邢云路对《授时历》日躔过宫推步的改进

考察明末邢云路所撰《古今律历考》中述及的日躔推步实例与先期恢复的《授时历》和《大统历》方法进行推步比对.采用邢云路改进的《授时历》法推步万历己亥岁(1599年)日躔交宫时间,结果与邢氏的标准偏差为5.93刻(=85.39 min),同时交宫夜半黄道宿度的偏差0.06古度(=0.059°);其中若扣除戌宫可能因数据错误产生的较大误差,则标准偏差将降为1.38刻(=19.87 min)和0.01古度(=0.0099°).其次,采用《大统历》计算该年日躔交宫,与邢云路计算的标准偏差为1.09刻(=15.70 min),交宫夜半黄道宿度的标准误差为0.05古度(=0.049°).据此可认为:基本恢复了邢氏的日躔推步方法;邢云路并未对《授时历》的日躔推步方法作本质上的改进,只是修改了其中的年长、周天分及宫界度.研究表明,邢氏所得《大统历》推交宫的结果与《授时历》偏差过大,原因在于其修改了《授时历》的参数,邢氏有厚《授时》薄《大统》之嫌.     

明嘉靖六年《大统历》历书的气朔推步精度

历书是历法的民用本.考察了明嘉靖六年(1527年)<大统历>历书,根据历书所颁朔日和节气时刻,以及先期恢复的<授时历>和<大统历>推步术,并利用现代天文历算结果,可考校得出:(1)历书所载朔日和节气日期、时刻确由<大统历>推得;(2)<大统历>与<授时历>推步结果存在差异,推朔平均差33.35 min或34.93 min,推气平均差86.40 min,且两者均有差1日现象;(3)<大统历>与现代推算合朔时刻的平均误差为24.50 min或44.03 min,与现代推算节气时刻的差平均为1.25 d,若扣除太阳中心差则节气推步的误差将减少到86.40 min.     

邢云路《戊申立春考证》解析

根据明末邢云路所撰《戊申立春考证》,通过历法推步结果与实测数据的比验,详细考察了邢氏确定明万历三十六年(1608年)立春节气时刻的推演过程.分析了邢氏观测误差约2°的原因.完整给出依《授时历》和《大统历》推步该年的气朔结果,两者仅立春异日.且邢氏实测所得立春时刻=14.912333 d和年长=365.2421 90 d与《授时历》的符合率远优于《大统历》.古代的节气测算方法并不精确,为褒《授时历》贬《大统历》,邢氏有隐匿数据和修改数据之嫌,但实测年长史上最佳亦不排除巧合.给出邢氏为使历法推步结果与实测密合可能所做的数据调整方案,包括历数及观测数据的修改.     

《授时历》五星推步的精度研究

着重考察了《授时历》的步五星术,考校、复原了其推步方法.(1)推步了1299年木星历,并与已有研究进行比对,从而确认恢复方法的正确性.(2)得出《授时历》在1280～1650年间推步五星黄经的精度,木星、火星、土星、金星和水星的误差的绝对值平均分别为0.49°、1.91°、0.70°、2.82°和5.01°,木星、土星的精度较高.(3)指出将现代天文方法获取的《授时历》五星参数(周率、历率、度率、合应及历应)精确值代入《授时历》推步模型,木星、土星的推步精度并未提高,误差分别为1.83°和1.21°,而水星、金星和火星的误差却大幅加大,结果分别为30.04°、54.86°和10.82°.说明某些重要参数的修正并不能改善推步结果.     

中国历代荧惑守列宿与四星聚、五星聚考查

利用授时历法和现代天文计算方法,对中国历代天文志记录的荧惑(火星)守列宿、四星聚、五星聚进行分析研究,结果表明:65条荧惑守列宿,正误率分别为49%和51%.如果把荧惑留、留守、在某宿等运动形态也考虑为守的范围,共有95条,其正误率分别为56%和44%.12条四星聚正误率各占一半,即50%.11条五星聚正误率分别为82%和18%(其中含五星并见).并对错误记录的原因做了初步探讨.     

中国古历定朔推步综述

“朔”简言之表日月黄经相等，先民对其认识经历了一个从平朔到定朔的过程，通过研究古历，文中分析并归纳了不同时期中国古历日制度的基本元素之一－朔的两种推步方法：“积年法”和“《授时历》法”，其中包括平朔，日躔，月离，及定朔的推步方法等；得出了由各历的基本历数直接推出的中国古历定朔计算的一般公式，同时亦给出了《授时历》的推朔法和部分算例。     

《授时历》预报2012年日食

元代郭守敬等1280年编制的《授时历》是中国本土科学家研制的最后一部历法,具有极高的精度。采用其仍可预报2012年5月21日发生的日食,其预报北京地区的见食情况时食甚时刻误差4 min,食分误差为0.04。给出了《授时历》推步的1990～2050年北京的见食情况及精度,其中食甚时刻的标准偏差为103.04 min,食分的标准偏差则不低于0.33。通过考察1280～2050年间186个日食计算结果,可得出《授时历》自行用以来推步日食的误差,考虑到存在错报(不可见)和漏报因素的影响,其食甚时刻和食分的标准偏差分别不低于50.65 min和0.19;同时指出,随着行用时间的延长其推时误差也逐步放大。     

