NOVAS C3.1：美国海军天文台天体测量软件用户手册

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"美国海军天文台天体测量例程库使用手册" 该手册详细介绍了美国海军天文台（U.S. Naval Observatory, USNO）的NOVAS（Naval Observatory Vector Astrometry Software）C语言版本3.1的使用方法。NOVAS是一个强大的天体测量软件库，用于计算天体的位置、运动以及相关的天文数据。这份用户指南由John Bangert、Wendy Puatua、George Kaplan、Jennifer Bartlett、William Harris、Amy Fredericks和Alice Monet等人编写，并于2011年3月发布。在本手册中，读者可以找到以下关键知识点： 1. **天文学背景**： - **天文坐标系统**：涵盖地心坐标、黄道坐标、赤道坐标等不同系统的转换与应用。 - **可观测量的计算**：包括天体的位置、亮度、视差等的计算方法。 - **时间尺度在天文学中的应用**：如UT（世界时）、TAI（国际原子时）、TT（历元 Terrestrial Time）和GPS时间等。 - **地球自转和公转模型**：介绍预cession（岁差）和nutation（章动）的模型。 - **地球-天球关系**：讨论地球的运动如何影响我们观测到的天体位置。 2. **安装NOVAS**： - **分发文件列表**：列出所有必要的文件及其功能。 - **安装与基本验证**：详细步骤指导用户正确安装和验证软件运行。 - **外部太阳系星历文件的使用**：如何集成和利用这些文件来获取更精确的行星位置数据。 - **外部小行星星历文件的使用**：适用于对小行星观测和研究的用户。 - **外部CIO文件的使用**：CIO（Celestial Intermediate Pole）文件对于精确的坐标转换至关重要。 3. **程序接口和应用**：这部分可能涉及如何调用NOVAS库中的函数，进行天体位置计算，以及如何将结果整合到用户的应用程序中。 4. **参考文献和符号**：提供了进一步学习和理解相关概念的参考资料，以及常用缩写和符号的定义。该手册旨在帮助天文学家、软件开发者和其他对精确天体位置计算有需求的人员有效地利用NOVAS库。通过深入阅读和实践，用户能够掌握如何利用这个工具进行复杂的天体测量任务。

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consistent with it to within the data’s inherent accuracy. [place, ephemeris] The latter case

will probably apply to most FK5-compatible data specified with respect to the mean equator

and equinox of J2000.0 (the “J2000.0 system”). The distinction between the ICRS and the

J2000.0 system becomes important only when an accuracy of 0.02 arcsecond or better is

important. [frame_tie] Nevertheless, because NOVAS is designed for the highest-accuracy

applications, the ICRS is mentioned as the reference system of choice for many input

arguments to NOVAS functions.

Reference Systems for NOVAS Output Data: For output coordinates (e.g., the position of

Mars on a certain date), three options for the coordinate system are available. (The

coordinates themselves can be right ascension and declination or the components of a unit

vector.) You can request coordinates expressed in the GCRS, the equator and equinox of

date, or the Celestial Intermediate Reference System (equator and CIO of date). These

coordinate systems can be requested for either geocentric or topocentric output. [place,

gcrs2equ]

NOVAS can also convert topocentric right ascension and declination, with respect to the

equator and equinox of date, to local horizon coordinates, zenith distance and azimuth. The

angular shift due to atmospheric refraction can be included as an option. [equ2hor] Another

function is available to transform right ascension and declination to ecliptic longitude and

latitude. [equ2ecl] Still another transforms right ascension and declination to galactic

longitude and latitude. [equ2gal]

Reference System for the Location of the Observer: The location of an Earth-based observer

is specified in NOVAS by longitude, latitude, and height with respect to the World Geodetic

System 1984 (WGS-84) reference ellipsoid. Coordinates provided by GPS (if uncorrected for

the local datum) are referred to WGS-84, which is also sometimes called the Earth-centered,

Earth-fixed (ECEF) system. The International Terrestrial Reference System (ITRS) is a

geocentric rectangular coordinate system used for high-precision work. WGS-84 coordinates

are functionally equivalent (within a few centimeters) to ITRS coordinates. Thus, the

geodetic positions used by NOVAS are consistent with the ITRS. [geo_posvel]

