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Satellite-Based Mobile Communications
Published in Lal Chand Godara, Handbook of Antennas in Wireless Communications, 2018
At geostationary altitudes, satellites have an orbital period equal to the period of rotation of Earth. Consequently, they remain in a fixed position in respect to a given point on Earth. An obvious advantage is they are available to all Earth stations within their shadow 100% of the time. The shadow of a satellite includes all Earth stations that have a line-of-sight (LOS) path to it and lie within the radiation pattern of the satellite antenna. At geostationary altitude, the satellite has coverage of 17.3° cone angle, or about 40% of Earth’s surface. However, the polar areas are not covered.
Mathematical formulas from the sciences
Published in Dan Zwillinger, CRC Standard Mathematical Tables and Formulas, 2018
orbital period 365.256366days $ 365.256366\,\,{\text{days}} $
Spaceborne Application of Electronically Scanned Arrays
Published in Arik D. Brown, Electronically Scanned Arrays, 2017
The orbital period is the time required for the satellite to complete one full revolution around the earth. The orbital period is defined by the semimajor axis, a, and the gravitational constant, μ, as shown in Equations (5.7) and (5.8). () T=2πa3μ () μ=G(mearth+msat)=3.986004415×105km3s2
On the evolution of global ocean tides
Published in Geophysical & Astrophysical Fluid Dynamics, 2021
Local geography, e.g. continental shorelines and oceanic basins, can greatly influence ocean tide. This effect has been extensively studied since 1970s (e.g., Platzman 1972). On the other hand, the global tide in the mid-ocean far away from continents evolves on the geologic timescale of Earth's rotation and tidal resonances can occur on this timescale. Take the Earth–Moon system for example. The total angular momentum conserves but the total energy does not. The energy dissipation arises mainly from the friction near the rough seafloors and pushes the Earth–Moon system to the equilibrium state of minimum energy, and eventually both Earth's and Moon's rotations will synchronise with the orbit. Because the total angular momentum deposits mainly in the orbit, the orbital period varies not too much. If the total angular momentum conservation is precisely calculated, i.e. the orbital angular momentum together with the Earth's and Moon's rotational angular momenta, then it is indeed that the orbital period slows down and the separation between Earth and Moon increases (Bills and Ray 1999). However, in the present study, we do not consider the mutual interaction of orbital dynamics and tidal friction but focus on the tidal resonance, i.e. how strong the global ocean tide can reach when tidal resonances occur. Moon's rotation has already reached the synchronisation state because of its small mass, and Earth's rotation slows down on a geologic timescale towards the synchronisation state. The present period of Earth's rotation is one day, but it was several hours when Earth formed in the past, e.g. 5 hours (Zahnle et al.2015) or 6 hours after giant impact (Cuk and Stewart 2012), and will reach about one month in the future. The observation shows that the mid-ocean experiences tide of 1 metre or less (Thurman 1994). Tide can be higher in the past and future when Earth's rotation is appropriate to induce tidal resonances.
Robust control for spacecraft rendezvous system with actuator unsymmetrical saturation: a gain scheduling approach
Published in International Journal of Control, 2018
In this section, we give a numerical simulation to demonstrate the effectiveness of the proposed approach. We consider a pair of adjacent spacecrafts, and the chaser transfers towards the target. We assume that the target spacecraft is on a geosynchronous orbit of radius R = 42, 241km with an orbital period of 24 hours. Thus, the orbit rate can be computed as ω = 7.2722 × 10−5rad/s.