Ñàíêò-Ïåòåðáóðãñêèé ãîñóäàðñòâåííûé óíèâåðñèòåò
Íàïðàâëåíèå (ñïåöèàëüíîñòü) àñòðîíîìèÿ
Ïðîôèëü (ñïåöèàëèçàöèÿ) àñòðîìåòðèÿ
Ìèðîíîâà Ñâåòëàíà Ìèõàéëîâíà
Àíàëèç àëãîðèòìîâ âû÷èñëåíèÿ âèäèìûõ ìåñò çâ¼çä
Äèïëîìíàÿ ðàáîòà
Íàó÷íûé ðóêîâîäèòåëü:
äîöåíò êàôåäðû àñòðîíîìèè, ê.ô.-ì.í., Ïåòðîâ Ñ.Ä.
Ðåöåíçåíò:
çàâ. ñåêòîðîì ãåîäèíàìèêè ÃÀÎ ÐÀÍ, ê.ô.-ì.í., Ãîðøêîâ Â. Ë.
Ñàíêò-Ïåòåðáóðã
2016
SAINT-PETERSBURG STATE UNIVERSITY
Main Field of Study (Speciality) astronomy
Area of Specialisation (Specialisation) astrometry
Mironova Svetlana Mihaylovna
Analysis of algorithms of evaluation of apparent places of stars
Graduation Thesis
Scienti c supervisor:
Assistant professor of the Astronomy Department, Ph. D., S. D. Petrov
Reviewer:
Head of Geodynamics sector, Central astronomical observatory, Ph. D., V. L.
Gorshkov
Saint-Petersburg
2016
Îãëàâëåíèå
1
Ââåäåíèå
4
2
Èñòîðè÷åñêàÿ ÷àñòü
6
3
Îáçîð òåêóùåãî ñîñòîÿíèÿ ïðîáëåìû
10
4
Íàáëþäåíèÿ çâåçä
26
5
Âûâîäû
37
Ëèòåðàòóðà . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
3
Ãëàâà 1
Ââåäåíèå
 àñòðîíîìèè îäíîé èç âàæíûõ çàäà÷ ÿâëÿåòñÿ îïðåäåëåíèå êîîðäèíàò
íåáåñíûõ îáúåêòîâ. Îäíàêî ïîëó÷åííûå â ðåçóëüòàòå íàáëþäåíèé ñ Çåìëè êîîäèíàòû áóäóò çàâèñåòü íå òîëüêî îò ïîëîæåíèÿ ñàìîãî îáúåêòà, íî è
îò ñîñòîÿíèÿ àòìîñôåðû, ïîëîæåíèÿ Çåìëè îòíîñèòåëüíî Ñîëíöà è äðóãèõ
ôàêòîðîâ, äåéñòâîâàâøèõ â òîò ìîìåíò. Åñëè ïîëó÷åííûå òàêèì îáðàçîì
êîîðäèíàòû îòñ÷èòûâàþòñÿ â ãåîöåíòðè÷åñêîé ñèñòåìå îòñ÷åòà è îòíåñåíû
ê ìãíîâåííûì ïîëþñó ìèðà è òî÷êå âåñåííåãî ðàâíîäåíñòâèÿ, òî èõ íàçûâàþò âèäèìûìè.  êàòàëîãàõ îáû÷íî ïðèâîäÿòñÿ ñðåäíèå ìåñòà çâåçä,
êîòîðûå îòíîñÿòñÿ ê ñðåäíåìó ýêâàòîðó è ðàâíîäåíñòâèþ äàòû íàáëþäåíèÿ â áàðèöåíòðè÷åñêîé ñèñòåìå îòñ÷åòà.
×òîáû ïåðåéòè îò ñðåäíèõ ê âèäèìûì ìåñòàì çâåçäû, íóæíî ó÷åñòü âëèÿíèå ãîäè÷íîé è ñóòî÷íîé àáåððàöèé, ïðåöåññèè è íóòàöèè [4]. Ãîäè÷íàÿ
àáåððàöèÿ âûçûâàåò ñìåùåíèå ïîëîæåíèÿ íàáëþäàòåëÿ èç-çà îáðàùåíèÿ
Çåìëè âîêðóã Ñîëíöà, ñóòî÷íàÿ èç-çà ñóòî÷íîãî âðàùåíèÿ Çåìëè âîêðóã
ñâîåé îñè. Ïîëîæåíèå îñè Çåìëè ìåíÿåòñÿ îòíîñèòåëüíî ñðåäíåãî ïîëîæåíèÿ èç-çà íåñôåðè÷íîñòè Çåìëè è íåñîâïàäåíèÿ ïëîñêîñòåé ýêâàòîðà è
ýêëèïòèêè è îïèñûâàåòñÿ ïðåöåññèåé è íóòàöèåé.
 ïîñëåäíåå âðåìÿ âíîâü ñòàíîâèòñÿ àêòóàëüíîé çàäà÷à êîîðäèíàòíûõ îïðåäåëåíèé ïî íàáëþäåíèÿì çâåçä, ïîñêîëüêó:
•
ãëîáàëüíûå íàâèãàöèîííûå ñïóòíèêîâûå ñèñòåìû (ÃÍÑÑ) êðèòè÷å-
4
ñêè óÿçâèìû â óëîâèÿõ ðàäèîýëåêòðîííîé áîðüáû;
•
äëÿ öåëîãî ðÿäà çàäà÷, òàêèõ êàê áàëëèñòèêà ðàêåò, ñòðîèòåëüñòâî,
ãðàâèìåòðèÿ, òðåáóþòñÿ èìåííî àñòðîíîìè÷åñêèå êîîðäèíàòû èëè
óêëîíåíèÿ îòâåñà;
•
â ñâîþ î÷åðåäü óêëîíåíèÿ îòâåñà íàèáîëåå òî÷íî îïðåäåëÿþòñÿ ïî
íàáëþäåíèÿì çâåçä;
•
ñîâðåìåííûå òåõíîëîãèè ïîçâîëÿþò ïîâûñèòü òî÷íîñòü àñòðîíîìè÷åñêèõ êîîðäèíàòíûõ îïðåäåëåíèé äî óðîâíÿ ÃÍÑÑ;
•
íà êàôåäðå àñòðîíîìèè âîçîáíîâëÿþòñÿ ðàáîòû ïî àñòðîíîìè÷åñêèì
îïðåäåëåíèÿì êîîðäèíàò ïóíêòîâ (Ñâåòëîå, Áîðîâè÷è), òðåáóþùèå
ñîâðåìåííîãî ýôåìåðèäíîãî îáåñïå÷åíèÿ.
Ïîñòàíîâêà çàäà÷è
Öåëüþ ðàáîòû ÿâëÿåòñÿ îöåíêà òåêóùåãî ñîñòîÿíèÿ àñòðîíîìè÷åñêîãî ýôåìåðèäíîãî îáåñïå÷åíèÿ, âêëþ÷àÿ:
•
ïîëîæåíèÿ è ñîáñòâåííûå äâèæåíèÿ ôóíäàìåíòàëüíûõ çâåçä êàòàëîãîâ FK6 è Hipparcos;
•
äîñòóïíûå àëãîðèòìû è ïðîãðàììíûå ñðåäñòâà äëÿ âû÷èñëåíèÿ âèäèìûõ ìåñò çâåçä;
•
âûïîëíåíèå íàáëþäåíèé çâåçä íà ïàññàæíîì èíñòðóìåíòå ñ öåëüþ
âîçìîæíîé âåðèôèêàöèè èõ âèäèìûõ ìåñò.
5
Ãëàâà 2
Èñòîðè÷åñêàÿ ÷àñòü
Áðàäëåé ïðîèçâåë ïåðâûå øàãè ïî îïðåäåëåíèþ îøèáîê èçìåðèòåëüíûõ
èíñòðóìåíòîâ. Åãî æóðíàëû íàáëþäåíèé ñâèäåòåëüñòâóþò î òîì, ÷òî îí
ñëåäèë çà ñîñòîÿíèåì èíñòðóìåíòà, îäíàêî ñïåöèàëüíûõ èññëåäîâàíèé ïðèáîðîâ íå ïðîâîäèë. Ââåë ðåãèñòðàöèþ ïîêàçàíèé òåðìîìåòðà è áàðîìåòðà
âî âðåìÿ íàáëþäåíèé, ýòè äàííûå ó÷èòûâàëèñü ïðè âû÷èñëåíèè ðåôðàêöèè.
Âêëàä Áåññåëÿ â ðàçâèòèå ìåòîäèêè íàáëþäåíèé è îáðàáîòêè ðåçóëüòàòîâ
ñëîæíî ïåðåîöåíèòü [8]. Äî íåãî íå áûëî åäèíîé ñèñòåìû îáðàáîòêè äàííûõ, íàáëþäàòåëè èñïîëüçîâàëè ðàçëè÷íûå ìåòîäèêè, ðåçóëüòàòû ðàçíûõ
îáñåðâàòîðèé áûëî ñëîæíî èëè äàæå íåâîçìîæíî ñðàâíèòü. Áåññåëü ðàçðàáîòàë òåîðèþ èíñòðóìåíòàëüíûõ è ëè÷íûõ îøèáîê, òåì ñàìûì ïîâûñèâ
òî÷íîñòü åäèíè÷íûõ èçìåðåíèé. Òàêæå îí ñîñòàâèë óíèôèöèðîâàííûå ðåäóêöèîííûå àëãîðèòìû è òàáëèöû, ïîçâîëÿþùèå ñðàâíèâàòü è îáúåäèíÿòü
äàííûå, ïîëó÷åííûå â ðàçíûõ îáñåðâàòîðèÿõ. Êðîìå òîãî, îí ïîâûñèë òî÷íîñòü è íàäåæíîñòü ðåçóëüòàòîâ ñåðèéíûõ íàáëþäåíèé ñ ïîìîùüþ ìàòåìàòè÷åñêîãî àïïàðàòà òåîðèè âåðîÿòíîñòåé è ìàòåìàòè÷åñêîé ñòàòèñòèêè,
ïðèìåíåííîãî ê îáðàáîòêå àñòðîíîìè÷åñêèõ âû÷èñëåíèé.
Äëÿ îïðåäåëåíèÿ âèäèìîãî ìåñòà ñâåòèëà íåîáõîäèìî èñïðàâèòü ïîëó÷åííûå â ðåçóëüòàòå íàáëþäåíèé êîîðäèíàòû îò èíñòðóìåíòàëüíûõ è ëè÷íûõ
îøèáîê, ó÷åñòü ðåôðàêöèþ. Àñòðîíîìè÷åñêàÿ ðåôðàêöèÿ ÿâëåíèå ïðåëîìëåíèÿ ëó÷åé îò íåáåñíîãî îáúåêòà ïðè ïðîõîæäåíèè çåìíîé àòìîñôåðû.
6
Ñìåùåíèå ïðîèñõîäèò ïî íàïðàâëåíèþ ê çåíèòó, âåëè÷èíà ñìåùåíèÿ çàâèñèò îò ïîêàçàòåëÿ ïðåëîìëåíèÿ âîçäóõà
δ
ñëåäóþùèì ñîîòíîøåíèåì:
µ, êîòîðûé ñâÿçàí ñ åãî ïëîòíîñòüþ
µ − 1 = cδ .
Çäåñü
c
íåêîòîðàÿ êîíñòàíòà.
