Orbit Computations in H.M. Nautical Almanac Office

by Don B.Taylor

Her Majesty’s Nautical Almanac Office (HMNAO) is part of the Space Data Division of the Space Science and Technology Department at the Rutherford Appleton Laboratory, UK. HMNAO publishes a number of books on astronomical and navigational subjects. The principal publications in these fields being The Astronomical Almanac (AsA) and The Nautical Almanac respectively, which are joint publications with the U.S.Naval Observatory. However, The Nautical Almanac is almost entirely a production of HMNAO whereas The Astronomical Almanac is prepared by both offices.

The AsA gives information on a host of different topics in astronomy. From fundamental data such as phenomena (eg Moon’s phases, eclipses, principal occultations, sunrise and sunset times etc.), time-scales and coordinate systems (eg calendar, precession, nutation, apparent place reduction etc.) to stars and stellar systems (eg lists of bright stars, variable stars, bright galaxies etc.).

A large portion of the book contains ephemerides and other information such as orbital elements and phenomena on solar system bodies. These include data on the Sun, planets, minor planets, satellites and comets.

An ephemeris is a table of calculated positions of a celestial object with the time as argument. To produce an ephemeris an analytical theory or a numerical integration of the body must be fitted to observations made of that body over a period of time. This is a major undertaking, for example in producing planetary ephemerides. Often different types of data and quality (eg photographic, CCD, spacecraft etc.) must be reduced in the orbit determination which adds considerably to the complexity of the fitting process. In the Astronomical Almanac the planetary ephemerides are from the Jet Propulsion Laboratory, U.S.A. The ephemerides for the larger minor planets in the Astronomical Almanac have been determined by J.L.Hilton at the U.S.N.O. Almanac Office. For ephemerides of the different satellite systems several authors have worked in this field. An important contribution to this subject has been made by HMNAO.

Since the 1960’s researchers in HMNAO have formulated satellite theories and fitted them to observations they have made in addition to published data. The theories used in the AsA of the two Martian satellites and the eight major satellites of Saturn were derived in HMNAO. A series of CCD observations of the five major satellites of Uranus made on La Palma in 1990-1991(Jones et al (1998)) were analysed by numerical integration (Taylor(1998)). The integration was fitted to observations in the time interval April 1977 to October 1995, which includes some of the best quality photographic data, the Voyager astrographic data, CCD data and meridian circle observations. Physical parameters of the system such as the satellite masses and dynamical flattening of Uranus were determined. The La Palma data was one of the most accurate ground-based datasets. Research into improving the orbits of the Uranian satellites is continuing.

The data given in the AsA on natural satellites is primarily for identification and for observation planning purposes. To aid in this, phenomena for the major satellites are given. This includes greatest western and eastern elongations and superior and inferior conjunctions. To facilitate these computations, from planet and satellite positions, offsets of the satellite are computed as seen in the plane of sky. These are sometimes termed differential tangent plane coordinates. From these coordinates over short intervals of time mixed functions of secular and periodic terms were fitted in which coefficients of the terms are determined (Taylor(1995)). The precision of the approximating function in each case being about 0.01". Offsets for a year can easily be represented by sets of these coefficients. From these, algorithms are set up to compute satellite phenomena (Taylor and Sinclair (2003)).

Mixed functions have been derived for the two Martian satellites, four Galilean satellites, eight major satellites of Saturn, five major satellites of Uranus and the largest satellite of Neptune. For the Galilean satellites the phenomena in the AsA are computed by the Bureau des Longitudes. The remaining major satellites, phenomena in the AsA is computed using the mixed functions representation of the satellite orbits.

The mixed functions representation of satellite differential coordinates gives a compact form for the orbits and is particularly suitable for setting up data on the web and for animations and other graphical output. Ephemerides of several of the major satellites are now given on The Astronomical Almanac Online at http://asa.nao.rl.ac.uk and http://asa.usno.navy.mil. The phenomena and website data based on the mixed functions is computed at the U.S.N.O. Almanac Office.

The AsA gives osculating elements for periodic comets returning to perihelion for the year of publication. These have been determined by B.G.Marsden at the Smithsonian Astrophysical Observatory. From a numerical integration with starting conditions from these elements and perturbations from the nine planets, tracks of the comet on the night sky can be drawn to help in locating the comet. This work is in progress and will appear on our website.

Links:
HMNAO: http://www.nao.rl.ac.uk/
Astronomical Almanac Online: http://asa.nao.rl.ac.uk
Jones, D.H.P, Taylor, D.B., Williams, I.P., 1998.: http://www.edpsciences.org/articles/aas/pdf/1998/10/ds1462.pdf
Taylor, D.B., 1995.: http://www.nao.rl.ac.uk/data/tn/naotn68.pdf
Taylor, D.B., 1998.: http://aa.springer.de/papers/8330001/2300362.pdf
Taylor, D.B., Sinclair, A.T., 2003.: http://www.nao.rl.ac.uk/data/tn/satelit4.pdf

Please contact:
Don Taylor, CCLRC, UK
Tel: +44 1235 445000
E-mail: hmnaonao.rl.ac.uk