1.2 Computing Observable Quantities

NOVAS is mostly used for computing, for a selected object, the instantaneous angular

coordinates (or the equivalent unit vector components) at which it might be observed within

one of several user-selected coordinate systems. Obviously the values of the angular

coordinates computed by NOVAS depend on the coordinate system requested, but there are

several phenomena that affect the observed position of a star or planet that are independent of

the coordinate system. For stars, the effects are

• Proper motion (generalized): the three-dimensional space motion of the star,

relative to that of the solar system barycenter, between the catalog epoch and the

date of interest. Assumed linear and computed from the catalog proper motion

components, radial velocity, and parallax. Projected onto the sky, the motion

amounts to less than 1 arcsecond per year (usually much less) except for a few

nearby stars. [starvectors, proper_motion]

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• Parallax: the change in our perspective on stars in the solar neighborhood due to the

position of the Earth in its orbit. Its magnitude is (distance in parsecs)

-1

and, hence,

is always less than 1 arcsecond. [bary2obs]

• Gravitational light bending: the apparent deflection of the light path in the

gravitational field of the Sun and, to a much lesser extent, the other planets.

Although it reaches 1.8 arcsecond at the limb of the Sun, it falls to 0.05 arcsecond

10º from the Sun and amounts to no more than a few milliarcseconds over the

hemisphere of the sky opposite the Sun. [grav_def, grav_vec]

• Aberration: the change in the apparent direction of light caused by the observer’s

velocity (v) with respect to the solar system barycenter. Independent of distance, it

is approximately equal to v/c, expressed as an angle. Therefore, it can reach

21 arcseconds for observers on the surface of the Earth and somewhat more for

instruments in orbit. [aberration]

• Atmospheric refraction: the total angular change in the direction of the light path

through the Earth’s atmosphere; applies only to an observer on, or near, the surface

of the Earth. The direction of refraction is always assumed to be parallel to the local

vertical and a function only of zenith distance although these assumptions may not

be true in all cases. At optical wavelengths, its magnitude is zero at the zenith,

about 1 arcminute at a zenith distance of 45°, and 0.5° at the horizon. Refraction is

roughly proportional to the atmospheric pressure at the observer, but it also depends

on other atmospheric parameters and the observational wavelength. [equ2hor,

refract]

The same effects are relevant to objects in the solar system, except that the proper motion

calculation is replaced by a function that retrieves the object’s barycentric position from its

ephemeris as part of an iterative light-time calculation. [light_time, ephemeris] Extragalactic

objects can be considered to be stars with zero parallax and proper motion. The star or planet

positions computed by considering all these effects obviously depend on the location of the

observer; so that an observer on the surface of the Earth will see a slightly different position

than one at the geocenter, the differences being greater for solar system objects, especially

nearby ones (reaching about 1º for the Moon).

In computing these effects, the same functions are used for stars and planets, because

NOVAS uses position vectors rather than directions; that is, internally, it places all objects at

their computed distance from the solar system barycenter. (Objects of unknown distance are

placed on the “NOVAS celestial sphere” at a radius of 1 Gigaparsec = 2 × 10

astronomical

units). [starvectors] These vectors are all defined within the BCRS until the relativistic

aberration calculation is applied, which effectively takes an input vector in the BCRS and

produces an output vector in the GCRS.

Nomenclature: When all these effects are included, we obtain star or planet coordinates in

the GCRS that reflect where the star or planet actually appears in the sky. The coordinates

can then be transformed to other reference systems, if desired. We will call the results of this

process, generically, the “apparent position” or “observed position” of the object.

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However, some caution with the semantics is in order, because the term apparent place has

traditionally been reserved specifically for the star or planet position we obtain by applying

all these effects (except refraction) for a geocentric observer, with the coordinates expressed

with respect to the true equator and equinox of date. For an observer on the surface of the

Earth, the corresponding term is topocentric place. If the apparent star or planet position is

instead expressed with respect to the mean equator and equinox of J2000.0, the terms used in

NOVAS have been virtual place and local place, respectively. (Although these last two

terms were suggested in the Kaplan et al. (1989) paper previously cited, they do not appear to

have been widely used outside of the context of NOVAS.)

