Is the mass of mercury 1/60000000?

3782 observations of Venus, made between 1914 and 1977 were used to estimate the mass of Mercury. To calculate Mercury's mass and, simultaneously, the initial conditions needed to integrate Venus's orbit, the simplex method was used. This method, in contrast to a differential correction, permits a full nonlinear solution to the problem and is applicable with any norm of the residuals, not just the L2 norm – the least squares criterion. The mass calculated from the least squares criterion is 1/60123000, with a range, as given by the covariance matrix, of 1/10670000 to 1/41285000. This agrees well with the official IAU value. But if we use the L1 norm, an extremely robust norm, the calculated value becomes 1/8970000. Although this lies within the range given by least squares, it nevertheless differs by thirty three per cent from the least squares value. And in any event one should not pay too much attention to the formal errors given by the covariance matrix. The optimum of a least squares solution, and consequently the reliability of the formal mean errors given by the covariance matrix, depends on a series of assumptions. But statistical tests show that some of these assumptions are invalid for the observations used in this study. It will be important to investigate why two distinct norms give such discordant results.Asociación Argentina de Astronomí

Modern ideas in data reduction

Data resolution is an important task in astronomy, one that is generally undertaken using the method of least squares. But mathematically the least squares criterion is only one of an infinite number of ways to minimize the p-th norm of the vector of residuals. Nevertheless, given certain assumptions one can show that the least squares solution is the best. Various alternative techniques for reducing data are presented. For a badly conditioned system a least squares reduction by orthogonal triangularization (Givens, Householder) may be useful. Iteratively reweighted least squares is a robust least squares procedure. The L₁ method is a robust, non-least squares procedure for solving an overdetermined system. A comparison of a least squares and an L₁ solution, with their respective errors, should give a good idea of the real errors present in the system.Asociación Argentina de Astronomí

¿Es la masa de Mercurio 1/6000000?

En 1980 Lyttleton publicó un artículo (Q.J. RAS, 1980, 21, 400) indicando que hay razones para pensar que el valor oficial de la masa de Mercurio, 1/6023600, es erróneo y el verdadero valor está más cerca a 1/9000000. Durante la reunión de la Asociación en San Juan en 1990 presenté evidencia, basada en más de 7.000 observaciones hechas con círculos meridianos, que Lyttleton tal vez tenga razón. Pero en el Interin he incorporado 1.083 observaciones con radar de la distancia Tierra-Venus a las observaciones con círculo meridiano. También cambié el algoritmo de minimización del método simplex, el método iterativo sin gradiente, de Powell. Mis resultados son: masa de Mercurio con norma L1, 1/6019300; masa con mínimos cuadrados, 1/6022600. Estos resultados, refutando la tesis de Lyttleton, son superiores a mis resultados anteriores porque: 1) el método Powell es mejor que simplex para problemas de esta naturaleza; 2) las observaciones con radar tienen más precisión que observaciones con el círculo meridiano.Asociación Argentina de Astronomí

Comparison of catalogues through asteroid observations

We have obtained 525 observations, made by four observatories between 1965 and 1989, of 16 minor planets to study the behaviour of the FK5 catalog near -30°. The minor planet coordinates to compare with the observations are generated by an n-body program that also integrates the major planets. The matrix of the equations of condition is 525 x 98. Because the resulting 98 x 98 linear system would occupy a great deal of memory, we have encountered a way to represent this kind of matrix, symmetric, positive definitive with fringes, that needs only 6% of the space required by a 2-dimensional array.Asociación Argentina de Astronomí

Comparison of catalogues from observations of minor planets

The errors of the fundamental catalog FK4 and its deficiencies to the south of -30° declination are well known. The present work consists of looking at the behaviour of the FK5 catalog using observations of more than 100 minor planets, obtained at one observatory located at a latitude of -31°.8.Asociación Argentina de Astronomí