Matter waves in a gravitational field: An index of refraction for massive particles in general relativity

We consider the propagation of massive-particle de Broglie waves in a static, isotropic metric in general relativity. We demonstrate the existence of an index of refraction that governs the waves and that has all the properties of a classical index of refraction. We confirm our interpretation with a WKB solution of the general-relativistic Klein-Gordon equation. Finally, we make some observations on the significance of the optical action.Comment: 20 pages, latex, ps and pdf. To appear in Am.J.Phys September, 200

X-ray Observation of SS 433 with RXTE

Apart from regular monitoring by ASM, the compact object SS 433 was observed with RXTE several times last two/three years. We present the first analysis of these observations. We also include the results of the recent exciting TOO campaign made during donour inferior (orbital phase $\phi=0$) and superior ($\phi=0.5$) conjunctions which took place on Oct. 2nd, 2003, and on March 13th, 2004 respectively, when the jet itself was directly pointing towards us (i.e., precessional phase $\psi \sim 0$). Generally, we found that two distinct lines fit the spectra taken on all these days. We present some of the light-curves and the X-ray spectra, and show that the Doppler shifts of the emitted lines roughly match those predicted by the kinematic model for the jets. We find that the line with a higher energy can be best identified with a FeXXVI Ly-$\alpha$ transition while the line with lower energy can be identified with a FeXXV (1s2p - 1s$^2$) transition. We observe that the X-ray flux on March 13th, 2004 (when the base of the jet is exposed) is more than twice compared to that on Oct. 2nd, 2003 (when the base is covered by the companion). We find the flux to continue to remain high at least till another orbital period. We believe that this is because SS 433 was undergoing a weak flaring activity during the recent observation.Comment: 15 pages, 6 figures, submitted for publication in MNRAS (April, 2004

Transfer Alignment for Space Vehicles Launched from a Moving Base

Alignment of the inertial measurement unit (IMU) is a prerequisite for any space vehicle with self-contained navigation and guidance for any mission-critical application. Normally, inertialmeasurement unit is aligned through gyro-compassing using the stored data for heading. In case of launch from a moving base, it is essential to align the inertial measurement unit in the vehicle (slave unit) with that mounted on the moving platform (master unit). The master inertial navigation system is more accurate, stable, and calibrated wrt the slave unit. An error propagation system involving the misalignment between the master and the slave has been formulated involving the three misalignment angles, three velocity errors, and three positional errors. The manoeuvre of the moving base excites the sensors of both the master and the slave inertial navigation systems for the generation of data to be used in aligning the slave inertial measurement unit of the inertial navigation system (strapdown mode). The entire duration of manoeuvre has to be reduced to a minimum with minimum effort of manoeuvre. This involves the deployment of an adaptive estimator and a linear quadratic Gaussian regulator for alignment of the strapdown slave inertial navigation system

Brans-Dicke theory: Jordan vs Einstein Frame

It is well known that, in contrast to general relativity, there are two conformally related frames, the Jordan frame and the Einstein frame, in which the Brans-Dicke theory, a prototype of generic scalar-tensor theory, can be formulated. There is a long standing debate on the physical equivalence of the formulations in these two different frames. It is shown here that gravitational deflection of light to second order accuracy may observationally distinguish the two versions of the Brans-Dicke theory.Comment: 10 pages, Accepted by Mod. Phys. Letts.