Optimal transfer between quasi-coplanar near-circular orbits

1982 ◽  
Keyword(s):  
Circular Orbits ◽  
Optimal Transfer

About the influence of second zonal harmonic on the motion of satellite in almost circular orbits

2019 ◽  
Vol 25 (2) ◽  
pp. 3-11
Author(s):  
A.V. Pirozhenko ◽  
◽  
A.I. Maslova ◽  
V.V. Vasilyev ◽  
◽  
...  
Keyword(s):  
Circular Orbits ◽  
Zonal Harmonic

scholarly journals General relativistic effects acting on the orbits of Galileo satellites

2021 ◽  
Vol 133 (4) ◽  
Author(s):  
K. Sośnica ◽  
G. Bury ◽  
R. Zajdel ◽  
K. Kazmierski ◽  
J. Ventura-Traveset ◽  
...  
Keyword(s):  
General Relativity ◽  
Orbit Determination ◽  
Final Height ◽  
Precise Orbit Determination ◽  
Satellite System ◽  
De Sitter ◽  
Circular Orbits ◽  
Precise Orbit ◽  
Artificial Earth Satellites ◽  
Artificial Earth

AbstractThe first pair of satellites belonging to the European Global Navigation Satellite System (GNSS)—Galileo—has been accidentally launched into highly eccentric, instead of circular, orbits. The final height of these two satellites varies between 17,180 and 26,020 km, making these satellites very suitable for the verification of the effects emerging from general relativity. We employ the post-Newtonian parameterization (PPN) for describing the perturbations acting on Keplerian orbit parameters of artificial Earth satellites caused by the Schwarzschild, Lense–Thirring, and de Sitter general relativity effects. The values emerging from PPN numerical simulations are compared with the approximations based on the Gaussian perturbations for the temporal variations of the Keplerian elements of Galileo satellites in nominal, near-circular orbits, as well as in the highly elliptical orbits. We discuss what kinds of perturbations are detectable using the current accuracy of precise orbit determination of artificial Earth satellites, including the expected secular and periodic variations, as well as the constant offsets of Keplerian parameters. We found that not only secular but also periodic variations of orbit parameters caused by general relativity effects exceed the value of 1 cm within 24 h; thus, they should be fully detectable using the current GNSS precise orbit determination methods. Many of the 1-PPN effects are detectable using the Galileo satellite system, but the Lense–Thirring effect is not.

The Tychonic Method for Calculating the Ratio between the Eccentricities of Mars

2021 ◽  
Vol 52 (2) ◽  
pp. 212-234
Author(s):  
Christián C. Carman
Keyword(s):  
The Sun ◽  
Circular Orbits ◽  
The One

In Chapter 16 of Astronomia nova, Kepler describes and applies a method for finding the parameters of what he will call the vicarious hypothesis: a model that still assumes circular orbits and an equant point, but does not assume the bisection of the eccentricity, that is, that the center of the orbit is halfway between the equant point and the Sun. The method allows Kepler to find independently both centers in a very elegant way, but its application is tedious. He confesses that he had to apply it seventy times over a period of 5 years to obtain trustable results. Years earlier, when Kepler arrived to work with Tycho, he found that Tycho and Longomontanus had rejected bisection and somehow had obtained a ratio between eccentricities that, as Kepler himself highlights, happened to be very close to the one Kepler would later find after so much effort. Kepler does not say how Tycho and Longomontanus obtained their parameters and, to the best of my knowledge, there is no single published work that attempts to answer this question. Still, it is a very interesting question to ask how they arrived at values so close to those that took so much pain for Kepler to obtain. Recently, I published a paper describing a method Tycho used for finding Saturn’s parameters. In this paper, I show that by applying this method to the data of Tychonic observations of oppositions, it is possible to arrive at parameters very close to those that we know Tycho found. In this way, I argue that this is the method Tycho applied for obtaining Mars’s parameters. The simplicity of the Tychonic method contrasts with the complexity of Kepler’s.

scholarly journals Stable circular orbits in caged black hole spacetimes

2021 ◽  
Vol 103 (8) ◽  
Author(s):  
Takahisa Igata ◽  
Shinya Tomizawa
Keyword(s):  
Black Hole ◽  
Circular Orbits ◽  
Black Hole Spacetimes

scholarly journals Time-optimal transfer of coherence

2012 ◽  
Vol 86 (5) ◽  
Author(s):  
Alberto Carlini ◽  
Tatsuhiko Koike
Keyword(s):  
Optimal Transfer ◽  
Time Optimal
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