µ
òàêæå çàâèñèò îò âëàæíîñòè âîçäóõà. Äëÿ âûâîäà ôîðìóëû ðåôðàêöèè
Áåññåëü ïîëüçîâàëñÿ ïðèíÿòûì òîãäà â ôèçèêå ñîîòíîøåíèåì ìåæäó ïîêàçàòåëåì ïðåëîìëåíèÿ âîçäóõà
íîñòè âîçäóõà îò âûñîòû
h
µ
è åãî ïëîòíîñòüþ
δ
è çàâèñèìîñòüþ ïëîò-
íàä ïîâåðõíîñòüþ çåìëè.
µ2 = 1 + 2kδ,
r0 + h
)−1
δ = δ0 exp −β(
r0
ãäå
k=
ëè;
β
µ20 −1
2δ0 ;
µ0 , δ0
çíà÷åíèÿ â ïðèçåìíîì ñëîå;
r0
ñðåäíèé ðàäèóñ Çåì-
êîíñòàíòà, îïðåäåëÿåòñÿ èç íàáëþäåíèé.
Èñòèííîå ìåñòî çâåçäû ìîæíî ïîëó÷èòü èç âèäèìîãî ìåñòà, åñëè ó÷åñòü
àáåððàöèþ [4]. Àáåððàöèÿ ïîÿâëÿåòñÿ èç-çà êîíå÷íîñòè ñêîðîñòè ðàñïðîñòðàíåíèÿ ñâåòà è ïåðåìåùåíèÿ íàáëþäàòåëÿ îòíîñèòåëüíî îáúåêòà íàáëþäåíèÿ, èñõîäÿ èç ýòîãî àáåððàöèîííîå ñìåùåíèå äåëÿò íà ïîïðàâêó çà àáåððàöèîííîå âðåìÿ è íà çâåçäíóþ àáåððàöèþ. Àáåððàöèÿ ñìåùàåò ãåîìåòðè÷åñêîå íàïðàâëåíèå íà çâåçäó â ñòîðîíó àïåêñà äâèæåíèÿ íàáëþäàòåëÿ.
∆θ = θ − θ0 ,
ãäå
θ(θ0 ) óãîë ìåæäó ãåîìåòðè÷åñêèì (âèäèìûì) íàïðàâëåíèåì íà çâåçäó
è àïåêñîì äâèæåíèÿ,
∆θ
àáåððàöèîííîå ñìåùåíèå
sin ∆θ =
Ñðåäíÿÿ âåëè÷èíà
V
sin θ0
c
V
c íàçûâàåòñÿ ïîñòîÿííîé àáåððàöèè
κ.
Ïîïðàâêà çà ñâåòîâîé ïðîìåæóòîê (àáåððàöèîííîå âðåìÿ) íå çàâèñèò îò
äâèæåíèÿ îáúåêòà è ðàâíà åãî ñìåùåíèþ ïî íåáåñíîé ñôåðå çà âðåìÿ ðàñïðîñòðàíåíèÿ ñèãíàëà îò èñòî÷íèêà äî ïðèåìíèêà.
Çåìëÿ êàê ìåñòî íàáëþäåíèÿ âðàùàåòñÿ âîêðóã ñâîåé îñè, äâèæåòñÿ ïî
îðáèòå âîêðóã áàðèöåíòðà Ñîëíå÷íîé ñèñòåìû è ïåðåìåùàåòñÿ âìåñòå ñ
áàðèöåíòðîì â ïðîñòðàíñòâå, ïîýòîìó çâåçäíóþ àáåððàöèþ ðàçäåëÿþò íà
7
ñóòî÷íóþ, ãîäè÷íóþ è âåêîâóþ. Áåññåëü íàøåë ïîñòîÿííóþ àáåððàöèè ïîñëå îáðàáîòêè íàáëþäåíèé Áðàäëåÿ è ñâîèõ íàáëþäåíèé.
Ñðåäíåå ìåñòî ïîëó÷àåòñÿ ïîñëå ó÷åòà íóòàöèè, ïåðåâîä ñðåäíåãî ìåñòà
èç îäíîé ýïîõè íà äðóãóþ ïîñëå ó÷åòà ïðåöåññèè [4]. ßâëåíèå ïðåöåññèè çàêëþ÷àåòñÿ â òîì, ÷òî òî÷êà âåñåííåãî ðàâíîäåíñòâèÿ, îòíîñèòåëüíî
êîòîðîé èçìåðÿþòñÿ ýêâàòîðèàëüíûå êîîðäèíàòû îáúåêòîâ, ïåðåìåùàåòñÿ ïî ýêëèïòèêå íàâñòðå÷ó Ñîëíöó. Ïåðèîäè÷åñêèå êîëåáàíèÿ òî÷êè âåñíû îïèñûâàþòñÿ íóòàöèåé. Îñü âðàùåíèÿ Çåìëè ìåíÿåò ñâîå ïîëîæåíèå
èç-çà âëèÿíèÿ Ëóíû è Ñîëíöà, êàê ñëåäñòâèå ïîëþñ ýêâàòîðà ñìåùàåòñÿ
îòíîñèòåëüíî ïîëþñà ýêëèïòèêè; ýòà ÷àñòü ïðåöåññèè íàçûâàåòñÿ ëóííîñîëíå÷íîé. Èçìåíåíèå ïîëîæåíèÿ ïîëþñà ýêëèïòèêè âûçûâàåò ïðåöåññèþ
îò ïëàíåò. Ñëîæèâ îáå êîìïîíåíòû ïðåöåññèè, ïîëó÷èì îáùóþ ïðåöåññèþ.
Ïðåöåññèîííûå ïàðàìåòðû Áåññåëü îïðåäåëèë ñ ïîìîùüþ òåîðèè Ëàïëàñà.
Ïîñòîÿííóþ ïðåöåññèè íàøåë èç ïðåäïîëîæåíèÿ î òîì, ÷òî âåêòîðû ñîáñòâåííûõ äâèæåíèé çâåçä ðàñïðåäåëåíû ñëó÷àéíûì îáðàçîì, ïîýòîìó èõ
ñóììîé íà îòäåëüíîé ïëîùàäêå íåáåñíîé ñôåðû ìîæíî ïðåíåáðå÷ü.
Ñîáñòâåííûì äâèæåíèåì çâåçäû íàçûâàåòñÿ èçìåíåíèå åå êîîðäèíàò íà
íåáåñíîé ñôåðå, âûçâàííûå îòíîñèòåëüíûì äâèæåíèåì ýòîãî ñâåòèëà è Ñîëíå÷íîé ñèñòåìû. Äëÿ ó÷åòà ñîáñòâåííûõ äâèæåíèé çà âðåìÿ îò ýïîõè
ýïîõå
t2
t1
ê
áûëè ïðèìåíåíû ôîðìóëû
∆α = µα (t2 − t1 )
∆δ = µδ (t2 − t1 ),
çäåñü
µα , µδ
ãîäè÷íûå ñîáñòâåííûå äâèæåíèÿ ñâåòèëà ïî ïðÿìîìó âîñ-
õîæäåíèþ è ñêëîíåíèþ ñîîòâåòñòâåííî.
Íåîáõîäèìî îòìåòèòü îïóáëèêîâàííîå â Êåíèãñáåðãñêèõ òàáëèöàõ [11] è
èñïîëüçóåìîå ñ íåêîòîðûìè ïîïðàâêàìè äàæå íà äàííûé ìîìåíò ñîîòíîøåíèå (ïðèìåíÿëîñü â [9] 1975 ãîä, îòñóòñòâóåò â [5] 1986 ãîä, ïðèñóòñòâóåò
â
[1] íàðàâíå ñ äðóãèì àëãîðèòìîì), îñóùåñòâëÿþùåå ïåðåâîä ìåæäó âè-
8
äèìûìè è ñðåäíèìè ìåñòàìè
αvid − αsr = Aa + Bb + Cc + Dd + E + µα t
δvid − δsr = Aa0 + Bb0 + Cc0 + Dd0 + µδ t
Âåëè÷èíû
A, B, C, D, E, a, b, c, d, a0 , b0 , c0 , d0
íàçûâàþòñÿ Áåññåëåâûìè ÷èñ-
ëàìè. ×èñëà, îáîçíà÷åííûå çàãëàâíûìè áóêâàìè, íå çàâèñÿò îò êîîðäèíàò
íàáëþäàåìîé çâåçäû è ÿâëÿþòñÿ ôóíêöèÿìè âðåìåíè. Îñòàëüíûå ÷èñëà
ñ÷èòàþòñÿ äëÿ êàæäîé çâåçäû îòäåëüíî.
9
Ãëàâà 3
Îáçîð òåêóùåãî ñîñòîÿíèÿ
ïðîáëåìû
t
ìîìåíò íàáëþäåíèÿ, çàäàí â øêàëå
T DB
t0 ìîìåíò âðåìåíè, çàäàí â øêàëå T DB
→
−
rb (t) âåêòîð ïîëîæåíèÿ ïëàíåòû â ìîìåíò t
îòíîñèòåëüíî áàðèöåíòðà
Ñîëíå÷íîé ñèñòåìû íà ñðåäíåå ðàâíîäåíñòâèå è ýêâàòîð ýïîõè
→
−
rb (t) âåêòîð ïîëîæåíèÿ çâåçäû â ýïîõó t0
îòíîñèòåëüíî áàðèöåíòðà Ñîë-
íå÷íîé ñèñòåìû íà ñðåäíåå ðàâíîäåíñòâèå è ýêâàòîð ýïîõè
−
→
Eb (t)
t0
t0
áàðèöåíòðè÷åñêèé âåêòîð ïîëîæåíèÿ Çåìëè â ýïîõó íàáëþäåíèÿ
t
îòíîñèòåëüíî áàðèöåíòðà Ñîëíå÷íîé ñèñòåìû íà ñðåäíåå ðàâíîäåíñòâèå è
ýêâàòîð ýïîõè
t0 .
Âèäèìûå ìåñòà, îòíåñåííûå ê èñòèííîìó ðàâíîäåíñòâèþ äàòû, ÿâëÿþòñÿ
îñíîâíûì òèïîì ýôåìåðèä íåáåñíûõ îáúåêòîâ, ïóáëèêóåìûõ â åæåãîäíèêàõ. Îíè âû÷èñëÿþòñÿ ñëåäóþùèì îáðàçîì [6]:
−
→
→
−
→
−
→
−̇
0
us (t ) = N (t)P (t, t0 )A G( rb (t0 ) + (t − t0 ) rb (t0 ) − Eb (t))
→
−
→
−
→
−
0
up (t ) = N (t)P (t, t0 )A G( rb (t − τ ) − E b (t)) ,
ãäå
t0 ýïîõà íàáëþäåíèÿ â øêàëå T T (T DT );
→
−̇
r (t ) âåêòîð ïðîñòðàíñòâåííîãî äâèæåíèÿ
b
0
çâåçäû, ó÷èòûâàþùèé ñîá-
ñòâåííîå äâèæåíèå, ðàäèàëüíóþ ñêîðîñòü è ïàðàëëàêñ çâåçäû äëÿ ýïîõè
10
t0 ;
τ
ñâåòîâîé ïðîìåæóòîê (àáåððàöèîííîå âðåìÿ), íàõîäèòñÿ èòåðàöèÿìè èç
ñëåäóþùåé ôîðìóëû
Ïóñòü
E ìîäóëü âåêòîðà ãåëèîöåíòðè÷åñêîãî ïîëîæåíèÿ Çåìëè, P
ïîëîæåíèÿ îáúåêòà,
10−9
Q
åãî ãåëèîöåíòðè÷åñêîãî ïîëîæåíèÿ,
µ
c2
ãåîöåíòðè÷åñê
= 9.8704 ∗
à.å. ãðàâèòàöèîííûé ðàäèóñ Ñîëíöà.
