There are many star atlases on the market. My own bias runs to Norton's Star Atlas, which I have consulted since I was a child. This is an old and famous star atlas, written by the amateur astronomer Arthur Philip Norton (1876–1955) and first published in 1910. The current edition is the 18th. This atlas is aimed at amateur astronomers, providing maps of the visible stars down to 6th magnitude and of interesting objects visible in a small telescope, such as the objects from the Messier catalog. The bulk of the atlas describes small telescopes, practical astronomy, and the characteristics of the moon, the planets, the stars, and the galaxies. The atlas includes tables of planetary data, such as the mass of a planet and the characteristics of a planet's moons. Other tables list the nearest stars and the brightest stars. This is an excellent book for a budding amateur astronomer.
For the characteristics of the planets listed on this web site, the author makes use of the book Global Earth Physics: A Handbook of Physical Constants, edited by T.J. Ahrens, which is published by the American Geophysical Union. This book is a collection of articles that cover the physics of Earth and the Solar System planets. Each article begins with a section describing the parameters to be presented, such as the parameters that describe the orbit of a planet, followed by tables of the best current values for those parameters. The articles of astronomical interest are “Astrometric and Geodetic Properties of Earth and the Solar System” by Charles F. Yoder, “Composition of the Solar System, Planets, Meteorites, and Major Terrestrial Reservoirs” by Horton E. Newsom, “Properties and Composition of the Terrestrial Oceans and of the Atmospheres of the Earth and Other Planets” by Bruce Fegley Jr., and “Earth Rotation” by Jean O. Dickey. Individual articles from the book are available online. The book is aimed at scientists, and is rather heavy in mathematics and physics.
Good technical references for astrophysical quantities and formulae are Astrophysical Formulae (now two volumes) by Kenneth R. Lang and Allen's Astrophysical Quantities. These books are very expensive, so get them from a university library rather than a bookstore.
For constants of physics, the best source is online at the National Institute of Standards and Technology (NIST). This site gives the current best values for such constants as Planck's constant, the gravitational constant, and the charge of the electron. The values on this site are also published at the end of summer each year in a supplement to the trade journal Physics Today.
Two online databases are given at the end of the reference list. The first, Simbad, is a database of astronomical objects, such as stars and galaxies. This database contains multiple names of object, their positions on the sky, and much more general information of their properties. The second, VizieR, is a database of astronomical catalogs. A catalog is data collected on a set of objects by one group. For instance, an important catalog from the early part of the twentieth century available online through the VizieR catalog service is the Henry Draper catalog of stars. This catalog collects the positions, magnitudes, and spectral types of stars down to about magnitude 9. This and other catalogs can be searched using the VizierR web interface.
Aherns, T. J., ed. Global Earth Physics: A Handbook of Physical Constants. AGU Reference Shelf, No. 1. Washington: American Geophysical Union, 1995.
Clark, Arthur, ed. Allen's Astrophysics Quantities. New York: Springer-Verlag, 2000.
Dickey, Jean O. “Earth Rotation.” In Global Earth Physics: A Handbook of Physical Constants, edited by T.J. Ahrens, 356–368. AGU Reference Shelf, No. 1. Washington: American Geophysical Union, 1995.
Fegley, Bruce Jr. “Properties and Composition of the Terrestrial Oceans and of the Atmospheres of the Earth and Other Planets.” In Global Earth Physics: A Handbook of Physical Constants, edited by T.J. Ahrens, 320–345. AGU Reference Shelf, No. 1. Washington: American Geophysical Union, 1995.
Lang, Kenneth R. Astrophysical Formulae: Volume 1. Radiation, Gas Processes, and High Energy Physics. 3rd ed. New York: Springer, 1999.
Lang, Kenneth R. Astrophysical Formulae: Volume 2. Space, Time, Matter, and Cosmology. 3rd ed. New York: Springer, 1999.
Ridpath, Ian, ed. Nortons's 2000.0: Star Atlas and Reference Handbook. 18th ed. Harlow, Essex, England: Longman Scientific and Technical, 1989.
NIST Reference on Constants, Units, and Uncertainty. National Institute of Standards and Technology (NIST).
Simbad Astronomical Object Database. Centre de Données astronomiques de Strasbourg.
VizieR Catalog Service. Centre de Données astronomiques de Strasbourg.