이 책은 동양(중국)천문학과 서양천문학의 교류 및 융합의 첫 결과물인《숭정역서(崇禎曆書)》(1631~1634)의 태양 이론편 <일전역지>와 그 계산절차 및 계산수치표가 종합된 <일전표>의 내용을 정리하고 분석한 것이다. 본서는 과학사 연구자뿐만 아니라 일반 대중도 16세기와 17세기의 서유럽 천문학이 동아시아 전통천문학적 환경 속으로 들어왔을 때 어떻게 동서 천문학의 만남과 교차가 이루어졌는지를 이해할 수 있도록 돕고자 한다. 이 책에서 다루고 있는 천문학적 내용의 이해를 위해 필요한 고전천문학의 기본 지식을 부록에 실어 두었다.
목차
책머리에 ·················································································································································3
《숭정역서(崇禎曆書)》와 서광계(徐光啟) ··············································································17
그림 1 왼쪽: 《숭정역서》 중 〈일전역지(日躔曆指)〉 권1, 첫 페이지, 중간: 《숭정역서》 중 〈측량전서(測量全書)〉 권3 안표지, 오른쪽: 사고전서본 《신법산서(新法算書)》, 제요(提要), 첫 페이지 ·······························································································································19
표 1 《숭정역서》 진상 서목과 간행 서목 및 《서양신법역서》 보각 서목 비교 ···················28
표 2 서광계의 연표(역법 관련 업적을 중심으로) ·······························································34
제1부 《숭정역서(崇禎曆書)》 〈일전역지(日躔曆指)〉····················································41
제1장 남북선(南北線 자오선) 정하기 ·······················································································46
제2장 북극출지도분(北極出地度分 북극고도 곧 관측지의 위도) 정하기 ·························54
제3장 청몽기차[淸蒙氣差 대기굴절에 의해 발생하는 고도 시차(視差)]에 대하여 ·········58
제4장 해마다 달라지는 황도와 적도 사이의 거도[距度 도수(度數)로 나타난 거리] 구하기-‘황도와 적도 사이의 거도’는 하짓날 태양의 적위[위(緯)]라고도 칭함 ················67
제5장 춘분과 추분 때 태양의 본도(本度 태양궤도[일륜본천(日輪本天)]상의 경도) ······80
제6장 태양의 등속운행[평행(平行)]과 실제운행[실행(實行)] ··············································93
제7장 태양의 원지점[최고(最高)]과 양심차(兩心差) 구하기 ·············································102
제8장 태양의 시차(視差), ‘태양∼지구’ 거리, 가감차(加減差) 구하기 ···························133
제9장 일차(日差 균시차 equation of time)에 대하여 ····················································143
부록 1. 지평좌표, 적도좌표, 황도좌표 사이의 관계 ·····························································145
부록 2. 태양의 운동을 기술하는 4가지 모델 ··········································································152
그림 1 남북선 그리기 ···············································································································47
그림 2 동서선 그리기 1 ···········································································································47
그림 3 동서선 그리기 2 ···········································································································48
그림 4 동서선 그리기 3 ···········································································································48
그림 5 동서선 그리기 4 ···········································································································50
그림 6 동서선 그리기 5 ··········································································································50
그림 7 동서선 그리기 6 ···········································································································50
그림 8 동서선 그리기 7 ··········································································································51
그림 9 동서선 그리기 8 ···········································································································51
그림 10 동서선 그리기 9 ···········································································································52
그림 11 동서선 그리기 10 ·········································································································53
그림 12 고도와 시차(視差) ·········································································································56
그림 13 청몽기차 1 ····················································································································62
그림 14 청몽기차 2 ····················································································································63
그림 15 청몽기차 3 ····················································································································64
그림 16 청몽기차 4 ····················································································································64
