Determination of some galactic constants using planetary nebulae

In this paper, Planetary Nebulae (PNe) are considered as a stellar system by which we succeed in determining the following Galactic constants: the Galactic pole coordinates (alpha(p), delta(p)), which are used for coordinate transformation in Galactic astronomy, the velocity and apex of the solar motion as an important kinematical parameter for stellar groups, Oorts's first constant (A) and the rotation curve for the theory of Galactic rotation. An analytical method is introduced to determine the Galactic pole. This method depends on the constrained optimization technique. A general computational algorithm for the procedure was established in order to find exact solutions for the equations involved. The methods used for the solar apex and speed, and also the determinations of Oort's first constant depend on the least squares technique. The velocity ellipsoid components are determined as a by-product from the solar elements. The resulting rotation curve derived by our sample is found to be similar to that obtained from planetary nebulae type I. We have derived the following constants: Galactic pole coordinates alpha(p) = 12(h)49(m), delta(p) = 27 degrees 22, the solar apex alpha(A) = 290 degrees, delta(A) = +30 degrees, solar speed S-. = 18.6 km s(-1), and Oort's first constant A = 15.2 km s(-1) kpc(-1), which are in good agreement with the standard and averaged values. (C) 1998 Elsevier Science B.V. All rights reserved.