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A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit…
I present a review of astrometric techniques and instrumentation utilized to search for, detect, and characterize extra-solar planets. First, I briefly summarize the properties of the present-day sample of extrasolar planets, in connection…
An elementary proof of Kepler's first law, i.e. that bounded planetary orbits are elliptical, is derived without the use of calculus. The proof is similar in spirit to previous derivations, in that conservation laws are used to obtain an…
We present a simple method to obtain the solution of a few orbital problems: the Kepler problem, the modified Kepler problem by the addition of an inverse square potential and linear force.
Pulsars are natural cosmic clocks. On long timescales they rival the precision of terrestrial atomic clocks. Using a technique called pulsar timing, the exact measurement of pulse arrival times allows a number of applications, ranging from…
The fields of occultation and microlensing are linked historically. Early this century, occultation of the Sun by the Moon allowed the apparent positions of background stars projected near the limb of the Sun to be measured and compared…
Astrometric measurements of stellar systems are becoming significantly more precise and common, with many ground and space-based instruments and missions approaching 1 microarcsecond precision. We examine the multi-wavelength astrometric…
Ptolemy-s planetary model is an ancient geocentric astronomical model, describing the observed motion of the Sun and the planets. Ptolemy accounted for the deviations of planetary orbits from perfect circles by introducing two small and…
Astronomical polarimetry is a powerful technique that can provide physical information sometimes difficult or impossible to obtain by any other type of observation. Almost every class of binary star can benefit from polarimetric…
We describe three useful applications of asteroseismology in the context of exoplanet science: (1) the detailed characterisation of exoplanet host stars; (2) the measurement of stellar inclinations; and (3) the determination of orbital…
Exact analytic expressions for planetary orbits and light trajectories in the Schwarzschild geometry are presented. A new parameter space is used to characterize all possible planetary orbits. Different regions in this parameter space can…
We introduce a new method of searching for and characterizing extra-solar planets. We show that by monitoring the center-of-light motion of microlensing alerts using the next generation of high precision astrometric instruments the…
This paper describes how commercially available spectrographs can be used to identify and measure some basic characteristics of planetary nebulae.
A method for asteroid deflection that makes use of a spacecraft moving back and forth on a segment of an appropriate Keplerian orbit about the asteroid is described and evaluated. It is shown that, on average, the spacecraft describing such…
Images of both rotating celestial bodies (e.g., asteroids) and spheroidal planets with banded atmospheres (e.g., Jupiter) can contain features that are well-modeled as a circle of latitude (CoL). The projections of these CoLs appear as…
High-precision pulsar timing relies on a solar-system ephemeris in order to convert times of arrival (TOAs) of pulses measured at an observatory to the solar system barycenter. Any error in the conversion to the barycentric TOAs leads to a…
This tutorial covers the use of absolute astrometry, in particular from the combination of the Hipparcos and Gaia missions, to identify faint companions to nearby stars and to measure the masses and orbits of those companions. Absolute…
An external reference system suitable for deep space navigation can be defined by fast spinning and strongly magnetized neutron stars, called pulsars. Their beamed periodic signals have timing stabilities comparable to atomic clocks and…
Asteroseismology involves probing the interiors of stars and quantifying their global properties, such as radius and age, through observationsof normal modes of oscillation. The technical requirements for conducting asteroseismology include…
The rotation rate of a star has important implications for the detectability, characterisation and stability of any planets that may be orbiting it. This chapter gives a brief overview of stellar rotation before describing the methods used…