그림 17 청몽기차 5 ····················································································································65
그림 18 메티우스의 《천문학강요》에 기록된 역대의 황적경사각 Adriaan Metius, Institvtionvm astronomicarum tomi tres (Franeker: A. Radaeus, 1608), 18쪽 ··················72
그림 19 적위 구하기 ·················································································································76
그림 20 황경 구하기 ···················································································································77
그림 21 적경 구하기1 ················································································································78
그림 22 적경 구하기2 ················································································································79
그림 23 태양 궤도와 종동천 ······································································································81
그림 24 춘분, 추분 근처의 황도와 적도 ···················································································84
그림 25 티코 브라헤가 관측한 5년간의 춘분시각과 추분시각 Tychonis Brahe Dani Scripta Astronomica, ed. I. L. E. Dreyer, Tomus II (Hauniae, 1913), 15쪽 ·············91
그림 26 《신법산서》와 《숭정역서》의 본문 비교 ·······································································95
그림 27 하지점과 원지점 ·········································································································103
그림 28 춘분 후의 태양운행을 이용한 양심차 구하기 ···························································105
그림 29 티코의 양심차 구하기(1588년 춘분에서 입하) ························································110
그림 30 《숭정역서》의 양심차 구하기(1588년 춘분에서 입하) ·············································110
그림 31 《숭정역서》의 양심차 구하기(1588년 춘분에서 입하) ·············································112
그림 32 티코의 양심차 구하기(1588년 춘분에서 입하) ························································113
그림 33 추분 전의 태양운행을 이용한 양심차 구하기 ···························································115
그림 34 티코의 양심차 구하기(1588년 입추에서 추분) ························································118
그림 35 《숭정역서》의 양심차 구하기(1588년 입추에서 추분) ·············································118
그림 36 《숭정역서》의 양심차 구하기(1588년 입추에서 추분) ·············································120
그림 37 원주각과 중심각의 관계 ····························································································121
그림 38 히파르코스의 양심차 구하기 ·····················································································124
그림 39 발테루스의 양심차 구하기 ·························································································128
그림 40 발테루스의 양심차 구하기(1488년 춘분에서 입하) ················································129
그림 41 《숭정역서》에 소개된 발테루스의 양심차 구하기(1488년 춘분에서 입하) ············129
그림 42 《숭정역서》에 소개된 발테루스의 양심차 구하기(1488년 춘분에서 입하) ············131
그림 43 시차(視差) ···················································································································133
그림 44 태양∼지구 거리 계산 1 ·····························································································134
그림 45 태양∼지구 거리 계산 2 ·····························································································135
그림 46 태양∼지구 거리 계산 3 ·····························································································136
그림 47 가감차 ·························································································································137
그림 48 가감차 계산 1 ·············································································································139
그림 49 가감차 계산 2 ·············································································································139
그림 50 지반경차 계산 1 ·········································································································140
그림 51 지반경차 계산 2 ·········································································································141
그림 52 지평좌표와 적도좌표의 관계 ·····················································································145
그림 53 적도좌표와 황도좌표의 관계 ·····················································································147