The above terminology is reflected in the names of the high-level functions that perform the

computations, where “app” stands for “apparent place”, “topo” stands for “topocentric

place”, etc. [app_star, app_planet, topo_star, topo_planet, virtual_star, virtual_planet,

local_star, local_planet] In addition, an astrometric place calculation can be used for some

differential measurements; it is the same as virtual place except that light bending and

aberration (and refraction) are not computed, under the assumption that these effects are the

same for all objects within a small field of view. [astro_star, astro_planet]

In response to the introduction of the new IAU-recommended coordinate systems, we must

make some adjustments and additions to the nomenclature. The mean equator and equinox

of J2000.0, considered as a geocentric system, has been replaced by the GCRS. The IAU

Working Group on Nomenclature (2003–2006) recommended that the term proper place be

used for what is called virtual place in NOVAS. With the introduction of the Celestial

Intermediate Reference System, with its right ascension origin at the CIO, we now have two

more possibilities for apparent positions, one geocentric and one topocentric. The geocentric

coordinates are called the object’s intermediate place, and right ascension measured with

respect to the CIO is called intermediate right ascension.

The complete table of nomenclature for apparent positions of various types, updated for

NOVAS 3.0, and later, is below.

Final Coordinate System Observer at Geocenter

Observer near

Surface of Earth

True equator and equinox of date apparent place topocentric place

Celestial Intermediate Reference System intermediate place [no name]

GCRS proper or virtual place local place

GCRS astrometric place* [no name]

*variant of proper or virtual place, in which some calculations are omitted

The only difference between a position expressed in the Celestial Intermediate Reference

System and the same position expressed with respect to the true equator and equinox of date

is an offset in right ascension, the equation of the origins. The equation of the origins is the

angle between the equinox and the CIO, both of which lie on the instantaneous equator.

[ira_equinox]

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NOVAS function place can be used to compute all of these types of positions; the input argu-

ments allow you to select both the location of the observer and the coordinate system in

which the computed position is to be expressed. These selections make the nomenclature

superfluous. place does not apply atmospheric refraction, but that can be added by a

subsequent call to equ2hor.

1.3 Time Scales for Astronomy

As explained in USNO Circular 179,

We almost always start with Coordinated Universal Time (UTC), which is the worldwide

basis for civil time. UTC (USNO) is obtained from the Global Positioning System (GPS). In

addition, UTC can be obtained with varying accuracy from Network Time Protocol (NTP)

services on the Internet and from radio time broadcasts (e.g., WWV, WWV, WWVB, and

CHU), cell phones, TV, etc. UTC is based on SI seconds at sea level on the rotating Earth.

From UTC, one adds an integral number of (SI) seconds to obtain International Atomic

Time (TAI): TAI = UTC + ∆AT, where ∆AT is a total count of leap seconds in UTC (for

example, ∆AT = 34 s for 2011). The USNO

basically two kinds of time scales are used in

astronomy; those that are based on the Système International (SI) second (“atomic time”) and

those that are tied to the irregular rotation of the Earth; in essence, “lab” time and

“astronomical” time, respectively. Theoretical time scales, not kept by any real clocks, are

also used that are the time basis for—that is, the fourth dimension of—the BCRS and GCRS.

Earth Orientation (EO) Department

Bulletin A

provides a

complete table of ∆AT values on-line. The current value may also be found at the beginning

NOVAS Time Arguments: Typically, the first input argument to most NOVAS functions is

the time of interest (for example, the time of an observation), expressed as a Julian date (JD).

Julian dates are simply a convenient format for representing a date and time in any time scale

and are discussed below. Two time scales are used as the basis for most of the Julian dates

that are input arguments to the higher-level NOVAS functions.

published by the International Earth Rotation and Reference System Service

(IERS). The addition of a leap second to UTC, which increases ∆AT by 1 second, is usually

done, when needed, at 23:59:59 UTC on December 31 and is announced about six months in

advance.

