We review the statistical properties of the main populations of radio sources, as emerging from radio and millimeter sky surveys. Recent determinations of local luminosity functions are presented and compared with earlier estimates still in widespread use. A number of unresolved issues are discussed. These include: the (possibly luminosity-dependent) decline of source space densities at high redshifts; the possible dichotomies between evolutionary properties of low- versus high-luminosity and of flat- versus steep-spectrum AGN-powered radio sources; and the nature of sources accounting for the upturn of source counts at sub-milli-Jansky (mJy) levels. It is shown that straightforward extrapolations of evolutionary models, accounting for both the far-IR counts and redshift distributions of star-forming galaxies, match the radio source counts at flux-density levels of tens of μJy remarkably well. We consider the statistical properties of rare but physically very interesting classes of sources, such as GHz Peak Spectrum and ADAF/ADIOS sources, and radio afterglows of γ-ray bursts. We also discuss the exploitation of large-area radio surveys to investigate large-scale structure through studies of clustering and the Integrated Sachs–Wolfe effect. Finally, we briefly describe the potential of the new and forthcoming generations of radio telescopes. A compendium of source counts at different frequencies is given in Supplementary Material.

Radio and Millimeter Continuum Surveys and their Astrophysical Implications

This paper deals with the numerical investigations of the locations of the five equilibrium points by taking into consideration the effect of oblateness of the more massive primary for some systems of astronomical interest. This note is further concerned with the periodic solutions of the linearized equations of motion around the five equilibrium points. Interesting differences in the trends of the angular frequencies of these motions have been noticed.

Stationary solutions and their characteristic exponents in the restricted three-body problem when the more massive primary is an oblate spheroid

This paper deals with the stationary solutions of the planar restricted three-body problem when the more massive primary is a source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. The collinear equilibria have conditional retrograde elliptical periodic orbits around them in the linear sense, while the triangular points have long- or short-periodic retrograde elliptical orbits for the mass parameter 0 ≤ μ < μcrit, the critical mass parameter, which decreases with the increase in oblateness and radiation force. Through special choice of initial conditions, retrograde elliptical periodic orbits exist for the case μ = μcrit, whose eccentricity increases with oblateness and decreases with radiation force for non-zero oblateness.

The linear stability of libration points of the photogravitational restricted three-body problem when the smaller primary is an oblate spheroid

We discuss the existence, location, and stability of the collinear equilibrium points of a generalized Hill problem with radiation of the primary (the Sun) and oblateness of the secondary (the planet), and present some remarkable fractals created as basins of attraction of Newton’s method applied for their computation in several cases of the parameters.

Collinear equilibrium points of Hill’s problem with radiation and oblateness and their fractal basins of attraction

In this paper, we prove that the locations of the triangular points and their linear stability are affected by the oblateness of the more massive primary in the planar circular restricted three-body problem, considering the effect of oblateness for J2 and J4. After that, we show that the triangular points are stable for 0<μ<μc and unstable when \(\mu_{c}\leq \mu\leq \frac{1}{2}\), where μc is the critical mass parameter which depends on the coefficients of oblateness. On the other hand, we produce some numerical values for the positions of the triangular points, μ and μc using planets systems in our solar system which emphasis that the range of stability will decrease; however this range sometimes is not affected by the existence of J4 for some planets systems as in Earth–Moon, Saturn–Phoebe and Uranus–Caliban systems.

https://www.tpbin.com/Uploads/Subjects/39bc02d2-48ed-4fe0-8a58-45605d133c56.pdf

Existence and stability of triangular points in the restricted three-body problem with numerical applications

/pdf/effect-of-oblateness-of-the-more-massive-primary-on-periodic-30dss9vk13.pdf

Effect of Oblateness of the More Massive Primary on Periodic Orbits in the Restricted Three-Body Problem

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.

/pdf/halo-orbits-at-sun-mars-l1-l2-in-the-photogravitational-54o95ucer6.pdf

Halo Orbits at Sun-Mars L1, L2 in the Photogravitational Restricted Three-Body Problem with Oblateness

A study on the orbital lifetime estimation of upper stages with different inclinations is carried out through response surface technique. The combined influence of the lunisolar perturbations and drag on lifetime variations plays an important role. In order to extract information on the lifetime from orbital data, the estimation of area to mass ratio, initial perigee altitude and ballistic coefficient is performed. In this context, it is noticed that when an object undergoes orbital resonance, bifurcation between the observed and predicted trajectories takes place. However, in some scenarios, simulation of apogee and perigee altitude profiles can still be performed to estimate relevant parameters. To capture only secular changes in apogee and perigee altitudes, osculating elements can be converted to their respective mean values by utilizing a suitable theory. Furthermore, a study on the re-entry of the object is examined closely by estimating different ballistic coefficients to match the position at different epochs. The non-uniform change in the ballistic coefficient provides an indication of possible chaotic motion.

/pdf/lifetime-estimation-of-upper-stages-re-entering-from-gto-4xr7sgphq0.pdf

Lifetime Estimation of Upper Stages Re-Entering from GTO with Different Inclinations

An attempt has been made to investigate the changes in the characteristics of aerosol optical properties and a columnar load of carbon monoxide (CO) induced during the Dashain celebration 2018 over Birtamode, Nepal. Ground-based measurements of Aerosol Optical Depth (AOD) were carried out using a Microtops II sun-photometer during 13th to 25th Oct, 2018. AOD values on days before Dashain were in the range of 0.6 which increased above 1 attaining a maximum value of 1.6 on 19th. The AOD values started dropping below 1 on 24th, attaining a daily average of 0.64. The peak values on the respective days were also captured by Moderate Resolution Imaging Spectroradiometer (MODIS) AOD retrievals. A similar pattern was observed with the TROPOspheric Measuring Instrument (TROPOMI) CO column with peak value on the 19th. The air mass trajectories show that the increase in the AOD and CO values is of local origin and the CAMS GFAS wildfire flux of CO and PM2.5 show no change during the study period. However, the spatial analysis of AOD shows that the increased values are of regional nature. The results highlight the necessity of installation of low-cost air quality sensors in the region and utilization of aerosol and trace gaseous products derived from satellite remote sensing instruments at high temporal resolution and the application of chemical transport models.

Ram Krishan Sharma

Papers

Effect of Oblateness of the More Massive Primary on Periodic Orbits in the Restricted Three-Body Problem

Halo Orbits at Sun-Mars L1, L2 in the Photogravitational Restricted Three-Body Problem with Oblateness

Lifetime Estimation of Upper Stages Re-Entering from GTO with Different Inclinations

Festival Induced Air Quality Perturbation over an Urban Center in Eastern Nepal

Limiting periodic orbits in the neighborhood of the triangular equilibrium points when the more massive primary is an oblate spheroid