cτ = P +
2µ E + Q + P
ln
c2 E + Q − P
G
ãðàâèòàöèîííîå îòêëîíåíèå ñâåòà
A
ó÷åò çâåçäíîé àáåððàöèè
P (t, t0 ) ìàòðèöà ïðåöåññèè äëÿ ïåðåõîäà îò ñðåäíåãî ðàâíîäåíñòâèÿ ýïîõè
t0
ê ñðåäíåìó â ýïîõó
Ìàòðèöû âðàùåíèÿ
t
(149)
Ri (ϕ)
îñóùåñòâëÿþò ïîâîðîòû ñèñòåìû êîîðäèíàò (ñ
ïåðïåíäèêóëÿðíûìè îñÿìè) ïðîòèâ ÷àñîâîé ñòðåëêè íà óãîë
íî îñåé
ϕ îòíîñèòåëü-
x, y, z(1, 2, 3)
1
0
0
R1 (ϕ) =
0
cos
ϕ
sin
ϕ
0 − sin ϕ cos ϕ
cos ϕ 0 − sin ϕ
R2 (ϕ) =
0
1
0
sin ϕ 0
cos ϕ
cos ϕ sin ϕ 0
R3 (ϕ) =
−
sin
ϕ
cos
ϕ
0
0
0
1
P = R3 (−zA )R2 (θA )R3 (−ξA )
ξA , zA , θA óãëû Ýéëåðà: ξA ïðåöåññèÿ â ýêâàòîðå çà âðåìÿ t−t0 , 90◦ +zA
ïðÿìîå âîñõîæäåíèå óçëà, îòñ÷èòûâàåìîãî ïî ýêâàòîðó
t, θA
íàêëîí ýêâàòîðà
N (t)
ìàòðèöà ó÷åòà íóòàöèè äëÿ ïåðåõîäà îò ñðåäíåãî ðàâíîäåíñòâèÿ ê
èñòèííîìó â ýïîõó
t
t îò ðàâíîäåíñòâèÿ
ê ýêâàòîðó
t0 .
t.
→
−
−
−
r = N→
rc = R1 (−0 − ∆s )R3 (−∆ψs )R1 (0 )→
rc
11
u(t0 )
âèäèìîå ãåîöåíòðè÷åñêîå ìåñòî çâåçäû íà ìîìåíò íàáëþäåíèÿ
t0
â
øêàëå TT, îòíåñåííîå ê èñòèííîìó ðàâíîäåíñòâèþ è ýêâàòîðó.
Äëÿ ïðèâåäåíèÿ íà âèäèìîå ìåñòî áûëè èñïîëüçîâàíû ïàêåòû SOFA (Standards
Of Fundamental Astronomy) è NOVAS (Naval Observatory Vector Astrometry
Software), ñàéòû NAOJ è GAVO, à òàêæå àëãîðèòì, îïèñàííûé â
[6] è èñ-
ïîëüçóþùèé êîîðäèíàòû èç Àñòðîíîìè÷åñêîãî Åæåãîäíèêà çà 2016 ãîä [1].
 ðàñ÷åòàõ SOFA è NOVAS èñïîëüçîâàëèñü ýôåìåðèäû DE405, ñîçäàííûå
â 1997 ãîäó. Ñîãëàñíî äîêóìåíòó User's Guide to NOVAS Version C3.1, ïðîãðàììû SOFA è NOVAS ÿâëÿþòñÿ ïî÷òè íåçàâèñèìûìè, ïîýòîìó èõ ñðàâíåíèå èìååò ñìûñë.
SOFA IAU Service, êîòîðàÿ îáñëóæèâàåò Standing Working Group under
Division A (Fundamental Astronomy) [14]. ÌÀÑ óòâåðäèë èíèöèàòèâó SOFA
íà Ãåíåðàëüíîé Àññàìáëåå â 1994 ãîäó äëÿ ïóáëèêàöèè íàäåæíîãî íàáîðà
êîíñòàíò è ôóíäàìåíòàëüíîé àñòðîíîìèè è àëãîðèòìîâ. Íà ñëåäóþùåé Ãåíåðàëüíîé Àññàìáëåå â 1997 áûëî çàÿâëåíî î íàçíà÷åíèè of a review board è
âûáîðå ìåñòà äëÿ öåíòðà SOFA (âûõîäà ïðîäóêòîâ SOFA). Åå ïðîãðàììíîå
îáåñïå÷åíèå äîñòóïíî íà ÿçûêàõ Fortran è C è ñîäåðæèò 166 àñòðîíîìè÷åñêèõ è 55 âñïîìîãàòåëüíûõ âåêòîðíî-ìàòðè÷íûõ ïðîãðàìì.
Àñòðîìåòðè÷åñêîå ïðîãðàììíîå îáåñïå÷åíèå Ìîðñêîé Îáñåðâàòîðèè (NOVAS)
ýòî áèáëèîòåêè, ñîäåðæàùèå êîä íà ÿçûêàõ Fortran, C è Python. Âû÷èñëåíèÿ NOVAS èìåþò ìèëëèñåêóíäíóþ òî÷íîñòü. Ñóùåñòâóåò òðè óðîâíÿ
ôóíêöèé: áàçîâûå, óòèëèòàðíûå è óïðàâëÿþùèå. Áàçîâûå ôóíêöèè ïîñòàâëÿþò çíà÷åíèÿ ôóíäàìåíòàëüíûõ ïåðåìåííûõ, òàêèõ êàê óãëû íóòàöèè è
ãåëèîöåíòðè÷åñêèå ïîëîæåíèÿ òåë Ñîëíå÷íîé ñèñòåìû, íà ðàçëè÷íûå ýïîõè. Óòèëèòàðíûå ôóíêöèè âûïîëíÿþò âû÷èñëåíèÿ, ñîîòâåòñòâóþùèå èíäèâèäóàëüíûì ôèçè÷åñêèì ýôôåêòàì èëè ïðåîáðàçîâàíèÿì (àáåððàöèÿ,
èñêðèâëåíèå ñâåòà, ïðåöåññèÿ, äâèæåíèå ïîëþñà è ò. ä.). Óïðàâëÿþùèå
ôóíêöèè âûçûâàþò áàçîâûå è óòèëèòàðíûå ïîäïðîãðàììû â ñîîòâåòñòâóþùåì ïîðÿäêå, ÷òîáû ðàññ÷èòàòü êîîðäèíàòû çâåçä èëè òåë Ñîëíå÷íîé
12
ñèñòåìû íà îïðåäåëåííóþ äàòó è âðåìÿ. Ïðè æåëàíèè ïîëüçîâàòåëè ìîãóò
âçàèìîäåéñòâîâàòü èñêëþ÷èòåëüíî ñ óïðàâëÿþùèìè ôóíêöèÿìè è íå çàäóìûâàòüñÿ î ïîäðîáíîñòÿõ ãåîìåòðèè èëè ôèçè÷åñêèõ ìîäåëåé, âêëþ÷åííûõ
â ðàñ÷åòû.
Âåðñèÿ NOVAS íà ÿçûêå Fortran îòíîñèòñÿ ê êîíöó 1970õ, íî ðåãóëÿðíî îáíîâëÿëÿñü, ÷òîáû èñïîëüçîâàòü íîâûå, áîëåå òî÷íûå ìîäåëè, êîòîðûå ïðåäñòàâëÿþò ðàçâèâàþùèåñÿ ñòàíäàðòû ìåæäóíàðîäíîãî àñòðîíîìè÷åñêîãî è
ãåîäåçè÷åñêîãî îáùåñòâ.  íà÷àëå 1990õ ãðóïïà îïòè÷åñêîãî èíòåðôåðîìåòðà Ìîðñêîé Îáñåðâàòîðèè ÑØÀ/Ìîðñêîé Íàó÷íî-èññëåäîâàòåëüñêîé Ëàáîðàòîðèè ïðåîáðàçîâàëà ÷àñòü NOVAS â Ñ äëÿ èñïîëüçîâàíèÿ â ñâîèõ ïðîåêòàõ.Ýòà ðàáîòà ñôîðìèðîâàëà îñíîâó ïåðâîãî ïîëíîãî èçäàíèÿ NOVAS
â Ñ, êîòîðîå áûëî çàâåðøåíî USNO Astronomical Applications Department
è âûïóùåíî â 1996. Îñíîâíîå èçäàíèå NOVAS íà ÿçûêå Fortran ïîÿâèëîñü â 1998 ñ ïåðâîíà÷àëüíîé öåëüþ ïîääåðæàòü äàííûå, ñîîòâåòñòâóþùèå
Ìåæäóíàðîäíîé Íåáåñíîé Ñèñòåìå Îòñ÷åòà. Âñêîðå ïîñëå ýòîãî C-âåðñèÿ
NOVAS áûëà îáíîâëåíà äî C2.0, ÷òîáû îòðàçèòü èçìåíåíèÿ íà Fortran
è ðàñøèðèòü âîçìîæíîñòè. Ïîçæå NOVAS ïðåäñòàâèëà èçäàíèå íà ÿçûêå Python.
Ïðè âû÷èñëåíèÿõ ñ ïîëíîé òî÷íîñòüþ, èñïîëüçóþùèõ îäèíàêîâûå èñòî÷íèêè äàííûõ, ðàçëè÷èÿ â ðåçóëüòàòàõ Fortran è C èçäàíèÿõ NOVAS ïðè
îäèíàêîâûõ ðàñ÷åòàõ äîëæíû íå ïðåâûøàòü
íîé ñèñòåìû è
7 ∗ 10−10
ìñä (3
∗ 10−15 ðàä)
6 ∗ 10−8 ìñä
äëÿ òåë Ñîëíå÷-
äëÿ çâåçä [12].
Äëÿ ïîëó÷åíèÿ êîîðäèíàò Ïîëÿðíîé çâåçäû ñ ïîìîùüþ ïàêåòà SOFA ïîíàäîáèòñÿ ïîäïðîãðàììà iauAtco13, êîòîðàÿ ïðåîáðàçóåò ñêëîíåíèå è ïðÿìîå
âîñõîæäåíèå
[α, δ]
íà ýïîõó
J2000.0
(â êà÷åñòâå âñïîìîãàòåëüíûõ äàííûõ
òðåáóþòñÿ ñîáñòâåííûå äâèæåíèÿ âäîëü
α
è âäîëü
δ,
ïàðàëëàêñ, ëó÷åâàÿ
ñêîðîñòü, þëèàíñêàÿ äàòà, UT1-UTC, äîëãîòà, ãåîäåçè÷åñêàÿ øèðîòà, âûñîòà íàä ýëëèïñîèäîì, êîîðäèíàòû ïîëþñîâ, äàâëåíèå, òåìïåðàòóðà, âëàæíîñòü, äëèíà âîëíû) è ïîëó÷àåò âèäèìûå ìåñòà îáúåêòà (âèäèìûé àçèìóò,
âèäèìîå çåíèòíîå ðàññòîÿíèå, âèäèìûé ÷àñîâîé óãîë, âèäèìîå ñêëîíåíèå,
èäèìîå ïðÿìîå âîñõîæäåíèå), è òå ïîäïðîãðàììû, íà êîòîðûå îíà ññûëà-
13
åòñÿ [13].
 òàáëèöàõ 3.1,
3.2 ïðåäñòàâëåíû ýêâàòîðèàëüíûå êîîðäèíàòû Ïîëÿðíîé
çâåçäû ñ 1 ìàðòà 12 ÷àñîâ ïî 1 èþíÿ 0 ÷àñîâ ñ øàãîì 12 ÷àñîâ.
