On the secular decrease in the semimajor axis of Lageos orbit

The semimajor axis of the Lageos orbit is decreasing secularly at the rate of -1.1 mm/day due to an unknown force. Nine possible mechanisms are investigated. Five of the mechanisms, resonance with the Earth's gravitational field, gravitational radiation, the Poynting-Robertson effect, transfer of spin angular momentum to the orbital angular momentum, and drag from near Earth dust are ruled out because they are too small to require unacceptable assumptions to account for the observed rate. Three other mechanisms, the Yarkovsky effect, the Schach effect, and terrestrial radiation pressure could possibly give the proper order of magnitude for the decay rate, but the characteristic signatures of these perturbations do not agree with the observed secular decrease. Atmospheric drag from a combination of charged and neutral particles is the most likely cause for the orbital decay. This mechanism explains at least 71 percent of the observed rate of decrease of the semimajor axis

Information theory lateral density distribution for Earth inferred from global gravity field

Information Theory Inference, better known as the Maximum Entropy Method, was used to infer the lateral density distribution inside the Earth. The approach assumed that the Earth consists of indistinguishable Maxwell-Boltzmann particles populating infinitesimal volume elements, and followed the standard methods of statistical mechanics (maximizing the entropy function). The GEM 10B spherical harmonic gravity field coefficients, complete to degree and order 36, were used as constraints on the lateral density distribution. The spherically symmetric part of the density distribution was assumed to be known. The lateral density variation was assumed to be small compared to the spherically symmetric part. The resulting information theory density distribution for the cases of no crust removed, 30 km of compensated crust removed, and 30 km of uncompensated crust removed all gave broad density anomalies extending deep into the mantle, but with the density contrasts being the greatest towards the surface (typically + or 0.004 g cm 3 in the first two cases and + or - 0.04 g cm 3 in the third). None of the density distributions resemble classical organized convection cells. The information theory approach may have use in choosing Standard Earth Models, but, the inclusion of seismic data into the approach appears difficult

Information Theory and the Earth's Density Distribution

An argument for using the information theory approach as an inference technique in solid earth geophysics. A spherically symmetric density distribution is derived as an example of the method. A simple model of the earth plus knowledge of its mass and moment of inertia lead to a density distribution which was surprisingly close to the optimum distribution. Future directions for the information theory approach in solid earth geophysics as well as its strengths and weaknesses are discussed

General relativity and satellite orbits

The general relativistic correction to the position of a satellite is found by retaining Newtonian physics for an observer on the satellite and introducing a potential. The potential is expanded in terms of the Keplerian elements of the orbit and substituted in Lagrange's equations. Integration of the equations shows that a typical earth satellite with small orbital eccentricity is displaced by about 17 cm. from its unperturbed position after a single orbit, while the periodic displacement over the orbit reaches a maximum of about 3 cm. The moon is displaced by about the same amounts. Application of the equations to Mercury gives a total displacement of about 58 km. after one orbit and a maximum periodic displacement of about 12 km

Inverting x,y grid coordinates to obtain latitude and longitude in the vanderGrinten projection

The latitude and longitude of a point on the Earth's surface are found from its x,y grid coordinates in the vanderGrinten projection. The latitude is a solution of a cubic equation and the longitude a solution of a quadratic equation. Also, the x,y grid coordinates of a point on the Earth's surface can be found if its latitude and longitude are known by solving two simultaneous quadratic equations

Tidal parameters derived from the perturbations in the orbital inclinations of the BE-C, GEOS-1 and GEOS-2 satellites

Effective tidal Love numbers and phase angles for the O sub one, K sub one, M sub two, K sub two, P sub one, and S sub two, tides are recovered. The effective tidal phase angles tend to be on the order of a few degrees. The effective tidal Love numbers are generally less than the solid earth Love number K sub two, of about 0.30. This supports the contention that the ocean tides give an apparent depression of the solid earth Love number. Ocean tide amplitudes and phases are calculated for the above tides assuming K sub two = 0.30 and the solid earth lag angle O sub two = 0. The results show good agreement on GEOS-1 but not on GEOS-II

The orbit of Lageos and solar eclipses

An eclipse of the Sun by the Moon as seen by the Lageos satellite can affect the orbital semimajor axis at the centimeter level. The weakened radiation pressure acting on Lageos perturbs the orbit differently from that due to full sunlight. This difference amounted to less than 2 mm in the semimajor axis for 23 of the 30 eclipses Lageos experienced between launch in 1976 and the end of 1983. However, it was 17.6 mm for the eclipses on 28 March 1979 and 11.2 mm for the one on 15 December 1982. Differences such as these generate large enough along-track errors to make it worthwhile to include eclipses in complex orbit determination programs such as GEODYN which integrate the orbit. Eclipses cannot explain the presently unmolded variations in along-track acceleration which have a magnitude of about 3 x 10(-12) ms(-2)

Earth Albedo and the orbit of LAGEOS

The long-period perturbations in the orbit of the Lageos satellite due to the Earth's albedo have been found using a new analytical formalism. The Earth is assumed to be a sphere whose surface diffusely reflects sunlight according to Lambert's law. Specular reflection is not considered. The formalism is based on spherical harmonics; it produces equations which hold regardless of whether the terminator is seen by the satellite or not. Specializing to the case of a realistic zonal albedo shows that Lageos' orbital semimajor axis changes periodically by only the a few millimeters and the eccentricity by one part in 100,000. The longitude of the node increases secularly. The effect considered here can explain neither the secular decay of 1.1 mm/day in the semimajor axis nor the observed along-track variations in acceleration of order 2 x 10 to the minus 12 power/sq ms

The early history of the lunar inclination

The effect of tidal friction on the inclination of the lunar orbit to the earth's equator for earth-moon distances of less than 10 earth radii is examined. The results obtained bear on a conclusion drawn by Gerstenkorn and others which has been raised as a fatal objection to the fission hypothesis of lunar origin, namely, that the present nonzero inclination of the moon's orbit to the ecliptic implies a steep inclination of the moon's orbit to the earth's equatorial plane in the early history of the earth-moon system. This conclusion is shown to be valid only for particular rheological models of the earth. The earth is assumed to behave like a highly viscous fluid in response to tides raised in it by the moon. The moon is assumed to be tideless and in a circular orbit about the earth. The equations of tidal friction are integrated numerically to give inclination of the lunar orbit as a function of earth-moon distance

Gravitational potential energy of the earth: A spherical harmonic approach

A spherical harmonic equation for the gravitational potential energy of the earth is derived for an arbitrary density distribution by conceptually bringing in mass-elements from infinity and building up the earth shell upon spherical shell. The zeroth degree term in the spherical harmonic equation agrees with the usual expression for the energy of a radial density distribution. The second degree terms give a maximum nonhydrostatic energy in the mantle and crust of -2.77 x 10 to the twenty-ninth power ergs, an order of magnitude. If the earth is assumed to be a homogeneous viscous oblate spheroid relaxing to an equilibrium shape, then a lower limit to the mantle viscosity of 1.3 x 10 to the twentieth power poises is found by assuming the total geothermal flux is due to viscous dissipation. If the nonequilibrium figure is dynamically maintained by the earth acting as a heat engine at one per cent efficiency, then the viscosity is ten to the twenty second power poises, a number preferred by some as the viscosity of the mantle