The first is Terrestrial Time (TT), which is effectively just a constant offset from TAI:

TT = TAI + 32.184 s. Therefore, TT = UTC + ∆AT + 32.184 s. Historically, TT is

considered continuous with the obsolete time scales Ephemeris Time (ET) and Terrestrial

Dynamical Time (TDT). It is meant to be a smooth and continuous “coordinate” time scale

independent of the rotation of the Earth. The high-level NOVAS functions that compute the

apparent direction of an object at a specified time use Julian dates based on TT. [place,

app_star, topo_star, app_planet, transform_cat]

http://www.usno.navy.mil/USNO/astronomical-applications/publications/circ-179

http://maia.usno.navy.mil/ser7/tai-utc.dat

http://maia.usno.navy.mil/ser7/ser7.dat

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The second time scale is Universal Time (UT1), which is based on the rotation of the Earth.

It is needed for computing sidereal time [sidereal_time] or the Earth Rotation Angle (ERA or

θ) [era], which in turn allows one to compute hour angles, altitude and azimuth, or other

topocentric quantities. UT1 is also obtained from UTC: UT1 = UTC + (UT1−UTC). The

value of UT1−UTC is available in a daily-interval tabulation on the IERS web site

Bulletin B

(data

marked “P” are predictions); IERS publishes historical values in .

A few of the lower-level NOVAS functions use time arguments based on Barycentric

Dynamical Time (TDB). [

The values of

UT1−UTC often change at the millisecond level over one day. In computing the topocentric

direction of a celestial object with respect to Earth-fixed axes (e.g., altitude and azimuth),

1-arcsecond accuracy in the final angles requires 67-ms accuracy in UT1. Because

UT1−UTC can have an absolute value up to 900 ms, it is an important correction for all but

the crudest applications; that is, in most cases, it is not acceptable to approximate UT1 as

being equal to UTC.

e_tilt, precession, ephemeris, solarsystem] TDB differs from TT

only by periodic variations (due mainly to the Earth’s elliptical orbit and described by

General Relativity), the largest of which has an amplitude of 1.6 ms and a period of one year.

[tdb2tt] The difference between the two time scales can often be neglected in practice as

noted in the function preambles where appropriate. TDB is equivalent to T

eph

the barycentric

coordinate time argument of the Jet Propulsion Laboratory (JPL) planetary and lunar

ephemerides.

As previously mentioned, time is specified within NOVAS as Julian dates, which can be used

for any of the above time scales. Julian dates are a simple count of days since noon on 4713

BC January 1, so that any date in recorded human history has a positive JD. Over 2.4 million

days have elapsed since JD 0, and thus, for current dates, seven digits of precision are taken

up just by the day count; if the JD is given by a standard double-precision floating-point

number, about 9 digits are left to represent the time of day. Therefore, we expect a double-

precision floating-point JD can represent time to a precision of about 10

-9

day ≈ 100 μs.

However, after further examination, Kaplan, Bartlett, and Harris (2011) determined that the

actual precision is closer to 20.1 μs. In those NOVAS functions where more precision is

appropriate, the JD can be split between two input arguments, one that carries the high-order

part of the JD (e.g., the day count) and the other that carries the low-order part (e.g., the

fraction of a day). Note that for 0h (TT, UT1, or TDB), the fractional part of the Julian date

is 0.5. An online calendar-date-to-Julian-date converter is available at the AA Department

web site.

The epoch J2000.0 is considered to be an event at the geocenter at Julian date 2451545.0 TT,

which is 2000 January 1, 12h TT.

NOVAS has utility functions to convert between calendar date and Julian date

and vice versa. They work for any time scale; that is, their input and output arguments should

be considered to be just different ways of expressing the same instant within the same time

scale. [julian_date, cal_date]

http://maia.usno.navy.mil/ser7/mark3.out

http://www.iers.org/IERS/EN/Publications/Bulletins/bulletins.html

http://www.usno.navy.mil/USNO/astronomical-applications/data-services/cal-to-jd-conv

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