숭정역서에 기술된 태양의 운동

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