  The equations of general relativity in the form of timelike and null
geodesics that describe motion of test particles and photons in Kerr spacetime
are solved exactly including the contribution from the cosmological constant.
We then perform a systematic application of the exact solutions obtained to the
following cases. The exact solutions derived for null, spherical, polar and
non-polar orbits are applied for the calculation of frame dragging
(Lense-Thirring effect) for the orbit of a photon around the galactic centre,
assuming that the latter is a Kerr black hole for various values of the Kerr
parameter including those supported by recent observations. Unbound null polar
orbits are investigated, and an analytical expression for the deviation angle
of a polar photon orbit from the gravitational Kerr field is derived. In
addition, we present the exact solution for timelike and null equatorial
orbits. In the former case, we derive an analytical expression for the
precession of the point of closest approach (perihelion, periastron) for the
orbit of a test particle around a rotating mass whose surrounding curved
spacetime geometry is described by the Kerr field. In the latter case, we
calculate an exact expression for the deflection angle for a light ray in the
gravitational field of a rotating mass (the Kerr field). We apply this
calculation for the bending of light from the gravitational field of the
galactic centre for various values of the Kerr parameter and the impact factor.
