Analytical Study of Earth Tides on Low Orbits Satellites

The main objective of this paper is to calculate the perturbations of tide effect on LEO's satellites . In order to achieve this goal, the changes in the orbital elements which include the semi major axis (a) eccentricity (e) inclination , right ascension of ascending nodes ( ), and fifth element argument of perigee ( ) must be employed. In the absence of perturbations, these element remain constant. The results show that the effect of tidal perturbation on the orbital elements depends on the inclination of the satellite orbit. The variation in the ratio decreases with increasing the inclination of satellite, while it increases with increasing the time.

Accurate Evaluation of Vertical Tidal Displacement Determined by GPS Kinematic Precise Point Positioning: A Case Study of Hong Kong

Global Positioning System (GPS) kinematic precise point positioning (KPPP) is an effective approach for estimating the Earth’s tidal deformation. The accuracy of KPPP is usually evaluated by comparing results with tidal models. However, because of the uncertainties of the tidal models, the accuracy of KPPP-estimated tidal displacement is difficult to accurately determine. In this paper, systematic vector differences between GPS estimates and tidal models were estimated by least squares methods in complex domain to analyze the uncertainties of tidal models and determine the accuracy of KPPP-estimated tidal displacements. Through the use of GPS data for 12 GPS reference stations in Hong Kong from 2008 to 2017, vertical ocean tide loading displacements (after removing the body tide effect) for eight semidiurnal and diurnal tidal constituents were obtained by GPS KPPP. By an in-depth analysis of the systematic and residual differences between the GPS estimates and nine tidal models, we demonstrate that the uncertainty of the tidal displacement determined by GPS KPPP for the M2, N2, O1, and Q1 tidal constituents is 0.2 mm, and for the S2 constituent it is 0.5 mm, while the accuracy of the GPS-estimated K1, P1, and K2 tidal constituents is weak because these three tidal constituents are affected by significant common-mode errors. These results suggest that GPS KPPP can be used to precisely constrain the Earth’s vertical tidal displacement in the M2, N2, O1, and Q1 tidal frequencies.

The formation of close-in planets by the slingshot model

We investigated the efficiency of planet scatterings in producing close-in planets by a direct inclusion of the dynamical tide effect into the simulations. We considered a system consists of three Jovian planets. Through a planet-planet scattering, one of the planets is sent into shorter orbit. If the eccentricity of the scattered planet is enough high, the tidal dissipation from the star makes the planetary orbit circular. We found that the short-period planets are formed at about 30% cases in our simulation and that Kozai mechanism plays an important role. In the Kozai mechanism, the high inclination obtained by planet-planet scattering is transformed to the eccentricity. It leads the pericenter of the innermost planet to approach the star close enough for tidal circularization. The formed close-in planets by this process have a widely spread inclination distribution. The degree of contribution of the process for the formation of close-in planets will be revealed by more observations of Rossiter-McLaughlin effects for transiting planets.