그림 54 황경 에 따른 적위 그리고, °에 따른 적위 증분 ······························149
그림 55 황경 에 따른 적경과 황경의 차 그리고, °에 따른 적경 증분 149
그림 56 시간각 에 따른 태양의 고도 ···············································································150
그림 57 시간각 에 따른 태양의 방위각 ··········································································151
그림 58 방위각 에 따른 태양의 고도 ···············································································151
그림 59 이심원(Eccentric) 모델 ····························································································152
그림 60 이퀀트(Equant) 모델 ·································································································156
그림 61 코페르니쿠스(Copernicus) 모델 ·············································································158
그림 62 케플러(Kepler) 모델 ·································································································160
그림 63 케플러 모델과 《역상고성후편》의 가감차표 비교 ····················································162
그림 64 케플러 모델과 《역상고성후편》의 지구∼태양 거리 비교 ········································162
표 1 메티우스의 태양운동 이론과 〈일전역지〉 목차 비교 ··················································44
표 2 〈일전역지〉와 메티우스의 황적경사각 값의 비교(채색된 부분은 일치하는 값) ·······72
표 3 〈일전역지〉의 중국역법에 따른 환산값과 실제 계산값과의 비교(채색된 부분은 일치하는 값) ·······················································································74
표 4 〈일전역지〉가 중국역법에 따라 제시한 값을 서양역법으로 환산한 값 ·····················92
표 5 1회귀년의 계산 비교 ····································································································99
표 6 티코와 〈일전역지〉의 양심차와 원지점 계산 비교[1588년 티코가 측정한 춘분부터 입하까지 경과 시간을 이용한 계산, 티코의 계산 방식은 Tychonis Brahe Dani Scripta Astronomica , ed. I. L. E. Dreyer, Tomus II (Hauniae, 1913), 19~21쪽을 보라]····································································································································110
표 7 《숭정역서》의 양심차와 원지점 구하기(1588년의 ‘춘분∼입하’ 태양 운행 이용) 계산 흐름도 ·····························································································································111
표 8 티코 브리헤의 양심차와 원지점 구하기(1588년의 ‘춘분∼입하’ 태양 운행 이용) 계산 흐름도 ·····························································································································113
표 9 티코와 〈일전역지〉의 양심차와 원지점 계산 비교[1588년 티코가 측정한 입추부터 추분까지 경과 시간을 이용한 계산. 티코의 계산 방식은 Tychonis Brahe Dani Scripta Astronomica , ed. I. L. E. Dreyer, Tomus II (Hauniae, 1913), 21-23쪽을 보라]····································································································································118
표 10 《숭정역서》의 양심차와 원지점 구하기(추분 전의 태양 운행 이용) 계산 흐름도 ·· 119
표 11 발테루스(백이나와)와 〈일전역지〉의 양심차 계산 비교[1488년 발테루스가 측정한 ‘춘분∼입하’의 경과 시간을 이용한 계산. 발테우스의 계산값은 Tychonis Brahe Dani Scripta Astronomica, ed. I. L. E. Dreyer, Tomus II (Hauniae, 1913), 41쪽을 보라]····································································································································129
표 12 《숭정역서》에 소개된 백이나와의 양심차 구하기(1488년 ‘춘분∼입하’ 태양운행 이용) 계산 흐름도 ················································································································131
표 13 지평좌표와 적도좌표의 변환 ·····················································································146
표 14 프톨레마이오스와 이심원 모델의 가감차 비교 ························································153
표 15 티코와 이심원 모델의 가감차 비교 ···········································································154
보충자료 1. 메티우스(Metius, 1571~1635)의 《천문학 강요》와 〈일전역지〉의 목차 비교 ······ 43
보충자료 2. 동서선 구하기의 기하학적 도해 ··················································································50
보충자료 3. 동서선 구하기의 해석학적 접근 ··················································································51
보충자료 4. 춘·추분날 정오 태양의 고도 오차에 따른 경도 오차 ·················································54
보충자료 5. 노바야젬랴(Novaya Zemlya) 효과 ···········································································61
보충자료 6. 태양의 고도 계산예(옥스퍼드대본, 우한대본, 규장각본, 《서양신법역서》본에는 위의 내용 뒤에 다음의 계산예가 추가되어 있다) ···································································64