Òàáëèöà 3.1: ïðÿìîå âîñõîæäåíèå
αU M i
äàòà
åæåã.
novas
sofa1997
sofa2007
GAVO
NAOJ
2457449
2 51 32.61
32.65
33.27
33.3
32.6
33.3
2457449.5
2 51 31.85
31.89
32.51
32.54
31.84
32.54
2457450
2 51 31.09
31.14
31.75
31.79
31.09
31.79
2457450.5
2 51 30.33
30.38
30.99
31.03
30.33
31.03
2457451
2 51 29.57
29.62
30.23
30.26
29.57
30.27
2457451.5
2 51 28.79
28.84
29.46
29.49
28.79
29.49
2457452
2 51 28
28.06
28.67
28.71
28.01
28.71
2457452.5
2 51 27.2
27.26
27.87
27.91
27.21
27.91
2457453
2 51 26.39
26.44
27.05
27.09
26.39
27.09
2457453.5
2 51 25.54
25.6
26.21
26.25
25.55
26.25
2457454
2 51 24.69
24.74
25.36
25.39
24.69
25.39
2457454.5
2 51 23.81
23.87
24.48
24.52
23.82
24.52
2457455
2 51 22.92
22.98
23.59
23.63
22.93
23.63
2457455.5
2 51 22.03
22.08
22.69
22.73
22.03
22.73
2457456
2 51 21.13
21.18
21.8
21.83
21.13
21.83
2457456.5
2 51 20.25
20.29
20.91
20.94
20.24
20.94
2457457
2 51 19.38
19.42
20.04
20.07
19.37
20.07
2457457.5
2 51 18.54
18.57
19.19
19.22
18.52
19.22
2457458
2 51 17.72
17.76
18.37
18.41
17.71
18.41
2457458.5
2 51 16.95
16.98
17.59
17.63
16.93
17.63
2457459
2 51 16.2
16.24
16.85
16.89
16.19
16.89
2457459.5
2 51 15.5
15.54
16.15
16.18
15.49
16.18
2457460
2 51 14.83
14.87
15.48
15.52
14.82
15.52
2457460.5
2 51 14.19
14.23
14.85
14.88
14.18
14.88
2457461
2 51 13.57
13.62
14.23
14.27
13.57
14.27
2457461.5
2 51 12.98
13.02
13.64
13.67
12.97
13.67
14
2457462
2 51 12.38
12.43
13.05
13.08
12.38
13.08
2457462.5
2 51 11.79
11.85
12.46
12.5
11.8
12.5
2457463
2 51 11.2
11.26
11.87
11.9
11.21
11.9
2457463.5
2 51 10.6
10.65
11.27
11.3
10.6
11.3
2457464
2 51 9.98
10.04
10.65
10.69
9.991
10.69
2457464.5
2 51 9.35
9.41
10.02
10.06
9.36
10.06
2457465
2 51 8.71
8.763
9.377
9.412
8.713
9.412
2457465.5
2 51 8.04
8.099
8.713
8.748
8.049
8.747
2457466
2 51 7.36
7.418
8.033
8.067
7.369
8.067
2457466.5
2 51 6.67
6.724
7.339
7.373
6.675
7.373
2457467
2 51 5.97
6.019
6.634
6.668
5.97
6.668
2457467.5
2 51 5.26
5.307
5.921
5.956
5.257
5.956
2457468
2 51 4.54
4.59
5.205
5.239
4.541
5.239
2457468.5
2 51 3.83
3.874
4.488
4.523
3.825
4.523
2457469
2 51 3.11
3.163
3.777
3.811
3.113
3.811
2457469.5
2 51 2.41
2.459
3.074
3.108
2.41
3.108
2457470
2 51 1.72
1.769
2.383
2.417
1.719
2.417
2457470.5
2 51 1.05
1.094
1.708
1.742
1.044
1.742
2457471
2 51 0.39
0.4373
1.051
1.086
0.3876
1.086
2457471.5
2 50 59.76
59.8
0.4164
0.451
59.75
0.451
2457472
2 50 59.15
59.19
59.8
59.84
59.14
59.84
2457472.5
2 50 58.57
58.6
59.22
59.25
58.55
59.25
2457473
2 50 57.99
58.04
58.65
58.69
57.99
58.69
2457473.5
2 50 57.46
57.5
58.12
58.15
57.45
58.15
2457474
2 50 56.94
56.99
57.6
57.64
56.94
57.64
2457474.5
2 50 56.46
56.49
57.11
57.14
56.45
57.14
2457475
2 50 55.98
56.02
56.64
56.67
55.97
56.67
2457475.5
2 50 55.53
55.57
56.18
56.22
55.52
56.22
2457476
2 50 55.08
55.13
55.74
55.78
55.08
55.78
2457476.5
2 50 54.65
54.7
55.32
55.35
54.65
55.35
2457477
2 50 54.23
54.28
54.9
54.93
54.23
54.93
2457477.5
2 50 53.82
53.87
54.48
54.52
53.82
54.52
2457478
2 50 53.41
53.45
54.07
54.1
53.41
54.1
15
2457478.5
2 50 52.99
53.04
53.65
53.69
52.99
53.69
2457479
2 50 52.57
52.61
53.23
53.26
52.57
53.26
2457479.5
2 50 52.13
52.18
52.8
52.83
52.13
52.83
2457480
2 50 51.69
51.74
52.35
52.39
51.69
52.38
2457480.5
2 50 51.22
51.28
51.89
51.93
51.23
51.93
2457481
2 50 50.75
50.8
51.42
51.45
50.76
51.45
2457481.5
2 50 50.26
50.32
50.93
50.96
50.27
50.97
2457482
2 50 49.76
49.82
50.43
50.46
49.77
50.47
2457482.5
2 50 49.26
49.31
49.92
49.96
49.26
49.96
2457483
2 50 48.74
48.8
49.41
49.44
48.75
49.44
2457483.5
2 50 48.24
48.29
48.9
48.93
48.24
48.93
2457484
2 50 47.74
47.79
48.4
48.44
47.74
48.44
2457484.5
2 50 47.28
47.31
47.92
47.96
47.26
47.96
2457485
2 50 46.82
46.86
47.47
47.51
46.81
47.51
2457485.5
2 50 46.42
46.45
47.06
47.09
46.4
47.09
2457486
2 50 46.01
46.07
46.69
46.72
46.02
46.72
2457486.5
2 50 45.71
45.74
46.36
46.39
45.69
46.39
2457487
2 50 45.4
45.45
46.07
46.1
45.4
46.1
2457487.5
2 50 45.18
45.21
45.82
45.85
45.16
45.85
2457488
2 50 44.94
44.99
45.61
45.64
44.94
45.64
2457488.5
2 50 44.77
44.81
45.42
45.45
44.76
45.45
2457489
2 50 44.59
44.64
45.25
45.29
44.59
45.29
2457489.5
2 50 44.43
44.48
45.09
45.13
44.43
45.13
2457490
2 50 44.27
44.32
44.93
44.97
44.27
44.97
2457490.5
2 50 44.1
44.16
44.77
44.8
44.11
44.8
2457491
2 50 43.93
43.98
44.59
44.63
43.93
44.63
2457491.5
2 50 43.73
43.79
44.4
44.44
43.74
44.44
2457492
2 50 43.54
43.58
44.2
44.23
43.53
44.23
2457492.5
2 50 43.31
43.36
43.97
44.01
43.31
44.01
2457493
2 50 43.08
43.12
43.73
43.77
43.07
43.77
2457493.5
2 50 42.82
42.87
43.48
43.51
42.82
43.52
2457494
2 50 42.56
42.6
43.22
43.25
42.55
43.25
2457494.5
2 50 42.28
42.33
42.94
42.98
42.28
42.98
16
2457495
2 50 42.01
42.05
42.67
42.7
42
42.7
2457495.5
2 50 41.73
41.78
42.39
42.43
41.73
42.42
2457496
2 50 41.45
41.51
42.12
42.15
41.46
42.15
2457496.5
2 50 41.2
41.24
41.86
41.89
41.19
41.89
2457497
2 50 40.94
40.99
41.6
41.64
40.94
41.64
2457497.5
2 50 40.72
40.76
41.37
41.4
40.71
41.4
2457498
2 50 40.5
40.54
41.15
41.19
40.49
41.19
2457498.5
2 50 40.31
40.34
40.96
40.99
40.29
40.99
2457499
2 50 40.12
40.17
40.79
40.82
40.12
40.82
2457499.5
2 50 39.99
40.03
40.64
40.67
39.98
40.67
2457500
2 50 39.86
39.91
40.52
40.55
39.86
40.55
2457500.5
2 50 39.78
39.81
40.43
40.46
39.76
40.46
2457501
2 50 39.69
39.74
40.36
40.39
39.69
40.39
2457501.5
2 50 39.66
39.7
40.31
40.35
39.65
40.35
2457502
2 50 39.63
39.68
40.29
40.33
39.63
40.33
2457502.5
2 50 39.64
39.68
40.29
40.32
39.63
40.32
2457503
2 50 39.65
39.69
40.31
40.34
39.64
40.34
2457503.5
2 50 39.68
39.72
40.34
40.37
39.67
40.37
2457504
2 50 39.72
39.76
40.38
40.41
39.71
40.41
2457504.5
2 50 39.77
39.81
40.42
40.46
39.76
40.46
2457505
2 50 39.82
39.86
40.48
40.51
39.81
40.51
2457505.5
2 50 39.86
39.91
40.53
40.56
39.86
40.56
2457506
2 50 39.91
39.96
40.57
40.61
39.91
40.61
2457506.5
2 50 39.94
40
40.61
40.65
39.95
40.65
2457507
2 50 39.98
40.03
40.64
40.67
39.98
40.67
2457507.5
2 50 39.99
40.05
40.66
40.69
40
40.69
2457508
2 50 40
40.05
40.66
40.7
40
40.7
2457508.5
2 50 39.99
40.04
40.66
40.69
39.99
40.69
2457509
2 50 39.98
40.02
40.64
40.67
39.97
40.67
2457509.5
2 50 39.95
39.99
40.61
40.64
39.95
40.64
2457510
2 50 39.91
39.96
40.57
40.61
39.91
40.61
2457510.5
2 50 39.88
39.92
40.54
40.57
39.88
40.57
2457511
2 50 39.85
39.89
40.51
40.54
39.85
40.54
17
2457511.5
2 50 39.85
39.88
40.49
40.53
39.83
40.52
2457512
2 50 39.84
39.88
40.49
40.53
39.83
40.53
2457512.5
2 50 39.88
39.91
40.53
40.56
39.86
40.56
2457513
2 50 39.93
