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diff --git a/math/slalib/doc/pertue.hlp b/math/slalib/doc/pertue.hlp new file mode 100644 index 00000000..4f5cf166 --- /dev/null +++ b/math/slalib/doc/pertue.hlp @@ -0,0 +1,152 @@ +.help pertue Jun99 "Slalib Package" +.nf + + SUBROUTINE slPRTE (DATE, U, JSTAT) + + - - - - - - - + P R T E + - - - - - - - + + Update the universal elements of an asteroid or comet by applying + planetary perturbations. + + Given: + DATE d final epoch (TT MJD) for the updated elements + + Given and returned: + U d(13) universal elements (updated in place) + + (1) combined mass (M+m) + (2) total energy of the orbit (alpha) + (3) reference (osculating) epoch (t0) + (4-6) position at reference epoch (r0) + (7-9) velocity at reference epoch (v0) + (10) heliocentric distance at reference epoch + (11) r0.v0 + (12) date (t) + (13) universal eccentric anomaly (psi) of date, approx + + Returned: + JSTAT i status: + +102 = warning, distant epoch + +101 = warning, large timespan ( > 100 years) + +1 to +8 = coincident with major planet (Note 5) + 0 = OK + -1 = numerical error + + Called: slPLNT, slUEPV, slPVUE + + Notes: + + 1 The "universal" elements are those which define the orbit for the + purposes of the method of universal variables (see reference 2). + They consist of the combined mass of the two bodies, an epoch, + and the position and velocity vectors (arbitrary reference frame) + at that epoch. The parameter set used here includes also various + quantities that can, in fact, be derived from the other + information. This approach is taken to avoiding unnecessary + computation and loss of accuracy. The supplementary quantities + are (i) alpha, which is proportional to the total energy of the + orbit, (ii) the heliocentric distance at epoch, (iii) the + outwards component of the velocity at the given epoch, (iv) an + estimate of psi, the "universal eccentric anomaly" at a given + date and (v) that date. + + 2 The universal elements are with respect to the J2000 equator and + equinox. + + 3 The epochs DATE, U(3) and U(12) are all Modified Julian Dates + (JD-2400000.5). + + 4 The algorithm is a simplified form of Encke's method. It takes as + a basis the unperturbed motion of the body, and numerically + integrates the perturbing accelerations from the major planets. + The expression used is essentially Sterne's 6.7-2 (reference 1). + Everhart and Pitkin (reference 2) suggest rectifying the orbit at + each integration step by propagating the new perturbed position + and velocity as the new universal variables. In the present + routine the orbit is rectified less frequently than this, in order + to gain a slight speed advantage. However, the rectification is + done directly in terms of position and velocity, as suggested by + Everhart and Pitkin, bypassing the use of conventional orbital + elements. + + The f(q) part of the full Encke method is not used. The purpose + of this part is to avoid subtracting two nearly equal quantities + when calculating the "indirect member", which takes account of the + small change in the Sun's attraction due to the slightly displaced + position of the perturbed body. A simpler, direct calculation in + double precision proves to be faster and not significantly less + accurate. + + Apart from employing a variable timestep, and occasionally + "rectifying the orbit" to keep the indirect member small, the + integration is done in a fairly straightforward way. The + acceleration estimated for the middle of the timestep is assumed + to apply throughout that timestep; it is also used in the + extrapolation of the perturbations to the middle of the next + timestep, to predict the new disturbed position. There is no + iteration within a timestep. + + Measures are taken to reach a compromise between execution time + and accuracy. The starting-point is the goal of achieving + arcsecond accuracy for ordinary minor planets over a ten-year + timespan. This goal dictates how large the timesteps can be, + which in turn dictates how frequently the unperturbed motion has + to be recalculated from the osculating elements. + + Within predetermined limits, the timestep for the numerical + integration is varied in length in inverse proportion to the + magnitude of the net acceleration on the body from the major + planets. + + The numerical integration requires estimates of the major-planet + motions. Approximate positions for the major planets (Pluto + alone is omitted) are obtained from the routine slPLNT. Two + levels of interpolation are used, to enhance speed without + significantly degrading accuracy. At a low frequency, the routine + slPLNT is called to generate updated position+velocity "state + vectors". The only task remaining to be carried out at the full + frequency (i.e. at each integration step) is to use the state + vectors to extrapolate the planetary positions. In place of a + strictly linear extrapolation, some allowance is made for the + curvature of the orbit by scaling back the radius vector as the + linear extrapolation goes off at a tangent. + + Various other approximations are made. For example, perturbations + by Pluto and the minor planets are neglected, relativistic effects + are not taken into account and the Earth-Moon system is treated as + a single body. + + In the interests of simplicity, the background calculations for + the major planets are carried out en masse. The mean elements and + state vectors for all the planets are refreshed at the same time, + without regard for orbit curvature, mass or proximity. + + 5 This routine is not intended to be used for major planets. + However, if major-planet elements are supplied, sensible results + will, in fact, be produced. This happens because the routine + checks the separation between the body and each of the planets and + interprets a suspiciously small value (0.001 AU) as an attempt to + apply the routine to the planet concerned. If this condition is + detected, the contribution from that planet is ignored, and the + status is set to the planet number (Mercury=1,...,Neptune=8) as a + warning. + + References: + + 1 Sterne, Theodore E., "An Introduction to Celestial Mechanics", + Interscience Publishers Inc., 1960. Section 6.7, p199. + + 2 Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983. + + P.T.Wallace Starlink 18 March 1999 + + Copyright (C) 1999 Rutherford Appleton Laboratory + Copyright (C) 1995 Association of Universities for Research in Astronomy Inc. + +.fi +.endhelp + +.fi +.endhelp |