보충자료 7. 태양의 고도 측정예(옥스퍼드대본, 우한대본, 규장각본, 《서양신법역서》본에는 위의 내용 뒤에 다음의 측정예가 추가되어 있다) ···································································66
보충자료 8. 〈일전역지〉와 메티우스가 기록한 역대의 황적경사각 ···············································71
보충자료 9. 적도지방에서 지평선에 의해 잘리는 황경을 가지고 적경 구하기 ····························79
보충자료 10. 임의의 날 정오에 태양의 황경 측정하기 : 옥스퍼드대본, 우한대본, 규장각본, 《서양신법역서》본에는 위의 내용 뒤에 다음과 같은 첨언(添言)과 측정예가 추가되어 있다 89
보충자료 11. 5년간 춘분점과 추분점의 관측 ···················································································91
보충자료 12. 태양의 매일 등속운행[평행(平行)] 분(分)수 계산법[산매일태양평행분법(算每日太陽平行分法)]: 옥스퍼드대본, 우한대본, 규장각본, 《서양신법역서》본에는 위 (4)항의 소단락 대신 다음과 같은 내용의 대단락이 (3)항의 내용 뒤에 있다 ·····································97
보충자료 13. 티코와 《숭정역서》, 《신법산서》의 회귀년 계산 비교 ·················································98
보충자료 14. 티코와 〈일전역지〉의 양심차 계산 비교(춘분에서 입하까지 관측값 이용) ············109
보충자료 15. 티코와 〈일전역지〉의 양심차와 원지점 계산 비교(입추에서 추분까지 관측값 이용)
····································································································································117
보충자료 16. 원주각과 중심각의 관계 ····························································································121
보충자료 17. 발테루스(백이나와)와 〈일전역지〉의 양심차와 원지점 계산 비교(춘분에서 입하까지 관측 값 이용) ··················································································································129
보충자료 18. 《숭정역서》의 〈지반경차표〉와 태양 운행 모델 ························································141
제2부 《숭정역서(崇禎曆書)》 〈일전표(日躔表)〉···························································· 163
제1권 표 해설Ⅰ 역원 후 200항년 표 해설 [역원후이백항년표설(曆元後二百恒年表說)]
············································································································································165
제1권 표Ⅰ 제1표. 역원 후 200항년 표 [역원후이백항년표(曆元後二百恒年表)] ········189
제1권 표Ⅱ 제2표. 태양의 연중 매일 평균운행 누적 도수 표[태양주세평행표(太陽周歲平行表)] ············································································198
제2권 표 Ⅲ 제3표. 태양의 가감차 표 [일전가감차표(日躔加減差表)] ···························203
제2권 표 Ⅳ 제4표. 태양의 동지 근처 실제운행 도수를 시간으로 변환한 표[태양동지자행변시표(太陽冬至自行變時表)] ·························································215
제2권 표 해설Ⅱ 태양의 ‘세밀 행도[세행細行]’를 시간으로 변환한 표의 사용법[태양세행변시표용법(太陽細行變時表用法)] ·····························································219
제2권 표 Ⅴ 제5표. 태양의 세밀 평균운행 도수를 시간으로 변환한 표[태양세평행변시표(太陽細平行變時表)] ·····································································222
제2권 표 Ⅵ 제6표. 하루 중의 시간에 대한 태양의 평균운행 도수 표[주일시대준일행표(周日時對準日行表)] ·····································································225
제2권 표 해설Ⅲ 일차표의 사용법 [일차표용법(日差表用法)] ··········································228
제2권 표 Ⅶ 제7표. 균시차 표 [일차표(日差表)] ··································································229
제2권 표 해설Ⅳ <청몽기차표>와 <지반경차표>의 사용법[청몽지반경표용법(淸蒙地半徑表用法)] ·····································································236
제2권 표 Ⅷ 제8표. ‘태양의 고도[일고(日高)]’에 따른 청몽기차 표[일고청몽기차표(日高淸蒙氣差表)] ·············································································238
제2권 표 Ⅸ 제9표. 원지점 거리 등 태양까지 거리를 세 가지로 대별하여 나타낸 지반경차표[최고삼거지반경차표(最高三距地半徑差表)] ·························································242
제2권 표 Ⅹ 제10표. 지구 중심으로부터 태양까지 거리 표 [태양거지심표(太陽距地心表)]
············································································································································246
그림 1 천정동지 시각 구하기(정동지 시각이 자정을 넘지 않는 경우) ·······························179
그림 2 천정동지 시각 구하기(정동지 시각이 자정을 넘는 경우) ········································180
그림 3 태양의 황경 구하기 ····································································································187
그림 4 마기니의 태양의 일일 평균운행 도수표(일부) [Svpplementvm ephemeridvm, ac tabvlarvm secvndorvm mobilivm.... (Venetiis: Apud Haeredem Damiani Zenarij, 1614), 46-47쪽] ·······················································································202
그림 5 마기니의 가감차표(일부) [Svpplementvm ephemeridvm, ac tabvlarvm secvndorvm mobilivm.... (Venetiis: Apud Haeredem Damiani Zenarij, 1614), 53쪽] · 211
