Stellar Paths

This is the latest effort in a sequence of presentations begun in 1949 with a series of lectures on long-focus photographic astrometry given by the author as Fulbright professor in Paris at the invitation by the late H. Mineur, at that time Director of the Institut d' Astrophysique. These earlier lectures were published as a series of review articles in Popular Astronomy (1951) and appeared both as Contributions de l'Institut d'Astrophysique, Serie A, No. 81 and as reprint No. 75 of Sproul Observatory. A more elaborate presenta­ tion was given in 1963 in Stars and Stellar Systems, which was followed by Principles of Astrometry (1967, W. H. Freeman & Co.). During the second half of 1974, again under Fulbright auspices, at the invitation of Pik Sin The, I lectured at the Astronomical Institute in Amster­ dam, followed by a short course in May-June 1978 at the invitation of E. P. J. van den Heuvel. I gave a more extensive course at the Institut d' As­ trophysique at the invitation of J. C. Pecker of the College de France and of J. Audouze, Director of the LA.P. Both in Amsterdam and in Paris I had presented occasional astrometric topics at various times. The opportunity to lecture in France and in Holland has facilitated, influenced and improved the organization and contents of the presentations on the subject of long-focus photographic astrometry.

1. Astrometry: Historical Highlights..- (a) Fundamental astronomy. Long-focus photographic astrometry.- (b) Precession, Heliocentric viewpoint. Kepler’s three laws, proper motions., Stellar Aberration., Nutation.- (c) Solar motion. Binary stars. Parallax. Perturbations.- (d) The two star streams or preferential motion, Asymmetry. High velocity stars. The galactocentric viewpoint. Galactic rotation.- 2. Long-focus Photographic Astrometry. Telescope; Measuring Machine.- (a) Telescope. Refractors: dispersion, focal ratio, coma, spherical aberration; Rayleigh’s criterion.- (b) The USNO reflector.- (c) Measuring machines. The SAMM and SCAN machines at USNO.- (d) The Grant machine at Sproul Observatory.- 3. Observational Errors. Instrumental Equation.- (a)Accidental errors.- (b)Systematic errors.- (c) Instrumental equation: Sproul refractor.- (d) Time of night effect.- 4. Stellar Paths. Reduction of Measurements.- (a)Image plane and tangential plane; Equatorial and standard coordinates.- (b)Scale, orientation and tilt effects.- (c)Reference stars: Standard frame, linear plate constants.- (d)Dependences; geometric accuracy.- 5. Path of single star. Relative Parallax, Proper Motion, Quadratic Time Effect..- (a) At the telescope.- (b) Plate weight; plate, night, year, measurement errors, double plates, night weights.- (c) Analysis for relative parallax, proper motion and quadratic time effect.- (d) Attainable accuracy.- (e) Calculation of accuracy of quadratic time effect.- 6. Reduction to Absolute. Accuracy: Cosmic Errors..- (a) Dependence background of reference stars; spurious acceleration.- (b) Reduction to fixed background.- (c) Observational and cosmic errors.- (d) Accuracy of reduction to absolute quadratic time effect.- (e) Reduction to absolute parallax.- 7. Parallax Results for Nearest Stars. H-R Diagrams.- (a) Review.- (b)H-R diagrams.- (c) Stars nearer than 5 parsec.- 8. Perspective Secular Changes in Proper Motion, Radial Velocity, and Parallax.- (a) Introduction.- (b) Basic considerations and relations.- (c) Changes of ?, V, and p with time.- (d) Changes of d?t/dt, dV/dt, and dp/dt with time or anomaly.- (e) Determination of perspective secular acceleration. Examples: Barnard’s star and van Maanen’s star.- (f) Astrometric determination of radial velocity.- (g) Evaluation and elimination of quadratic time effect.- 9. Reduction from Heliocentric to Barycentric..- (a) Perturbation of solar path.- (b) Heliocentric and barycentric parallax factors.- (c)Illustration: Barnard’s star.- 10. Visual Binaries, Orbital Elements..- (a) Introduction.- (b) Multiple exposure technique.- (c) Kepler’s problem. Elliptical rectangular coordinates.- (d) Apparent and true orbits. Orbital elements.- (e) Derivation of dynamical elements.- (f) Derivation of geometric elements. Thiele - Innes constants.- (g) Derivation of conventional from geometric elements.- 11. Path of Star with Orbital Motion. Photocenter..- (a) Resolved astrometric binary; mass-ratio.- (b)Unresolved astrometric binary; photocenter and photocentric orbit.- (c)Alternate analysis: parallactic and apparent orbit. Orbital factors.- 12. Mass-Ratio and Masses. Harmonic Relation.- (a) Fractional mass, mass-ratio. Harmonic relation.- (b) Mass-luminosity relation.- (c) Mass-ratio determination for long-period visual binary: Example: 61Cygni.- (d) Derivation of harmonic relation.- 13. Perturbations in Stellar Paths. History. Analysis.- (a) History. Discovery.- (b)Orbital analysis: dynamical and geometric elements.- (c) Mass-function. Orbital constant. Dynamical interpretation.- (d)Once more: systematic errors.- (e) Perturbations in visual binaries.- 14. Unseen Astrometric Companions. Illustrations.- (a) Review.- (b) Illustrations.- 15. Unseen astrometric Companions. General..- (a) Mass-luminosity relation.- (b) Number- and mass-density.- 16. Planetary Companions. Barnard’s Star.- (a) Introduction.- (b) Barnard’s star: history, general data.- (c) Early results for perturbation.- (d) Latest Sproul solution for parallax, proper motion, and quadratic time effect.- (e) Normal points and weights.- (f) Orbital solutions.- (g) Dynamical interpretation.- (h)Possible influence of reference stars.- 17. Long-period eclipsing binaries: VV Cephei and Epsilon Aurigae..- (a) Apparent orbit vs annual parallax.- (b) Concept of orbital parallax.- (c)VV Cephei.- (d) Epsilon Aurigae.- (e) Summary.- 18. Epilogue. Attainable Accuracy. Substellar and Planetary Detectability.- (a)Review.- (b)Separating small perturbations from random errors.- (c)Long-range telescope stability.- (d)Substellar and planetary detection capability and probability.