39.98
40.59
40.63
39.93
40.63
2457513.5
2 50 40.06
40.09
40.7
40.73
40.04
40.73
2457514
2 50 40.19
40.24
40.85
40.88
40.19
40.88
2457514.5
2 50 40.4
40.43
41.04
41.08
40.38
41.08
2457515
2 50 40.61
40.66
41.28
41.31
40.61
41.31
2457515.5
2 50 40.9
40.93
41.55
41.58
40.88
41.58
2457516
2 50 41.19
41.23
41.84
41.88
41.18
41.88
2457516.5
2 50 41.51
41.55
42.16
42.19
41.5
42.19
2457517
2 50 41.83
41.87
42.48
42.52
41.82
42.52
2457517.5
2 50 42.15
42.2
42.81
42.84
42.15
42.84
2457518
2 50 42.47
42.51
43.13
43.16
42.47
43.16
2457518.5
2 50 42.76
42.82
43.43
43.47
42.77
43.47
2457519
2 50 43.06
43.11
43.72
43.75
43.06
43.75
2457519.5
2 50 43.32
43.37
43.99
44.02
43.33
44.02
2457520
2 50 43.58
43.62
44.23
44.27
43.57
44.27
2457520.5
2 50 43.8
43.85
44.46
44.5
43.8
44.5
2457521
2 50 44.02
44.07
44.68
44.71
44.02
44.71
2457521.5
2 50 44.22
44.27
44.88
44.92
44.22
44.92
2457522
2 50 44.42
44.46
45.08
45.11
44.42
45.11
2457522.5
2 50 44.61
44.66
45.27
45.3
44.61
45.3
2457523
2 50 44.8
44.85
45.46
45.5
44.8
45.5
2457523.5
2 50 45.01
45.05
45.66
45.7
45
45.7
2457524
2 50 45.21
45.26
45.87
45.9
45.21
45.9
2457524.5
2 50 45.44
45.48
46.09
46.13
45.43
46.13
2457525
2 50 45.68
45.72
46.33
46.36
45.67
46.36
2457525.5
2 50 45.94
45.98
46.59
46.62
45.93
46.62
2457526
2 50 46.21
46.25
46.87
46.9
46.21
46.9
2457526.5
2 50 46.52
46.56
47.17
47.21
46.51
47.2
2457527
2 50 46.84
46.89
47.5
47.53
46.84
47.53
2457527.5
2 50 47.2
47.24
47.85
47.89
47.19
47.89
18
2457528
2 50 47.57
47.62
48.23
48.26
47.57
48.26
2457528.5
2 50 47.98
48.02
48.63
48.67
47.97
48.67
2457529
2 50 48.4
48.44
49.06
49.09
48.4
49.09
2457529.5
2 50 48.86
48.89
49.5
49.54
48.84
49.54
2457530
2 50 49.31
49.35
49.97
50
49.31
50
2457530.5
2 50 49.8
49.83
50.45
50.48
49.79
50.48
2457531
2 50 50.28
50.32
50.94
50.97
50.28
50.97
2457531.5
2 50 50.78
50.82
51.43
51.47
50.77
51.47
2457532
2 50 51.28
51.32
51.94
51.97
51.28
51.97
2457532.5
2 50 51.78
51.82
52.44
52.47
51.78
52.47
2457533
2 50 52.27
52.32
52.93
52.97
52.27
52.97
2457533.5
2 50 52.76
52.81
53.42
53.46
52.76
53.46
2457534
2 50 53.24
53.29
53.9
53.94
53.24
53.94
2457534.5
2 50 53.7
53.76
54.37
54.4
53.71
54.41
2457535
2 50 54.16
54.21
54.82
54.86
54.16
54.86
2457535.5
2 50 54.6
54.65
55.26
55.3
54.6
55.3
2457536
2 50 55.03
55.07
55.69
55.72
55.03
55.72
2457536.5
2 50 55.44
55.49
56.1
56.13
55.44
56.13
2457537
2 50 55.84
55.89
56.5
56.54
55.84
56.54
2457537.5
2 50 56.24
56.29
56.9
56.94
56.24
56.94
2457538
2 50 56.65
56.69
57.31
57.34
56.64
57.34
2457538.5
2 50 57.06
57.1
57.71
57.75
57.05
57.75
2457539
2 50 57.48
57.52
58.13
58.17
57.47
58.17
2457539.5
2 50 57.93
57.96
58.57
58.61
57.91
58.61
2457540
2 50 58.39
58.43
59.04
59.08
58.38
59.08
2457540.5
2 50 58.9
58.93
59.54
59.58
58.88
59.58
Òàáëèöà 3.2: ñêëîíåíèå
αU M i
äàòà
åæåã.
novas
sofa1997
sofa2007
GAVO
NAOJ
2457449
89 20 7.91
7.91
7.98
7.97
7.91
7.97
2457449.5
89 20 7.83
7.83
7.9
7.9
7.84
7.9
19
2457450
89 20 7.76
7.76
7.83
7.83
7.77
7.83
2457450.5
89 20 7.7
7.69
7.76
7.76
7.7
7.76
2457451
89 20 7.63
7.63
7.7
7.69
7.63
7.69
2457451.5
89 20 7.57
7.56
7.63
7.63
7.57
7.63
2457452
89 20 7.5
7.5
7.57
7.56
7.5
7.56
2457452.5
89 20 7.44
7.43
7.5
7.5
7.44
7.5
2457453
89 20 7.37
7.37
7.44
7.44
7.38
7.44
2457453.5
89 20 7.31
7.31
7.38
7.37
7.31
7.37
2457454
89 20 7.24
7.24
7.31
7.3
7.24
7.3
2457454.5
89 20 7.17
7.17
7.24
7.23
7.17
7.23
2457455
89 20 7.09
7.09
7.16
7.16
7.1
7.16
2457455.5
89 20 7.01
7.01
7.08
7.08
7.02
7.08
2457456
89 20 6.93
6.92
6.99
6.99
6.93
6.99
2457456.5
89 20 6.83
6.83
6.9
6.89
6.83
6.89
2457457
89 20 6.73
6.73
6.8
6.79
6.73
6.79
2457457.5
89 20 6.62
6.62
6.69
6.69
6.63
6.69
2457458
89 20 6.51
6.51
6.58
6.57
6.51
6.57
2457458.5
89 20 6.4
6.39
6.46
6.46
6.4
6.46
2457459
89 20 6.28
6.27
6.35
6.34
6.28
6.34
2457459.5
89 20 6.16
6.16
6.23
6.22
6.16
6.22
2457460
89 20 6.04
6.04
6.11
6.1
6.04
6.1
2457460.5
89 20 5.93
5.92
5.99
5.99
5.92
5.99
2457461
89 20 5.81
5.81
5.88
5.87
5.81
5.87
2457461.5
89 20 5.7
5.7
5.77
5.76
5.7
5.76
2457462
89 20 5.59
5.59
5.66
5.65
5.59
5.65
2457462.5
89 20 5.49
5.49
5.55
5.55
5.49
5.55
2457463
89 20 5.39
5.38
5.45
5.45
5.39
5.45
2457463.5
89 20 5.29
5.29
5.36
5.35
5.29
5.35
2457464
89 20 5.2
5.19
5.26
5.25
5.19
5.25
2457464.5
89 20 5.1
5.09
5.16
5.16
5.1
5.16
2457465
89 20 5
5
5.07
5.06
5
5.06
2457465.5
89 20 4.9
4.9
4.97
4.96
4.9
4.96
2457466
89 20 4.8
4.8
4.87
4.87
4.8
4.86
20
2457466.5
89 20 4.7
4.7
4.77
4.76
4.7
4.76
2457467
89 20 4.6
4.59
4.66
4.66
4.6
4.66
2457467.5
89 20 4.49
4.48
4.55
4.55
4.49
4.55
2457468
89 20 4.38
4.37
4.44
4.44
4.38
4.44
2457468.5
89 20 4.26
4.25
4.32
4.32
4.26
4.32
2457469
89 20 4.14
4.13
4.2
4.2
4.14
4.2
2457469.5
89 20 4.01
4.01
4.08
4.07
4.01
4.07
2457470
89 20 3.88
3.88
3.95
3.94
3.88
3.94
2457470.5
89 20 3.75
3.74
3.81
3.81
3.75
3.81
2457471
89 20 3.61
3.61
3.68
3.67
3.61
3.67
2457471.5
89 20 3.47
3.47
3.54
3.53
3.47
3.53
2457472
89 20 3.33
3.33
3.4
3.39
3.33
3.39
2457472.5
89 20 3.19
3.18
3.25
3.25
3.19
3.25
2457473
89 20 3.04
3.04
3.11
3.11
3.04
3.1
2457473.5
89 20 2.9
2.89
2.96
2.96
2.9
2.96
2457474
89 20 2.75
2.75
2.82
2.81
2.75
2.81
2457474.5
89 20 2.61
2.6
2.67
2.67
2.61
2.67
2457475
89 20 2.47
2.46
2.53
2.53
2.47
2.53
2457475.5
89 20 2.33
2.32
2.39
2.39
2.32
2.39
2457476
89 20 2.19
2.18
2.25
2.25
2.19
2.25
2457476.5
89 20 2.05
2.04
2.11
2.11
2.05
2.11
2457477
89 20 1.92
1.91
1.98
1.98
1.91
1.98
2457477.5
89 20 1.79
1.78
1.85
1.84
1.78
1.84
2457478
89 20 1.65
1.65
1.72
1.71
1.65
1.71
2457478.5
89 20 1.53
1.52
1.59
1.59
1.52
1.59
2457479
89 20 1.4
1.4
1.46
1.46
1.4
1.46
2457479.5
89 20 1.28
1.27
1.34
1.34
1.28
1.34
2457480
89 20 1.15
1.15
1.22
1.22
1.15
1.21
2457480.5
89 20 1.03
1.03
1.1
1.09
1.03
1.09
2457481
89 20 0.9
0.902
0.971
0.967
0.906
0.97
2457481.5
89 20 0.78
0.776
0.845
0.841
0.781
0.84
2457482
89 20 0.65
0.648
0.719
0.715
0.652
0.71
2457482.5
89 20 0.52
0.516
0.586
0.582
0.52
0.58
21
2457483
89 20 0.38
0.379
0.449
0.445
0.383
0.44
2457483.5
89 20 0.24
0.236
0.305
0.301
0.24
0.3
2457484
89 20 0.09
0.0878
0.157
0.154
0.092
0.15
2457484.5
89 19 59.9
59.9
0.0024
60
59.9
0
2457485
89 19 59.8
59.8
59.8
59.8
59.8
59.8
2457485.5
89 19 59.6
59.6
59.7
59.7
59.6
59.7
2457486
89 19 59.4
59.4
59.5
59.5
59.4
59.5
2457486.5
89 19 59.3
59.3
59.3
59.3
59.3
59.3
2457487
89 19 59.1
59.1
59.2
59.2
59.1
59.2
2457487.5
89 19 59
58.9
59
59
58.9
59
2457488
89 19 58.8
58.8
58.9
58.8
58.8
58.9
2457488.5
89 19 58.6
58.6
58.7
58.7
58.6
58.7
2457489
89 19 58.5
58.5
58.5
58.5
58.5
58.5