中国古代太阳中天观测及二至点测算精度

研究了元代《授时历议))所保存的天象观测和推步资料，得出：(1)在AD1277—1280年问所作的98次太阳中天观测的时刻及地平高度的绝对值平均误差分别为2．64min和6．78′．(2)6部古历——《大衍历》、《宣明历》、《纪元历》、《统天历》、《重修大明历》和《授时历》推步BC522年前的3个冬至时刻的误差范围为0．97—3．51d；而AD435—1280年间的45个冬至时刻的绝对值平均误差则分别为9．35、10．42、5．54、2．97、5．68、3．36h．(3)古代确定的AD442—1280年间的16个二至时刻的绝对值平均误差为199．59min，其中元代的误差为27．89min．     

中国汉代记载的五星运动精度考查

五星运动的观测与研究是古代历法重要内容之一,也是检验历法疏密的主要方法之一,因此深受古代天文学家重视.《汉书·天文志》和《续汉书·天文志》记载有具体时间和位置的五星运动约160条.利用现代天文计算方法,对诸条进行计算、验证、分析与研究,并将正误结果用图和表反映出来.结果表明:160条记录中绝大多数是准确和比较准确的,占77.5%.错误的仅有36条,占22.5%.此外,160条行星运动记录中,其中有3种典型的或者说特殊的运动形态,即"守"、"合"、"犯"的运动分别占总数9%(14条),14%(22条)和29%(46条).对这3种特殊的运动形态进行了深入细致的分析研究,结果列于图表中.研究表明:汉代的行星运动记录为观测实录,至于36条错误记录,错误原因是多方面的,但主要是后人对观测资料加工、整理、编辑和出版时造成的.     

陶寺观象台遗址的天文学分析

对陶寺观象台遗址的外观形态,用天文方法分析了12个测缝与日出日期的对应关系和天文学作用,对比了考古队的模拟观测与理论计算的结果.分析指出,测缝E2一E12对应于一周年的日出方向,大致均分,产生一个不均匀的时间体系.E1对应于"月南至",提供一个18-19年的年代指示.这是一个集礼仪祭祀和观象授时为一体的建筑.     

Acceleration of Numerical Integration of the Equations of Motion of Asteroids

Solar System Research - Finding and studying possible collisions of asteroids approaching the Earth requires a significant amount of computation. This paper describes the R0 program created to...     

Equation of state and anisotropy of pressure of magnetars

Magnetars are the neutron stars with the highest magnetic fields up to 10¹⁵–10¹⁶ G. It has been proposed that they are also responsible for a variety of extra-galactic phenomena, ranging from giant flares in nearby galaxies to fast radio bursts. Utilizing a relativistic mean field model and a variable magnetic field configuration, we investigate the effects of strong magnetic fields on the equation of state and anisotropy of pressure of magnetars. It is found that the mass and radius of low-mass magnetars are weakly enhanced under the action of the strong magnetic field, and the anisotropy of pressure can be ignored. Unlike other previous investigations, the magnetic field is unable to violate the mass limit of the neutron stars.     

Observations of the intensity of the penumbra of sunspots

Observations of the penumbral intensity of sunspots in 13 wavelength regions are presented. In 4 wavelength regions 54 sunspots are measured. In the other wavelength regions the number of sunspots considered ranges from 3–19.The penumbral intensity alters with position within the spot. This intensity variation is found to be comparable with the change in intensity from one spot to another. The penumbral intensity is found to be independent of spot size in the sample considered.The penumbra model of Kjeldseth Moe and Maltby (1969) with = 0.055 is supported by the measurements.     

A survey of orbits of co-orbitals of Mars

Many asteroids with a semimajor axis close to that of Mars have been discovered in the last several years. Potentially some of these could be in 1:1 resonance with Mars, much as are the classic Trojan asteroids with Jupiter, and its lesser-known horseshoe companions with Earth. In the 1990s, two Trojan companions of Mars, 5261 Eureka and 1998 VF₃₁, were discovered, librating about the L₅ Lagrange point, 60° behind Mars in its orbit. Although several other potential Mars Trojans have been identified, our orbital calculations show only one other known asteroid, 1999 UJ₇, to be a Trojan, associated with the L₄ Lagrange point, 60° ahead of Mars in its orbit. We further find that asteroid 36017 (1999 ND₄₃) is a horseshoe librator, alternating with periods of Trojan motion. This asteroid makes repeated close approaches to Earth and has a chaotic orbit whose behavior can be confidently predicted for less than 3000 years. We identify two objects, 2001 HW₁₅ and 2000 TG₂, within the resonant region capable of undergoing what we designate “circulation transition”, in which objects can pass between circulation outside the orbit of Mars and circulation inside it, or vice versa. The eccentricity of the orbit of Mars appears to play an important role in circulation transition and in horseshoe motion. Based on the orbits and on spectroscopic data, the Trojan asteroids of Mars may be primordial bodies, while some co-orbital bodies may be in a temporary state of motion.     

Graphical representation of periodic motion of the line of nodes of the Moon

In the text-books of astronomy, sections generally related to the Moon deal with the orbital elements of the Earth-Moon system such asa, e, i, , and the time of perigee passage. While the MEAN of the first of the three elements do not vary, mean longitude of the ascending node-mean longitude of the lunar perigee and the time of perigee passage undergoes secular as well as periodic changes due predominantly to the action of the Sun's gravitational attraction. While to a certain degree, explanations related to the calculation of the lunar orbit parameters are given, not a single graphical representation of these short- or long-periodic changes are presented. We allow the number of data related to these periodic changes must cover a large span of time; and if regression of the line of nodes or advances of the line of apses are to be graphically seen, data covering 18.61 and 8.85 yr, respectively, are needed. In this work we particularly aim at the graphical representation of the periodic changes of the line of nodes.