Advances in Astrophysics

8

Authors: H.-J. Fahr, M. Heyl

According to present cosmological views, the energy density of CMB (Cosmic Microwave Background) photons, freely propagating through the expanding cosmos, varies proportional to 1/S4 with S being the scale factor of the universe. This behavior is expected because General Theory of Relativity, in application to FLRW- (Friedmann-Lemaitre-Robertson-Walker) cosmological universes, leads to the conclusion that the photon wavelengths increase during their free passage through the spacetime metrics of the universe by the same factor as does the scale factor S. This appears to be a reasonable explanation for the presently observed Planckian CMB spectrum with its actual temperature of about 2.7 K, while at the time of its origin after the last scattering during the recombination phase its temperature should have been about 3000 K, at an epoch of about 380 ky after the Big Bang, when the scale of the universe Sr was smaller by roughly a factor of S/Sr = 1 + zr = 1100 compared to the present scale S = S0 of the universe. In this paper we start from putting the question whether the scale-behavior of the CMB energy density that enters the energy-momentum tensor of the field equations describing the expanding universe is really falling off like S −4 and, if in fact a deviation from a behavior according to S −4 would occur, why do we nevertheless presently observe a CMB energy density which appears to be in accordance with such a S −4 -scaling? This question arises from another basic and fundamental question, namely: Can we really assume that the wavelength of the freely propagating photon during its travel all the way along its light geodetic is permanently affected by the expansion of the universe, i.e continuously recognizes the expansion of the cosmic scale S? With other words: Do freely propagating photons really undergo a permanent change of their wavelengths when freely traveling through cosmic space-time or is the observationally apparent energy loss of cosmologically red-shifted photons an effect which only occurs just in the moment of photon registration at some specific world point? If the latter would prove to be true , then it would mean that the energy density of freely propagating, non-interacting CMB photons, due to non-changing, conserved wavelengths, is behaving with respect to cosmic scale variation different from conventional expectations, but rather would turn out to behave just like the energy density of matter, namely according to S −3 . Hence the photon part of the energy momentum tensor would become different and associated solutions of FLRW-equations would undergo corresponding modifications. In consequence, the CMB energy density as far as it enters the energy-momentum tensor generated by freely propagating CMB photons during the expansion period of the universe after the recombination era would no longer become negligible for the cosmic dynamics, since its value would stay in the same order of magnitude as that of baryonic or dark matter.

13

Authors: A. Safiya Beevi, Ram Krishan Sharma

The motion of a particle in the restricted three-body problem is explored by treating the more massive primary as an oblate spheroid with its equatorial plane coincident with the plane of motion of the primaries using a perturbation method. Initial conditions for the infinitesimal periodic orbits around the more massive primary are generated and the effect of oblateness on the perigee of these orbits is studied as well. It is observed that when oblateness coefficient is increased, the perigee of the orbit shifts towards both the primaries depending upon the increase in period and mass ratio. It is further noticed that during this transition, for certain periods, the perigee of the orbit remains unaltered with the increase in the oblateness coefficient.

17

Authors: Nishanth Pushparaj, Ram Krishan Sharma

Photogravitational Restricted Three-Body Problem (PRTBP) with smaller primary being an oblate spheroid with its equatorial plane coincident with the plane of motion of the primaries is considered and halo orbits in the vicinity of Sun-Mars Lagrangian points L1 and L2 are computed numerically. The effects of perturbations on size, shape, location and time period of the halo orbits are studied. It is found that the increase in solar radiation pressure at constant oblateness elongates the halo orbits at L1 and the orbits move towards the radiating body. At L2, the halo orbits shrink and move towards the smaller primary with increase in solar radiation pressure at constant oblateness. For constant radiation pressure, increase in oblateness causes the location of L1 and L2 halo orbits to move away from the smaller primary. The time period of L1 halo orbits increases with increase in radiation pressure for constant oblateness and decreases with increase in oblateness for constant radiation pressure. However, the effect of solar radiation pressure and oblateness for L2 halo orbits is reversed.