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An elementary pedagogical derivation of the Lense-Thirring precession is given based on the use of Hamilton vector. The Hamilton vector is an extra constant of motion of the Kepler/Coulomb problem related simply to the more popular Runge-Lenz vector. When a velocity-dependent Lorentz-like gravitomagnetic force is present, the Hamilton vector, as well as the canonical orbital momentum are no longer conserved and begin to precess. It is easy to calculate their precession rates, which are related to the Lense-Thirring precession of the orbit.
The geodesics of bound spherical orbits i.e. of orbits performing Lense-Thirring precession, are obtained in the case of the $Lambda$-term within gravito-electromagnetic formalism. It is shown that the presence of the $Lambda$-term in the equations o
The orbital Lense-Thirring precession is considered in the context of constraints for weak-field General Relativity involving the cosmological constant $Lambda$. It is shown that according to the current accuracy of satellite measurements the obtaine
The timing properties of X-ray binaries are still not understood, particularly the presence of quasi-periodic oscillations (QPOs) in their X-ray power spectra. The solid-body regime of Lense-Thirring precession is one prominent model invoked to expla
We develop a Monte-Carlo code to compute the Compton scattered X-ray flux arising from a hot inner flow which undergoes Lense-Thirring precession. The hot flow intercepts seed photons from an outer truncated thin disk. A fraction of the Comptonized p
The presence of neutron stars in at least three ultraluminous X-ray sources is now firmly established and offers an unambiguous view of super-critical accretion. All three systems show long-timescale periods (60-80 days) in the X-rays and/or optical,