그림 6 티코의 가감차 표 [Tychonis Brahe Dani Scripta Astronomica, ed. I. L. E. Dreyer, Tomus II (Hauniae, 1913), 49-50쪽] ·································································214
그림 7 (8)식을 이용하여 그린 균시차 곡선과 《신법산서》와 《숭정역서》의 자료 비교 ····· 233
그림 8 (11)식을 이용하여 그린 균시차 곡선과 《신법산서》와 《숭정역서》의 자료 비교 ··· 235
그림 9 (12)식을 이용하여 그린 균시차 곡선과 《신법산서》와 《숭정역서》의 자료 비교 ··· 235
그림 10 티코의 굴절표 [Tychonis Brahe Dani Scripta Astronomica , ed. I. L. E. Dreyer, Tomus II (Hauniae, 1913), 64쪽] ········································································240
그림 11 《숭정역서》의 청몽기차와 현대천문학에서 제공하는 굴절값과의 비교 ·················241
그림 12 티코의 지반경차표 [Tychonis Brahe Dani Scripta Astronomica , ed. I. L. E. Dreyer, Tomus II (Hauniae, 1913), 65쪽] ·························································245
그림 13 《숭정역서》와 이퀀트(Equant) 모델에서 지구∼태양 거리 비교 ····························247
그림 14 티코와 마기니의 지구∼태양 거리 표 비교 [Tychonis Brahe Dani Scripta Astronomica, ed. I. L. E. Dreyer, Tomus II (Hauniae, 1913), 83쪽; Svpplementvm ephemeridvm, ac tabvlarvm secvndorvm mobilivm.... (Venetiis: Apud Haeredem Damiani Zenarij, 1614), 59쪽] ······························································································248
표 1 천정동지 시각 ‘계산 예 1’의 계산 흐름도 ································································176
표 2 천정동지 시각 ‘계산 예 2’의 계산 흐름도 ································································178
표 3 태양 운동 모델에 따른 거리 과 가감차 ·······························································186
표 4 태양 경도 ‘계산 예’의 계산 흐름도 ···········································································188
표 5 평동지 시각∼동지 다음 날 새벽 자정 사이 경도차(분) ··········································190
표 6 평동지∼근지점의 태양 경도차(도) ···········································································196
표 7 태양의 연중 매일 평균운행 누적 도수표 ··································································198
표 8 원지점의 연중 매일 운행 누적 도수표 ······································································200
표 9 《숭정역서》의 태양 가감차표 ·····················································································204
표 10 《숭정역서》, 《신법산서》, 《역상고성》, 이퀀트 모델의 태양 가감차 비교 ···············210
표 11 《숭정역서》의 가감차와 마가니의 가감차 비교(6도 간격) ·······································212
표 12 태양의 동지 근처 실제 운행 도수-시간 환산표 비교 : 태양의 ‘겉보기 운행[자행(自行)]’
도수값(분, 초)을 시간값(시, 분)으로 변환한 표 ·······················································216
표 13 태양의 평균운행 도수-시간 환산표 : 태양의 평균운행 도수값(분, 초)을 시간값(시, 분)으로 변환한 표 ···········································································································222
표 14 태양의 평균운행 시간-도수 환산표 : 태양의 평균운행 시간 값(시, 분, 초)을 도수 값(도, 분, 초)으로 변환한 표 ·······························································································225
표 15 일차표 ·························································································································230
표 16 청몽기차표 ··················································································································238
표 17 지반경차표 ··················································································································242
표 18 지구~태양 거리표(태양본천의 반경 100000) ·························································246
보충자료 1. 모델을 이용한 태양의 황경 예측 ···············································································185
보충자료 2. 마기니(Magini)가 제시한 태양의 평균운행 누적 도수표 ·······································201
보충자료 3. 《숭정역서》, 《신법산서》, 《역상고성》, 이퀀트(Equant) 모델의 태양 가감차 비교 209
보충자료 4. 마기니(Magini) 가감차표와의 비교 ·····································································211
보충자료 5. 태양이 연 평균 1′(각분) 움직이는 데 걸리는 시간 ·················································224
보충자료 6. 태양의 연 평균 시간 당 운행 도수 ············································································227
보충자료 7. 《숭정역서》와 《신법산서》의 일차표 비교 ·································································231
보충자료 8. 균시차(Equation of Time) ·····················································································231
보충자료 9. 《숭정역서》의 <청몽기차표>와 티코의 굴절표의 비교 ·············································240
보충자료 10. 《숭정역서》의 청몽기차와 현대 천문학의 대기에 의한 굴절값 비교 ······················241
