• Journal of Astronomy and Space Sciences
• /
• v.41 no.2
• /
• pp.87-106
• /
• 2024

The objective of this research is to address the issue of frozen orbits in charged satellites by incorporating geopotential zonal harmonics up to J6 and the initial tesseral harmonics. The employed model starts from the first normalized Hamiltonian to calculate specific sets of long-term frozen orbits for charged satellites. To explore the frozen orbits acquired, a MATHEMATICA CODE is developed. The investigation encompasses extensive variations in orbit altitudes by employing the orbital inclination and argument of periapsis as freezing parameters. The determined ranges ensuring frozen orbits are derived from the generated figures. Three-dimensional presentations illustrating the freezing inclination in relation to eccentricity, argument of periapsis, and semi-major axis parameters are presented. Additional three-dimensional representations of the phase space for the eccentricity vector and its projection onto the nonsingular plane are examined. In all investigated scenarios, the impacts of electromagnetic (EM) field perturbations on the freezing parameters of a charged satellite are demonstrated.

• Journal of Astronomy and Space Sciences
• /
• v.37 no.1
• /
• pp.1-9
• /
• 2020

Frozen orbit is an attractive option for orbital design owing to its characteristics (its argument of pericenter and eccentricity are kept constant on an average). Solar sails are attractive solutions for massive and expensive missions. However, the solar radiation pressure effect represents an additional force on the solar sail that may greatly affect its orbital behavior in the long run. Thus, this force must be included as a perturbation force in the dynamical model for more accuracy. This study shows the calculations of initial conditions for a lunar solar sail frozen orbit. The disturbing function of the problem was developed to include the lunar gravitational field that is characterized by uneven mass distribution, third body perturbation, and the effect of solar radiation. An averaging technique was used to reduce the dynamical problem to a long period system. Lagrange planetary equations were utilized to formulate the rate of change of the argument of pericenter and eccentricity. Using the reduced system, frozen orbits for the Moon sail orbiter were constructed. The resulting frozen orbits are shown by two 3Dsurface (semi-major, eccentricity, inclination) figures. To simplify the analysis, we showed inclination-eccentricity contours for different values of semi-major axis, argument of pericenter, and values of sail lightness number.

• Bulletin of the Korean Space Science Society
• /
• 2011.04a
• /
• pp.24.4-24.4
• /
• 2011

Frozen orbit concept is very useful in designing particular mission orbits including the Sun-synchronous and minimum altitude variation orbits. In this work, variety of frozen and Sun-synchronous orbit conditions around the Moon is investigated and analyzed. The first two zonal harmonics of the Moon, J2 and J3, are considered to determine mean orbital elements to be a frozen orbit. To check the long-term behavior of a frozen orbit, formerly developed YonSei Precise Lunar Orbit Propagator (YSPLOP) is used. First, frozen orbit solutions without conditions to be the Sun-synchronous orbit is investigated. Various mean semi-major axes having between ranges from 1,788 km to 1,938 km with inclinations from 30 deg to 150 deg are considered. It is found that a polar orbit (90 deg of inclination) having 100 km of altitude requires the orbital eccentricity of about 0.01975 for a frozen orbit. Also, mean apolune and perilune altitudes for this case is about 136.301 km and 63.694 km, respectively. Second, frozen orbit solutions with additional condition to be the Sun-synchronous orbit is investigated. It is discovered that orbital inclinations are increased from 138.223 deg to 171.553 deg when mean altitude ranged from 50 km to 200 km. For the most usual mission altitude at the Moon (100 km), the Sun-synchronous orbit condition is satisfied with the eccentricity of 0.01124 and 145.235 deg of inclination. For this case, mean apolune and perilune altitudes are found to be about 120.677 km and 79.323 km, respectively. The results analyzed in this work could be useful to design a preliminary mapping orbit as well as to estimate basic on-board payloads' system requirements, for a future Korea's lunar orbiter mission. Other detailed perturbative effects should be considered in the further study, to analyze more accurate frozen orbit conditions at the Moon.