The Measurement of Dynamic Tidal Contribution to Apsidal Motion in Heartbeat Star KIC 4544587

Apsidal motion is a gradual shift in the position of periastron. The impact of dynamic tides on apsidal motion has long been debated, because the contribution could not be quantified due to the lack of high-quality observations. KIC 4544587 with tidally excited oscillations has been observed by Kepler high-precision photometric data based on long-time-baseline and short-cadence schema. In this paper, we compute the rate of apsidal motion that arises from the dynamic tides as 19.05 ± 1.70 mrad yr−1 via tracking the orbital phase shifts of tidally excited oscillations. We also calculate the procession rate of the orbit due to the Newtonian and general relativistic contribution as 21.49 ± 2.8 and 2.4 ± 0.06 mrad yr−1, respectively. The sum of these three factors is in excellent agreement with the total observational rate of apsidal motion 42.97 ± 0.18 mrad yr−1 measured by eclipse timing variations. The tidal effect accounts for about 44% of the overall observed apsidal motion and is comparable to that of the Newtonian term. Dynamic tides have a significant contribution to the apsidal motion. The analysis method mentioned in this paper presents an alternative approach to measuring the contribution of the dynamic tides quantitatively.

Effect of the Tide On Flood Modeling and Mapping in Kota Tinggi, Johor Malaysia

This study aimed at mapping the Kota Tinggi flood event in 2006/07 that had caused massive damages to properties and the environment. The flood was associated with unusually high intensity and continuous rainfall. Therefore, a reliable technique of floodplain mapping is crucial for the improvement of flood control strategies and for preparing an evacuation plan. The main objective of this study is to compare the effect of tide on flood modeling analysis. The inundated areas were mapped for various annual recurrent intervals using peak flow data from 1965 to 2010. The study used Light Detection and Ranging (LiDAR) data for flood modeling. HEC-HMS, HEC-RAS, and HEC-GeoRAS were used to develop the flood model. The results reaffirm that the GEV model is the best for fitting the annual flood. The HEC-HMS hydrologic model was calibrated and validated using observed hydrographs in Sep 2002 and Jan 2003, respectively. Upon successful calibration and validation, the model was used to simulate flood hydrograph in Jan 2007. The modeling took into account the tidal effect. When the tidal effect was not considered, the simulated flood depth was 43 % lower than the observed flood. However, the inclusion of the tidal effect has reduced the simulation error with an average similarity of 91.4%. The simulation results show that the river flow starts to over bank for ARIs exceeded 25 years.

Periastron shift of compact stellar orbits from general relativistic and tidal distortion effects near Sgr A*

ABSTRACT The Galactic Centre (Sgr A*), hosting a supermassive black hole, carries sufficient potential for testing gravitational theories. Existing astrometric facilities on Very Large Telescope (VLT) and the Keck Telescope have enabled astronomers to study stellar orbits near Sgr A* and perform new astronomical tests of gravitational theories. These observations have provided strong field tests of gravity (ϕ/c2 ∼ 10−3, which is much greater than ϕ/c2 for the Solar system). In this work, we have estimated magnitudes of various contributions to the periastron shift of compact stellar orbits near Sgr A* for pericentre distance in the range rp = (0.3 – 50)au at a fixed orbital inclination, i = 90°. We take the spin of the black hole as χ = 0.1, 0.44, and 0.9 and eccentricities of the orbit as e = 0.9. The relativistic effects including orders beyond 1PN and spin induced effects are incorporated in the contributions. Effect of tidal distortion on periastron shift has also been added into the estimation by considering gravitational Love numbers for polytropic models of the stars. For the tidal effect, we have considered updated mass–radii relations for low-mass stars and high-mass stars. It has been found that the tidal effect on periastron shift arising from stars represented by polytropes of indices n = 1 and n = 3 terminate above rp ∼ 2 au and rp ∼ 1 au, respectively. The periastron shift angle for the stars has been compared with the astrometric capabilities of existing large telescopes and upcoming extremely large telescopes. Challenges and prospects associated with the estimations are highlighted.

Figures of Pluto and Charon and their relative motion

The comparative effect of two factors on the translatory motion of the centres of mass of the Pluto-Charon system is investigated. The first important factor is the non-sphericity of the shape and gravitational field of the bodies in the system. The second is the gravitation of the Sun. As a measure of the influence of both factors we use the ratio of the corresponding perturbing acceleration to the main one. The main acceleration is caused by the mutual Newtonian attraction of Pluto and Charon. It has been established that for the first factor this measure is of the order of 10^−6, while for the second factor it is two orders of magnitude smaller. This explains why the Lidov-Kozai effect (despite a large mutual slope of 96 between the planes of the satellite’s orbit around the planet, and the barycentre of the system around the Sun) does not appear. The situation is similar to the case with the satellites of Uranus. As a result, the Pluto-Charon system remains stable at least on a timescale of millions of years. The tidal effect of the Sun on the surface shape of the bodies under study is also estimated. The ratio of the tidal potential of the Sun at a point on the surface of the body to the gravitational potential of the body itself at this point is taken as a measure of impact. It turned out to be of the order of 3 · 10^−12, which is more than six orders less than the influence of rotation and mutual attraction of Pluto and Charon. In fact, the Sun does not affect the figures of the bodies of the system.