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Estabrook, F. B.

Publications and source records attributed to Estabrook, F. B..

36 records · Page 2

Interplanetary phase scintillation and the search for very low frequency gravitational radiation

Observations of radio-wave phase scintillation are reported which used the Viking spacecraft having an earth-spacecraft link very similar to that which will be used in very low-frequency (VLF) gravitational-wave searches. The phase power-spectrum level varies by seven orders of magnitude as the sun-earth-spacecraft (elongation) angle changes from 1 to 175 deg. It is noteworthy that a broad minimum in the S-band (2.3 GHz) phase fluctuation occurs in the antisolar direction; the corresponding fractional frequency stability (square root Allan variance) is about 3 x 10 to the -14th for 1000-s integration times. A simultaneous two-frequency two-station observation indicates that the contribution to the phase fluctuation from the ionosphere is significant but dominated by the contribution from the interplanetary medium. Nondispersive tropospheric scintillation was not detected (upper limit to fractional frequency stability about 5 x 10 to the -14th). Evidently, even observations in the antisolar direction will require higher radio frequencies, phase scintillation calibration, and correlation techniques in the data processing, for detection of gravitational bursts at the anticipated strain amplitude levels of no more than 10 to the -15th.

Armstrong, J. W.

Gravitational radiation detection with spacecraft Doppler tracking - Limiting sensitivities and prospective missions

The prospects of using spacecraft Doppler tracking, in NASA missions, for the detection of gravitational waves are examined. The sensitivity limits of such detection are characterized in terms of plasma scintillation, troposphere scintillation, receiver noise, MDA and ODA quantization error, and clock jitter. Current and possible future NASA missions that will involve gravitational wave experiments are briefly reviewed, including the Galileo, solar polar, Halley/Tempel-2, and solar probe missions.

Estabrook, F. B.

Prospects for detection of gravitational radiation by simultaneous Doppler tracking of several spacecraft

This paper reports a calculation of the effect of gravitational radiation on the observed Doppler shift of a sinusoidal electromagnetic signal transmitted to, and coherently transponded from, distant spacecraft. It is found that the effect of plane gravitational waves on such observations is not intuitively immediate, and in fact depends sensitively on the spacecraft direction, which suggests the possibility of detecting such plane waves by simultaneous Doppler tracking of several spacecraft. The need for broad band gravitational wave observations, the required stabilities of time keeping standards, and astrophysical sources expected in the Very Low Frequency band are briefly discussed.

Estabrook, F. B.

Application of DSN spacecraft tracking technology to experimental gravitation

Spacecraft tracking technology of the Deep Space Net (DSN) has been used in the past to measure the general-relativistic increase in round-trip group delay between earth and a spacecraft. As the DSN technology continues to improve, other gravitational experiments will become possible. Two possibilities are discussed in this paper. The first concerns the application of solar-system dynamics to the testing of general relativity. The second involves the detection of VLF gravitational radiation (0.1 to 0.0001 Hz) by means of Doppler tracking of spacecraft.

Anderson, J. D.

Prolongation structures of nonlinear evolution equations. II

The prolongation structure of a closed ideal of exterior differential forms is further discussed, and its use illustrated by application to an ideal (in six dimensions) representing the cubically nonlinear Schroedinger equation. The prolongation structure in this case is explicitly given, and recurrence relations derived which support the conjecture that the structure is open - i.e., does not terminate as a set of structure relations of a finite-dimensional Lie group. We introduce the use of multiple pseudopotentials to generate multiple Baecklund transformation, and derive the double Baecklund transformation. This symmetric transformation concisely expresses the (usually conjectured) theorem of permutability, which must consequently apply to all solutions irrespective of asymptotic constraints.

Estabrook, F. B.

The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

Estabrook, F. B.

Prolongation structures of nonlinear evolution equations

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

Wahlquist, H. D.

Response of Doppler spacecraft tracking to gravitational radiation

A calculation is made of the effect of gravity waves on the observed Doppler shift of a sinusoidal electromagnetic signal transmitted to, and transponded from, a distant spacecraft. We find that the effect of plane gravity waves on such observations is not intuitively immediate and in fact can have surprisingly different spectral signatures for different spacecraft directions and distances. We suggest the possibility of detecting such plane waves by simultaneous coherent Doppler tracking of several spacecraft.

Estabrook, F. B.

Backlund transformation for solutions of the Korteweg-de Vries equation

We present a Backlund transformation operating on solutions of the Korteweg-de Vries equation. It provides a unifying approach to the theory of solitary waves (solutions). Recursive application of the transformation to any solution of the Korteweg-de Vries equation generates a hierarchy of solutions for which an algebraic recursion relation is obtained. Every such hierarchy (one of which is the known family of pure multisoliton solutions) thus admits a nonlinear superposition principle.

Wahlquist, H. D.

Hamiltonian cosmology

Polynomial Hamiltonian for type VIII and IX vacuum cosmologies, suggesting quantized versions involving fluctuations of 3-space signature and topology

Estabrook, F. B.

Rigid motions in Einstein spaces.

General relativistic dyadic formalism applied to metrics of rigid bodies moving in Einstein space of uniform space-time curvature

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