2457489.5
89 19 58.3
58.3
58.4
58.4
58.3
58.4
2457490
89 19 58.2
58.2
58.2
58.2
58.2
58.2
2457490.5
89 19 58
58
58.1
58.1
58
58.1
2457491
89 19 57.9
57.9
58
58
57.9
58
2457491.5
89 19 57.8
57.8
57.8
57.8
57.8
57.8
2457492
89 19 57.6
57.6
57.7
57.7
57.6
57.7
2457492.5
89 19 57.5
57.5
57.6
57.5
57.5
57.5
2457493
89 19 57.4
57.3
57.4
57.4
57.3
57.4
2457493.5
89 19 57.2
57.2
57.3
57.3
57.2
57.3
2457494
89 19 57.1
57.1
57.1
57.1
57.1
57.1
2457494.5
89 19 56.9
56.9
57
57
56.9
57
2457495
89 19 56.8
56.8
56.8
56.8
56.8
56.8
2457495.5
89 19 56.6
56.6
56.7
56.7
56.6
56.7
2457496
89 19 56.5
56.5
56.5
56.5
56.5
56.5
2457496.5
89 19 56.3
56.3
56.4
56.4
56.3
56.4
2457497
89 19 56.1
56.2
56.2
56.2
56.2
56.2
2457497.5
89 19 56
56
56.1
56.1
56
56.1
2457498
89 19 55.8
55.8
55.9
55.9
55.8
55.9
2457498.5
89 19 55.7
55.7
55.7
55.7
55.7
55.7
2457499
89 19 55.5
55.5
55.6
55.6
55.5
55.5
22
2457499.5
89 19 55.3
55.3
55.4
55.4
55.3
55.4
2457500
89 19 55.1
55.1
55.2
55.2
55.1
55.2
2457500.5
89 19 55
55
55
55
55
55
2457501
89 19 54.8
54.8
54.9
54.9
54.8
54.9
2457501.5
89 19 54.6
54.6
54.7
54.7
54.6
54.7
2457502
89 19 54.5
54.5
54.5
54.5
54.5
54.5
2457502.5
89 19 54.3
54.3
54.4
54.4
54.3
54.4
2457503
89 19 54.1
54.1
54.2
54.2
54.1
54.2
2457503.5
89 19 54
54
54
54
54
54
2457504
89 19 53.8
53.8
53.9
53.9
53.8
53.9
2457504.5
89 19 53.7
53.7
53.7
53.7
53.7
53.7
2457505
89 19 53.5
53.5
53.6
53.6
53.5
53.6
2457505.5
89 19 53.4
53.4
53.4
53.4
53.4
53.4
2457506
89 19 53.2
53.2
53.3
53.3
53.2
53.3
2457506.5
89 19 53.1
53.1
53.1
53.1
53.1
53.1
2457507
89 19 52.9
52.9
53
53
52.9
53
2457507.5
89 19 52.8
52.8
52.9
52.9
52.8
52.9
2457508
89 19 52.6
52.6
52.7
52.7
52.7
52.7
2457508.5
89 19 52.5
52.5
52.6
52.6
52.5
52.6
2457509
89 19 52.4
52.4
52.4
52.4
52.4
52.4
2457509.5
89 19 52.2
52.2
52.3
52.3
52.2
52.3
2457510
89 19 52.1
52.1
52.1
52.1
52.1
52.1
2457510.5
89 19 51.9
51.9
52
52
51.9
52
2457511
89 19 51.8
51.8
51.8
51.8
51.8
51.8
2457511.5
89 19 51.6
51.6
51.7
51.7
51.6
51.7
2457512
89 19 51.5
51.4
51.5
51.5
51.5
51.5
2457512.5
89 19 51.3
51.3
51.4
51.3
51.3
51.4
2457513
89 19 51.1
51.1
51.2
51.2
51.1
51.2
2457513.5
89 19 50.9
50.9
51
51
50.9
51
2457514
89 19 50.8
50.8
50.8
50.8
50.8
50.8
2457514.5
89 19 50.6
50.6
50.7
50.7
50.6
50.7
2457515
89 19 50.4
50.4
50.5
50.5
50.4
50.5
2457515.5
89 19 50.3
50.3
50.3
50.3
50.3
50.3
23
2457516
89 19 50.1
50.1
50.2
50.2
50.1
50.2
2457516.5
89 19 49.9
49.9
50
50
49.9
50
2457517
89 19 49.8
49.8
49.9
49.9
49.8
49.9
2457517.5
89 19 49.6
49.6
49.7
49.7
49.6
49.7
2457518
89 19 49.5
49.5
49.6
49.6
49.5
49.6
2457518.5
89 19 49.4
49.4
49.4
49.4
49.4
49.4
2457519
89 19 49.2
49.2
49.3
49.3
49.2
49.3
2457519.5
89 19 49.1
49.1
49.2
49.2
49.1
49.2
2457520
89 19 49
49
49
49
49
49
2457520.5
89 19 48.8
48.8
48.9
48.9
48.8
48.9
2457521
89 19 48.7
48.7
48.8
48.8
48.7
48.8
2457521.5
89 19 48.6
48.6
48.6
48.6
48.6
48.6
2457522
89 19 48.4
48.4
48.5
48.5
48.4
48.5
2457522.5
89 19 48.3
48.3
48.4
48.4
48.3
48.4
2457523
89 19 48.1
48.1
48.2
48.2
48.2
48.2
2457523.5
89 19 48
48
48.1
48.1
48
48.1
2457524
89 19 47.9
47.9
47.9
47.9
47.9
47.9
2457524.5
89 19 47.7
47.7
47.8
47.8
47.7
47.8
2457525
89 19 47.5
47.5
47.6
47.6
47.6
47.6
2457525.5
89 19 47.4
47.4
47.5
47.5
47.4
47.5
2457526
89 19 47.2
47.2
47.3
47.3
47.2
47.3
2457526.5
89 19 47.1
47.1
47.1
47.1
47.1
47.1
2457527
89 19 46.9
46.9
47
47
46.9
47
2457527.5
89 19 46.8
46.8
46.8
46.8
46.8
46.8
2457528
89 19 46.6
46.6
46.7
46.7
46.6
46.7
2457528.5
89 19 46.5
46.4
46.5
46.5
46.5
46.5
2457529
89 19 46.3
46.3
46.4
46.4
46.3
46.4
2457529.5
89 19 46.1
46.1
46.2
46.2
46.1
46.2
2457530
89 19 46
46
46.1
46.1
46
46.1
2457530.5
89 19 45.9
45.9
45.9
45.9
45.9
45.9
2457531
89 19 45.7
45.7
45.8
45.8
45.7
45.8
2457531.5
89 19 45.6
45.6
45.6
45.6
45.6
45.6
2457532
89 19 45.5
45.4
45.5
45.5
45.5
45.5
24
2457532.5
89 19 45.3
45.3
45.4
45.4
45.3
45.4
2457533
89 19 45.2
45.2
45.3
45.3
45.2
45.3
2457533.5
89 19 45.1
45.1
45.1
45.1
45.1
45.1
2457534
89 19 45
45
45
45
45
45
2457534.5
89 19 44.8
44.8
44.9
44.9
44.8
44.9
2457535
89 19 44.7
44.7
44.8
44.8
44.7
44.8
2457535.5
89 19 44.6
44.6
44.7
44.7
44.6
44.7
2457536
89 19 44.5
44.5
44.6
44.6
44.5
44.6
2457536.5
89 19 44.4
44.4
44.5
44.4
44.4
44.5
2457537
89 19 44.3
44.3
44.3
44.3
44.3
44.3
2457537.5
89 19 44.1
44.1
44.2
44.2
44.1
44.2
2457538
89 19 44
44
44.1
44.1
44
44.1
2457538.5
89 19 43.9
43.9
44
44
43.9
44
2457539
89 19 43.8
43.8
43.8
43.8
43.8
43.8
2457539.5
89 19 43.6
43.6
43.7
43.7
43.6
43.7
2457540
89 19 43.5
43.5
43.6
43.6
43.5
43.5
2457540.5
89 19 43.4
43.3
43.4
43.4
43.3
43.4
25
Ãëàâà 4
Íàáëþäåíèÿ çâåçä
Äëÿ ïîëó÷åíèÿ âèäèìûõ ìåñò çâåçä èñïîëüçîâàëñÿ ïàññàæíûé èíñòðóìåíò
(ÏÈ). Ïðèíöèï åãî ðàáîòû îñíîâàí íà òîì, ÷òî â ìîìåíò ïåðåñå÷åíèÿ çâåçäîé èñòèííîãî ìåðèäèàíà, òî åñòü â ìîìåíò âåðõíåé èëè íèæíåé êóëüìèíàöèè îáúåêòà, åãî ÷àñîâîé óãîë
t
ïî îïðåäåëåíèþ ðàâåí íóëþ. Ïîýòîìó
ôîðìóëà äëÿ îïðåäåëåíèÿ çâåçäíîãî âðåìåíè
S
óïðîùàåòñÿ.
S =T +u=α+t
u = α − T,
çäåñü
T
âðåìÿ ïðîõîæäåíèÿ çâåçäû ÷åðåç íèòü îêóëÿðíîãî ìèêðîìåòð,
÷àñîâîé óãîë ñâåòèëà,
u
t
èñêîìàÿ ïîïðàâêà ÷àñîâ.
ÏÈ ÿâëÿåòñÿ îäíèì èç êëàññè÷åñêèõ àñòðîìåòðè÷àñêèõ èíñòðóìåíòîâ, èçîáðåòåí â XVII âåêå, îäíàêî èç-çà áîëåå ñîâðåìåííîãî ñïîñîáà ðåãèñòðàöèè
îòñ÷åòîâ âðåìåíè (ñåðåäèíà XIX âåêà, íàæàòèå êíîïêè) ïîçâîëÿåò ïîëó÷àòü êîîðäèíàòû ñ òî÷íîñòüþ, äîñòàòî÷íîé äëÿ ñðàâíåíèÿ ñ âû÷èñëåííûìè ðàíåå êîîðäèíàòàìè.
Ïàññàæíûé èíñòðóìåíò óñòàíàâëèâàåòñÿ íà äâóõ ôóíäàìåíòàõ, óäåðæèâàþùèõ ãîðèçîíòàëüíóþ îñü âðàùåíèÿ, ïåðïåíäèêóëÿðíî êîòîðîé ïðèêðåïëÿåòñÿ àñòðîíîìè÷åñêàÿ òðóáà. Äëÿ ðåãèñòðàöèè ïðîõîæäåíèé ñâåòèë ôèêñèðóþòñÿ ìîìåíòû èõ ïðîõîæäåíèé ÷åðåç íèòè îêóëÿðíîãî ìèêðîìåòðà,
ðàñïîëîæåííîãî â ôîêàëüíîé ïëîñêîñòè îáúåêòèâà. ÏÈ, íà êîòîðîì ïðîèçâîäèëèñü íàáëþäåíèÿ, óñòàíîâëåí íà äâóõ îïîðàõ òàê, ÷òîáû åãî òðóáà
26
äâèãàëàñü â ïëîñêîñòè ìåðèäèàíà. Ïîñëå òàêîé óñòàíîâêè èíñòðóìåíòà íà
íåì ìîæíî èçìåðÿòü ïðÿìûå âîñõîæäåíèÿ. Ðåæå ïàññàæíûé èíñòðóìåíò
óñòàíàâëèâàåòñÿ â ïåðâîì âåðòèêàëå, òîãäà íà íåì îïðåäåëÿþò ñêëîíåíèÿ
çâåçä.
Îøèáêà ïîëó÷åííûõ êîîðäèíàò ñîñòîèò èç îøèáêè èíñòðóìåíòà è îøèáêè
íàáëþäàòåëÿ (ñëó÷àéíîé è ñèñòåìàòè÷åñêîé). Ïðè÷èíîé îøèáêè èíñòðóìåíòà ÿâëÿåòñÿ òî, ÷òî èíñòðóìåíòàëüíûé ìåðèäèàí âñåãäà îòëè÷àåòñÿ îò
èñòèííîãî. Ïðè îáðàáîòêå íàáëþäåíèé ó÷èòûâàþò òàêîå ñìåùåíèå, ðàçäåëÿÿ åãî íà òðè êîìïîíåíòû: àçèìóò èíñòðóìåíòà
îñè
i,
êîëëèìàöèÿ
c.
a, íàêëîí ãîðèçîíòàëüíîé
Ñëó÷àéíàÿ êîìïîíåíòà óìåíüøàåòñÿ, åñëè óâåëè÷èòü
÷èñëî èçìåðåíèé, ñèñòåìàòè÷åñêàÿ íàçûâàòñÿ ëè÷íîé ðàçíîñòüþ è òðóäíåå
ïîääàåòñÿ èçìåðåíèþ.
