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Asteroid-n orbits at qn astronomical units (AU) from the sun at perihelion, and hence about (qn–1) AU from the earth at our closest approach over the past few centuries. Similarly, Ceres was (q1–1) AU from the earth at its closest approach. The apparent brightness of each scales with the square of these distances, and the last term uses the ratio of the absolute magnitudes to allow for the albedo (normally it would be expressed as an exponential to base 2.512, but has been expressed here to base e for convenience of combining in the other exponential term).
The justification for that other exponential term, though, is not quite so clean. It is not surprising for it to be exponential, since this is a good model for the rate of advancement in human knowledge (in telescope technology, for example). The square root in the argument, though, was determined by curve fitting.
This expression was found, empirically, to give a good fit (a coefficient of correlation of 0.93) with the other main-belt asteroids (2, 3, 4, 10, 11, 15, 16, 20, 45, 121, 140, 216, 243, 253, 433, 704, 951, 4979) whose masses have been determined elsewhere (Solarviews, SEDS, USNO Navy, Quasar, and http://www/mytangledweb.co.uk/aster.htm (link now broken)).
This preliminary result is already useful. However, it can be improved by taking the lines of regression on logarithmic axes. In this way, the result gives a more equally balanced weighting to small asteroids as to large ones.