16, #1 (1968), pp 1-29.
- Kurant R., Robbins G. Chto takoe matematika? OGIZ, M.-L., 1947.
- Faizullin R.T. An Approximations for Genetic Algorithms and Star's Pattern // 1 st On-Line Internet Conference of Soft Computing, Nagoya, Japan, 19-30 Aug 1996. 77-82.
- Faizullin R.T. Konechnoelementnye analogii pri modelirovanii nestandartnyh sploshnyh sred //Tr. XIV sessii Mezhdunarodnoi shkoly po modelyam sploshnoi sredy, Moskva:MGU, 1998. c. 233-238.
- Marochnik L.S., Suchkov A.A. Galaktika. M.: Nauka, 1984, 392 s.
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Publikacii s klyuchevymi slovami:
SETI - zaderzhki radiosignalov - paradoks Shtermera
Publikacii so slovami: SETI - zaderzhki radiosignalov - paradoks Shtermera | |
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