“When Infinite Systems succeed one another through an Infinite Space, and none is either inward or outward; may not all the Systems be situated in an accurate Poise; and, because equally attracted on all sides, remain fixed and unmoved? But to this we reply; that unless the very mathematical Center of Gravity of every System be placed and fixed in the very mathematical Center of the Attractive Power of all the rest; they cannot be evenly attracted on all sides, but must preponderate some way or other”.Richard Bentley (1926)
Abstract
Two distinct but fully compatible novel concepts are proposed here for solar/stellar velocity measurements. The first is that of absolute accelerometry proper. This involves two simultaneously, operating servo-control loops First, a variable path-difference Fabry-Perot interferometer is adjusted so that its bandpasses track the fluctuations of either a single spectral line (in the solar case, leading to the solar accelerometer), or of all lines simultaneously (stellar accelerometer). The second loop involves a tunable laser tracking one of the FP bandpasses. The net overall result is that a laser line tracks the stellar/solar ones: the problem of measuring Doppler-shift changes has been transferred from the incoherent to the coherent optics domain. One then measures the beat frequency generated by mixing the tunable laser beam with that of stabilized laser. Only velocity changes are accessible; the devices are true accelerometers, but absolute ones. All instrumental or spectral characteristics drop out; no calibration of any kind is required; hence, one may hope for an unusually low level of systematic errors.
The second concept is that of optimum measurement of Doppler shifts as far as photon count limitations are concerned. A simple but so far never performed calculation leads to the fundamental RMS velocity error corresponding to a given spectral profile and photon count. One next shows that a dispersive spectrometer with an image detector may closely approach that limit provided direct access to a computer is available, and the signal is treated by a specific algorithm. This treatment being precisely the one used in the stellar accelerometer, our device is seen as the first proposed one approaching fundamental limits in this field; however, standard radial velocity measurements (not involving accelerometry) should also benefit from our proposal. A full calculation shows that a velocity error reduction of the order of 30 is within reach relative to the most efficient so far available device, i.e., CORAVEL. For faint objects, detector noise must be added, but the treatment remains demonstrably optimum.
The two principal fields of application for absolute accelerometry are celestial seismology (a seismometer is nothing but an accelerometer), and the search for extra-solar planetary systems. In both cases a large number of objects will be accessible with a small telescope. One may also look for solar system accelerations (relative to some system of reference stars) due to any cause whatsoever: for instance a faint solar companion, or even gravitational waves.
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Connes, P. Absolute astronomical accelerometry. Astrophys Space Sci 110, 211–255 (1985). https://doi.org/10.1007/BF00653671
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DOI: https://doi.org/10.1007/BF00653671