Âûáîð çâåçä äëÿ òàáëèöû ýôåìåðèä
Ñîãëàñíî ïðîãðàììå íàáëþäåíèé, çà 1 íî÷ü òðåáîâàëîñü ïîëó÷èòü êîîðäèíàòû êàê ìèíèìóì 10 çåíèòíûõ è 10 þæíûõ çâåçä, ïðè÷åì êóëüìèíàöèÿ
òàêèõ ñâåòèë äîëæíà áûòü âåðõíåé. Òàáëèöà ïðÿìûõ âîñõîæäåíèé è ñêëîíåíèé áûëà ïîëó÷åíà èç ïðîãðàììû Stellarium, çåíèòíûå çâåçäû èìåþò
çåíèòíûå ðàññòîÿíèÿ
0 − 3◦ ,
þæíûå èìåþò ñêëîíåíèÿ
+20 − 10◦ .
Îïèñàíèå ìåòîäèêè íàáëþäåíèé
Ïåðåä íà÷àëîì íàáëþäåíèé ïðîèçâîäèëàñü ïðîâåðêà óðîâíÿ íåîáõîäèìî,
÷òîáû ïðàâîå è ëåâîå çíà÷åíèÿ íå çàøêàëèâàëè. Äàëåå óñòàíàâëèâàëîñü
çâåçäíîå âðåìÿ, íàõîäèëàñü èç òàáëèöû ýôåìåðèä ïîäõîäÿùàÿ ïî âðåìåíè çâåçäà. Çåíèòíàÿ ïîÿâëÿåòñÿ â ïîëå çðåíèÿ ïðèìåðíî çà 2 ìèíóòû äî
êóëüìèíàöèè, þæíàÿ çà 1 ìèíóòó; ðàçëè÷èå îáúÿñíÿåòñÿ òåì, ÷òî ñêîðîñòü çâåçäû ïðîïîðöèîíàëüíà êîñèíóñó åå ñêëîíåíèÿ [10]. Åùå ïðèìåðíî
1-2 ìèíóòû òðåáóåòñÿ íà íàâåäåíèå òðóáû íà ñâåòèëî è çàïèñü ïîêàçàíèé
óðîâíÿ. Ïîñëå ïîÿâëåíèÿ çâåçäû â îêóëÿðå íåîáõîäèìî ïåðåâåñòè åå òàê,
÷òîáû îíà îêàçàëàñü ìåæäó äâóìÿ öåíòðàëüíûìè íèòÿìè. Ïîñêîëüêó, êàê
ïðàâèëî, òàêàÿ äîâîäêà áûëà ñðàâíèòåëüíî íåáîëüøîé èëè (ðåæå) îòñóòñòâîâàëà, çíà÷åíèÿ óðîâíÿ ìîæíî ñ÷èòàòü äîñòàòî÷íî òî÷íûìè.
27
Îáðàáîòêà ðåçóëüòàòîâ
Äëÿ ïîëó÷åíèÿ íàáëþäàåìûõ êîîðäèíàò ñâåòèë áûëà íàïèñàíà ïðîãðàììà
íà ÿçûêå
c#,
àëãîðèòì âçÿò èç
[7].  êà÷åñòâå âõîäíûõ äàííûõ ñëåäó-
åò ïðåäîñòàâèòü äàòó íà÷àëà íàáëþäåíèé, êîëè÷åñòâî çâåçä, íîìåðà ýòèõ
îáúåêòîâ ïî êàòàëîãó Hipparcos, ñðåäíèé ïî íèòÿì ìîìåíò ïðîõîæäåíèÿ (â
UTC) è ïîêàçàíèÿ óðîâíÿ
i
äëÿ êàæäîãî ñâåòèëà.
Âíà÷àëå âû÷èñëÿþòñÿ êîýôôèöèåíòû ôîðìóëû Ìàéåðà
Ai , Ii ,
äëÿ ýòîãî
èñïîëüçóþòñÿ ýôåìåðèäû çâåçä èç îòäåëüíîãî ôàéëà.
Ai = sin zi sec δi
Ii = cos zi sec δi
Èç ñôåðè÷åñêîé àñòðîíîìèè çåíèòíîå ðàññòîÿíèå äëÿ âåðõíåé êóëüìèíàöèè
zi = |ϕ − δi |,
øèðîòà äëÿ Ñëóæáû Âðåìåíè ïðèíèìàëàñü ðàâíîé
ϕ=
59◦ 560 3200 .
Äàëåå äëÿ êàæäîé çâåçäû ïðîèçâîäèëñÿ ïåðåñ÷åò âðåìåíè ïðîõîæäåíèÿ èç
UT C
â çâåçäíîå âðåìÿ ñ ó÷åòîì ñìåíû äàòû â ïðîöåññå íàáëþäåíèé. Àëãî-
ðèòì ïåðåâîäà ê çâåçäíîìó âðåìåíè âçÿò èç
íàêëîííîñòü ãîðèçîíòàëüíîé îñè
[2]. Ïîñëå ýòîãî ó÷èòûâàëàñü
Ii.
Çàòåì óñðåäíÿëèñü ïî âñåì çåíèòíûì çâåçäàì ìîìåíòû ïðîõîæäåíèÿ è àçèìóòàëüíûå êîýôôèöèåíòû. Ïîëó÷åííûå çíà÷åíèÿ îáîçíà÷èì
ᾱz , Āz .
Ïîñëå ó÷åòà çåíèòíûõ çâåçä èñïîëüçóåì àçèìóòàëüíûå: íàéäåì äëÿ êàæäîé èç íèõ çíà÷åíèå àçèìóòà
óñðåäíåíèåì ïî
aj ,
îòñþäà ïîëó÷èì àçèìóò èíñòðóìåíòà
aj .
aj =
ãäå
αj
ā
ᾱz − αj
,
Āz − Aj
âðåìÿ ïðîõîæäåíèÿ ñ ó÷åòîì ïîïðàâîê óðîâíÿ.
Ðåçóëüòàò ðàáîòû ïðîãðàììû ñïèñîê íîìåðîâ çâåçä ïî êàòàëîãó Hipparcos;
íàáëþäàåìûå ìîìåíòû êóëüìèíàöèé, èñïðàâëåííûå çà àçèìóò è óðîâåíü;
ìîìåíòû êóëüìèíàöèé èç êàòàëîãà.
Ðåçóëüòàò íàáëþäåíèé ïðåäñòàâëåí òàáëèöåé 4.1, ïðîìåæóòî÷íûå çíà÷åíèÿ ìîæíî íàéòè â òàáëèöàõ 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10. Àçèìóò
28
ñ 4 ïî 6 ìàÿ èç-çà îòñóòñòâèÿ þæíûõ çâåçä ñðåäè èçìåðåííûõ áûë âçÿò ïîõîæèì íà àçèìóòû 7-9 ìàÿ. 9 ìàÿ èíñòðóìåíò áûë áîëåå òî÷íî óñòàíîâëåí
â ìåðèäèàí, èç-çà ÷åãî
ā
óìåíüøèëñÿ ïî÷òè íà 5 ñåêóíä. Â ïåðåðûâå ìåæ-
äó íàáëþäåíèÿìè 9 è 12 ìàÿ áûëè ïîëó÷åíû ïðåäâàðèòåëüíûå ðåçóëüòàòû
îáðàáîòêè, èñõîäÿ èç êîòîðûõ â ñïèñîê èçìåðÿåìûõ îáúåêòîâ äîáàâèëèñü
þæíûå çâåçäû.
Êðîìå âûøåïåðå÷èñëåííûõ ïîïðàâîê ñóùåñòâóåò ñèñòåìàòè÷åñêàÿ îøèáêà
â ôèêñèðîâàíèè âðåìåíè ïðîõîæäåíèÿ çâåçäû ÷åðåç íèòü îêóëÿðà, âïåðâûå
çàìå÷åííàÿ Áåññåëåì è îïèñàííàÿ èì â [3]. Òî÷íîñòü ðåçóëüòàòîâ, ïîëó÷åííûõ 12-14 ìàÿ, ÿâëÿåòñÿ ñëèøêîì íèçêîé äëÿ òîãî, ÷òîáû ââîäèòü ïîïðàâêó
çà ëè÷íóþ ðàçíîñòü.
