John B. Lundberg

Surfaces of zero velocity in the restricted problem of three bodies

Recent uses of computer graphics allow the representation of the three-dimensional surfaces of zero velocity, also known as Hills or the Jacobian surfaces. The purpose of this paper is to show the actual surfaces rather than their projections which are available in the standard literature. The analytical properties of the surfaces are also available; therefore, this paper offers the pertinent references rather than the derivations.

Spherical harmonic synthesis and least squares computations in satellite gravity gradiometry

The computational requirements in the simulations of geopotential estimation from satellite gravity gradiometry are discussed. Fast algorithms for spherical harmonic synthesis and least squares accumulation on a vectorizing supercomputers are presented. Using these methods, in a test case estimation of 2595 coefficients of a degree and order 50 gravity field, sustained program execution speeds of 275 Mflops (87 % peak machine speed) on a single processor of a CRAY Y-MP were achieved, with spherical harmonics computation accounting for less than 1 % of total cost. From the results, it appears that brute-force estimation of a degree and order 180 field would require 537 Million Words of memory and 85 hours of CPU time, assuming mission duration of 1 month, and execution speed of 1 Gflops. Both memory size and execution speed requirements are within the capabilities of modern multi-processor supercomputers.

Methodology to retrieve and assess the accuracy of atmospheric temperature profiles at the pixel level using satellite sounder data

In this paper, we present the first of a two part discussion to improve the specification of atmospheric transmission calculations using a new methodology to reduce the uncertainty in pixel-level temperature profiles derived from meteorological satellite sounder data. Temperature profiles are examined first, since these data are used to derive the moisture content of the atmosphere. Our results show that the uncertainty in the specification of temperature profiles, for pixel level retrievals of meteorological satellite sounder data, can be assessed using knowledge on the accuracy of the initial-guess to a physical relaxation algorithm.

Results from the Simulations of Geopotential Coefficient Estimation from Gravity Gradients

New information of the short and medium wavelength components of the geopotential is expected from the measurements of gravity gradients made by the future European Space Agency (ESA) Aristoteles and the NASA Superconducting Gravity Gradiometer (SGG) missions. In this paper, results are presented from preliminary simulations concerning the estimation of the spherical harmonic coefficients of the geopotential expansion from gravity gradients data.

Regions of Stability of Asteroids

Using Hill’s modified stability criterium, regions of orbital elements are established for conditions of stability. The model of the three-dimensional restricted problem of three bodies is used with the Sun and Jupiter as the primaries. Four different cases are studied: direct and retrograde, outside and inside asteroidal orbits. The directions of the asteroidal orbits refer to the synodical reference frame and the positions refer to Jupiter’s orbit. The orbital parameters of the asteroids are the semi-major axis (a), the eccentricity (e), and the inclination from Jupiter’s orbital plane (i). The effects of the other orbital elements are not investigated in this paper. The argument of the perihelion and the longitude of the ascending node are fixed at Ω = ω = 90° and the time of perihelion passage is T = 0 for all orbits.