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Stellar Paths

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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.

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