29
Òàáëèöà 4.1: ðåçóëüòàòû íàáëþäåíèé
äàòà
êîëè÷åñòâî çâåçä
çåíèòíûå
þæíûå
àçèìóò
∆α
4 ìàÿ
6
6
0
-26.5
0.48
5 ìàÿ
23
23
0
-26.5
0.20
6 ìàÿ
24
24
0
-26.5
-0.84
7 ìàÿ
31
27
1
-26.58
-1.35
8 ìàÿ
31
29
1
-26.56
-1.72
9 ìàÿ
17
15
1
-26.79
-1.59
12 ìàÿ
35
15
19
-21.56
-7.51
13 ìàÿ
30
14
14
-21.91
-8.46
14 ìàÿ
32
9
20
-22.51
-9.69
Òàáëèöà 4.2: 4 ìàÿ
αobs
íîìåð
αcalc
αobs
íîìåð
h
m
s
h
m
s
60978
12
30
43,94
12
30
42,67
62512
12
49
23,53
12
49
63503
13
1
25,52
13
1
αcalc
h
m
s
h
m
s
61767
12
40
18,07
12
40
18,01
21,78
62956
12
54
44,10
12
54
44,66
25,64
64208
13
10
13,78
13
10
13,30
30
Òàáëèöà 4.3: 5 ìàÿ
αobs
íîìåð
αcalc
αobs
íîìåð
h
m
s
h
m
s
60978
12
30
43,50
12
30
42,67
62512
12
49
23,63
12
49
64208
13
10
13,98
13
66198
13
34
44,51
67485
13
50
77738
15
79204
αcalc
h
m
s
h
m
s
61767
12
40
19,14
12
40
18,01
21,78
62956
12
54
44,25
12
54
44,66
10
13,30
65530
13
26
31,03
13
26
33,23
13
34
44,95
66700
13
40
57,84
13
40
57,19
17,38
13
50
17,55
68184
13
58
02,98
13
58
02,54
52
40,27
15
52
39,50
78527
16
2
13,82
16
2
11,69
16
10
16,49
16
10
13,38
79804
16
17
34,75
16
17
31,94
80331
16
24
13,54
16
24
13,03
80991
16
32
41,57
16
32
39,81
82020
16
45
37,59
16
45
36,57
82860
16
56
02,64
16
56
07,35
84496
17
16
30,96
17
16
41,49
85290
17
25
56,95
17
25
54,21
86036
17
35
10,11
17
35
10,00
86499
17
40
54,01
17
40
52,59
87585
17
53
49,96
17
53
48,80
Òàáëèöà 4.4: 6 ìàÿ
αobs
íîìåð
αcalc
αobs
íîìåð
h
m
s
h
m
s
58259
11
57
42,62
11
57
43,86
62956
12
54
43,27
12
54
64532
13
14
17,13
13
66198
13
34
44,07
67485
13
50
79125
16
80331
αcalc
h
m
s
h
m
s
60978
12
30
42,99
12
30
42,67
44,66
63503
13
1
25,02
13
1
25,64
14
16,99
65530
13
26
30,45
13
26
33,23
13
34
44,95
66700
13
40
57,31
13
40
57,19
16,88
13
50
17,55
68756
14
4
45,35
14
4
50,10
9
23,49
16
9
22,31
79804
16
17
33,95
16
17
31,94
16
24
13,33
16
24
13,03
80991
16
32
40,85
16
32
39,81
81451
16
38
23,88
16
38
22,89
82020
16
45
36,95
16
45
36,57
83289
17
1
31,00
17
1
29,61
83847
17
8
19,91
17
8
19,18
84496
17
16
18,31
17
16
41,49
85086
17
23
40,14
17
23
39,80
85692
17
31
00,74
17
30
59,46
86499
17
40
53,16
17
40
52,59
87478
17
52
41,03
17
52
37,31
90905
18
32
51,98
18
32
51,51
31
Òàáëèöà 4.5: 7 ìàÿ
αobs
íîìåð
αcalc
αobs
íîìåð
h
m
s
h
m
s
56211
11
32
04,67
11
32
21,44
58001
11
54
38,25
11
54
60316
12
22
49,96
12
62512
12
49
22,42
64208
13
10
65530
13
67103
αcalc
h
m
s
h
m
s
57399
11
46
49,97
11
46
54,46
41,04
59774
12
16
12,38
12
16
13,59
22
50,80
60978
12
30
42,79
12
30
42,67
12
49
21,78
63503
13
1
24,81
13
1
25,64
13,24
13
10
13,30
64532
13
14
16,30
13
14
16,99
26
30,08
13
26
33,23
66700
13
40
57,08
13
40
57,19
13
45
48,84
13
45
49,41
67485
13
50
16,90
13
50
17,55
78676
16
4
01,63
16
3
59,98
79804
16
17
34,11
16
17
31,94
80331
16
24
13,02
16
24
13,03
80991
16
32
41,07
16
32
39,81
81451
16
38
23,76
16
38
22,89
82020
16
45
37,13
16
45
36,57
82677
16
54
17,60
16
54
15,48
83289
17
1
31,03
17
1
29,61
83847
17
8
20,05
17
8
19,18
84465
17
16
18,75
17
16
16,00
85086
17
23
40,17
17
23
39,80
85692
17
31
00,87
17
30
59,46
86036
17
35
09,50
17
35
10,00
87585
17
53
48,81
17
53
48,80
89348
18
13
55,40
18
13
59,60
90156
18
23
53,01
18
24
08,00
91262
18
37
23,36
18
37
29,44
32
Òàáëèöà 4.6: 8 ìàÿ
αobs
íîìåð
αcalc
αobs
íîìåð
h
m
s
h
m
s
57399
11
46
49,65
11
46
54,46
58989
12
6
24,98
12
6
60316
12
22
49,33
12
61767
12
39
40,91
62956
12
54
64208
13
65530
αcalc
h
m
s
h
m
s
58001
11
54
38,21
11
54
41,04
28,57
59774
12
16
12,65
12
16
13,59
22
50,80
60992
12
30
49,98
12
30
49,84
12
40
18,01
62512
12
49
22,30
12
49
21,78
43,19
12
54
44,66
63503
13
1
24,74
13
1
25,64
10
12,67
13
10
13,30
64532
13
14
16,40
13
14
16,99
13
26
29,85
13
26
33,23
77738
15
52
39,38
15
52
39,50
78527
16
2
12,92
16
2
11,69
79125
16
9
23,21
16
9
22,31
79804
16
17
33,85
16
17
31,94
80309
16
24
12,55
16
24
00,43
80991
16
32
40,77
16
32
39,81
81451
16
38
23,52
16
38
22,89
82020
16
45
35,86
16
45
36,57
82677
16
54
16,85
16
54
15,48
83289
17
1
30,99
17
1
29,61
83847
17
8
19,78
17
8
19,18
85086
17
23
40,26
17
23
39,80
85692
17
31
00,44
17
30
59,46
86499
17
40
53,14
17
40
52,59
87585
17
53
48,74
17
53
48,80
88349
18
2
46,44
18
2
45,25
89348
18
13
55,05
18
13
59,60
90156
18
23
52,92
18
24
08,00
Òàáëèöà 4.7: 9 ìàÿ
αobs
íîìåð
αcalc
αobs
íîìåð
h
m
s
h
m
s
77272
15
46
56,94
15
46
58,30
78527
16
2
12,54
16
2
79804
16
17
33,75
16
80991
16
32
39,40
82020
16
45
83847
17
86036
αcalc
h
m
s
h
m
s
77738
15
52
37,99
15
52
39,50
11,69
79125
16
9
22,86
16
9
22,31
17
31,94
80331
16
24
13,30
16
24
13,03
16
32
39,81
81451
16
38
23,25
16
38
22,89
35,57
16
45
36,57
83289
17
1
30,82
17
1
29,61
8
19,89
17
8
19,18
84496
17
16
42,29
17
16
41,49
17
35
09,94
17
35
10,00
87585
17
53
48,16
17
53
48,80
89348
18
13
56,54
18
13
59,60
90156
18
23
52,23
18
24
08,00
91262
18
37
19,66
18
37
29,44
33
Òàáëèöà 4.8: 12 ìàÿ
αobs
íîìåð
αcalc
αobs
íîìåð
h
m
s
h
m
s
62512
12
49
21,97
12
49
21,78
63608
13
2
45,56
13
2
64852
13
18
11,52
13
66198
13
34
42,91
67275
13
47
77516
15
78527
αcalc
h
m
s
h
m
s
63090
12
56
10,66
12
56
25,63
59,41
64238
13
10
31,35
13
10
47,84
18
25,85
65530
13
26
31,07
13
26
33,23
13
34
44,95
66700
13
40
56,34
13
40
57,19
50,04
13
48
02,34
77272
15
46
57,32
15
46
58,30
50
12,82
15
50
28,52
78072
15
57
00,06
15
57
12,46
16
2
12,63
16
2
11,69
79043
16
8
36,73
16
8
48,85
79349
16
12
09,07
16
12
19,84
79882
16
18
55,32
16
19
11,22
80331
16
24
13,15
16
24
13,03
80991
16
32
41,00
16
32
39,81
81451
16
38
24,04
16
38
22,89
82073
16
46
23,56
16
46
37,04
82504
16
52
15,36
16
52
25,98
82860
16
56
04,31
16
56
07,35
83613
17
5
55,37
17
6
08,22
84379
17
15
31,51
17
15
42,24
85086
17
23
40,03
17
23
39,80
85692
17
31
00,14
17
30
59,46
86499
17
40
52,89
17
40
52,59
86974
17
46
56,12
17
47
05,82
87585
17
53
48,38
17
53
48,80
87933
17
58
14,21
17
58
24,05
88290
18
2
20,03
18
2
35,02
88601
18
6
01,99
18
6
17,23
89104
18
11
20,66
18
11
19,08
89962
18
21
53,50
18
22
09,33
91262
18
37
22,00
18
37
29,44
34
Òàáëèöà 4.9: 13 ìàÿ
αobs
íîìåð
αcalc
αobs
íîìåð
h
m
s
h
m
s
59774
12
16
12,20
12
16
13,59
61394
12
35
28,06
12
35
62512
12
49
22,38
12
63608
13
2
45,67
65530
13
26
78493
16
79593
αcalc
h
m
s
h
m
s
60742
12
27
34,34
12
27
45,03
40,89
61941
12
42
13,36
12
42
29,66
49
21,78
63090
12
56
10,58
12
56
25,63
13
2
59,41
64208
13
10
23,54
13
10
13,30
31,33
13
26
33,23
66700
13
40
56,68
13
40
57,19
1
56,22
16
2
05,91
79125
16
9
22,99
16
9
22,31
16
14
56,26
16
15
12,24
80331
16
24
13,54
16
24
13,03
80816
16
30
43,80
16
30
55,48
81451
16
38
23,77
16
38
22,89
82073
16
46
23,21
16
46
37,04
82677
16
54
17,34
16
54
15,48
83847
17
8
20,31
17
8
19,18
84379
17
15
31,32
17
15
42,24
85086
17
23
40,15
17
23
39,80
86032
17
35
28,35
17
35
41,62
86499
17
39
53,10
17
40
52,59
86974
17
46
55,89
17
47
05,82
87585
17
53
48,49
17
53
48,80
88048
17
59
38,70
17
59
55,60
88794
18
8
00,74
18
8
10,86
89348
18
13
57,47
18
13
59,60
89962
18
21
53,30
18
22
09,33
91262
18
37
22,00
18
37
29,44
35
Òàáëèöà 4.10: 14 ìàÿ
αobs
íîìåð
αcalc
αobs
íîìåð
h
m
s
h
m
s
60742
12
27
34,16
12
27
45,03
61941
12
42
12,94
12
42
63090
12
56
10,05
12
64238
13
10
30,94
66249
13
35
67275
13
79125
αcalc
h
m
s
h
m
s
61281
12
33
58,64
12
34
10,53
29,66
62512
12
49
22,31
12
49
21,78
56
25,63
63503
13
1
23,95
13
1
25,64
13
10
47,84
65530
13
26
31,12
13
26
33,23
15,51
13
35
31,77
66700
13
40
56,20
13
40
57,19
47
49,49
13
48
02,34
78493
16
1
55,78
16
2
05,91
16
9
22,91
16
9
22,31
79593
16
14
55,52
16
15
12,24
79882
16
18
54,70
16
19
11,22
80816
16
30
43,72
16
30
55,48
82504
16
52
14,70
16
52
25,98
83168
17
0
07,20
17
0
06,04
83847
17
8
20,13
17
8
19,18
84379
17
15
30,85
17
15
42,24
84833
17
20
49,66
17
21
02,14
85355
17
27
04,56
17
27
19,58
85693
17
31
13,03
17
31
24,01
86032
17
35
27,90
17
35
41,62
86974
17
46
55,47
17
47
05,82
87585
17
53
48,62
17
53
48,80
87933
17
58
13,65
17
58
24,05
88192
18
1
12,48
18
1
27,86
88771
18
7
53,20
18
8
07,53
89348
18
13
57,10
18
13
59,60
89962
18
21
52,76
18
22
09,33
91262
18
37
21,62
18
37
29,44
36
Ãëàâà 5
Âûâîäû
•
Ïîêàçàíî, ÷òî â êà÷åñòâå ôóíäàìåíòàëüíîãî êàòàëîãà ñëåäîâàëî áû
èñïîëüçîâàòü FK6, ðàáîòà íàä êîòîðûì íà çàêîí÷åíà. Ïîêà îñòàåòñÿ
òîëüêî Hipparcos, íåñìîòðÿ íà ýïîõó 25-ëåòíåé äàâíîñòè è íåðåàëèñòè÷íûå ñîáñòâåííûå äâèæåíèÿ.
•
Ñðàâíåíèå îñíîâíûõ àëãîðèòìîâ âû÷èñëåíèÿ âèäèìûõ ìåñò ïîêàçàëî, ÷òî îíè èìåþò ðàñõîæäåíèÿ íà óðîâíå
100 ,
ïðè÷èíû êîòîðûõ âû-
ÿñíèòü ïîêà íå óäàëîñü.
•
Âûïîëíåíû íàáëþäåíèÿ çâåçä íà ïàññàæíîì èíñòðóìåíòå, ýôåìåðèäû îáúåêòîâ áûëè ïîëó÷åíû èç ïðîãðàììû Stellarium.
•
Ê ñîæàëåíèþ, òî÷íîñòü íàáëþäåíèé îêàçàëàñü íåâûñîêîé, íà óðîâíå
10, ÷òî ìîæíî îáúÿñíèòü íåäîñòàòêîì îïûòà, è äîëæíû áûòü ïîâûøåíà â áóäóùåì.
37
Ëèòåðàòóðà
[1] Àñòðîíîìè÷åñêèé åæåãîäíèê íà 2016 ãîä. ÈÏÀ ÐÀÍ, ÑÏá, 2015, 689 ñ
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