보충자료 11. 티코의 지반경차표 ·····································································································245
보충자료 12. 《숭정역서》와 이퀀트(Equant) 모델에서 지구∼태양 거리 비교 ····························247
보충자료 13. 티코와 마기니의 지구∼태양 거리표 ········································································247
제3부 규장각본 《숭정역서》 〈일전표(日躔表)〉(奎中 3418-v.26) ·····················249
그림 1 규장각본의 12궁거수표 ·····························································································252
그림 2 《신법산서》의 12궁거수표 ·························································································252
그림 3 《숭정역서》 판나이 휘집본 ·························································································257
그림 4 《숭정역서》 규장각본 ·································································································257
그림 5 《신법산서》··················································································································257
제4부 《신법산서(新法算書)》 제25, 26권 〈일전표(日躔表)〉·······························259
그림 1 《신법산서》의 12궁거수표 ·························································································277
그림 2 2도9분/60도=0.03584의 양심차를 가지고 원지점에서 1도씩 떨어질 때 태양의 1일
운동[Tychonis Brahe Dani Scripta Astronomica , ed. I. L. E. Dreyer, Tomus II (Hauniae, 1913), 51-52쪽] ····················································································303
그림 3 원지점 전후의 가감차 계산1 ·····················································································310
그림 4 원지점 전후의 가감차 계산2 ·····················································································310
그림 5 원지점 전후의 가감차 계산3 ·····················································································310
그림 6 원지점 전후의 가감차 계산4 ·····················································································311
그림 7 이퀀트(Equant) 모델에서 가감차 구하기 ································································313
그림 8 근지점 전후의 가감차 계산1 ·····················································································316
그림 9 근지점 전후의 가감차 계산2 ·····················································································317
그림 10 근지점 전후의 가감차 계산3 ·····················································································318
그림 11 황경()에 따른 황경과 적경의 차( ) ·································································327
그림 12 일차 계산 예 ···············································································································334
그림 13 《신법산서》 〈일차표〉 값과 계산값의 비교 ································································340
그림 14 계산값과 《신법산서》 〈일차표〉 값의 차이 ·······························································340
표 1 〈역원 후 200항년 표〉의 ‘평동지∼동지 다음 날 새벽 자정’ 태양 경도차 ············282
표 2 〈역원 후 200항년 표〉의 ‘평동지∼근지점’의 태양 경도차(도) ·······························284
표 3 B.C.2276년∼A.D.5584년 동안 갑자년의 ‘평동지∼동짓날 자정’의 경도차 및 근지점의 경도 ························································································································287
표 4 60년 동안 매년 태양의 평균운행 및 근지점의 이동 누적 도수 ······························290
표 5 태양 실제운행의 1년 동안 매일 누적 경도 ·······························································295
표 6 1년 중 태양의 평균 운행 누적 도수 ··········································································299
표 7 태양의 평균 운행 누적 시간 ······················································································305
표 8 《신법산서》 가감차 계산과 함께 제시된 저자의 평을 재비평 ··································315
표 9 동지 전후 n일의 하루 중 운행 도수(분, 초) 누적에 따른 경과 시간 ······················324
표 10 《신법산서》 〈일차표〉 값과 계산값의 비교( =0.01792) ··········································337
보충자료 1. 《숭정역서》와 티코의 태양 연중 실제 1일 운행 도수 표 비교 ·································303
보충자료 2. 《신법산서》에서 제시한 가감차 계산 방법 ································································313
보충자료 3. 일차의 두 번째 원인 : 황경()에 따른 황경과 적경의 차( ) ····························327
보충자료 4. 춘분 때 가감차를 기준으로 계산한 각 절기의 균시차 ·············································333
보충자료 5. 《신법산서》의 〈일차표〉 값과 계산값의 비교 ····························································339