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Celestial Mechanics and Astrodynamics
Published in K.T. Chau, Applications of Differential Equations in Engineering and Mechanics, 2019
However, it is not energy efficient to travel to the Moon using an initial speed as discussed here. In a later section, we will see that the Hohmann transfer orbit is normally used (see Section 12.14). It is also known as the translunar orbit. It may be even more energy efficient to get into various stages of various elliptic orbits before getting into the actual translunar orbit. It is also more practical to send the spacecraft to a low Earth orbit before getting into a translunar orbit. This will be demonstrated in a later section. Another option is to station an spacecraft at the so-called Lagrangian Points between the Moon and the Earth, before landing on the Moon. There are five Lagrangian Points, at which the combined gravitational pull of two massive bodies (or the Moon and the Earth) precisely equals the centrifugal force of the small body to orbit with them. Therefore, the spacecraft at the Lagrangian Points will appear stationary relative to the motions of the Moon-Earth system. Three of the Lagrangian Points are collinear with the two large masses and were found by Euler and two other Lagrangian Points each form an equilateral triangle with the two masses that were found by Lagrange in 1772 in his prize memoir submitted to the Paris Academy. The collinear Lagrangian Points were shown by Joseph Liouville in 1845 to be unstable. The two triangular Lagrangian Points are, however, stable if the mass ratio between the two large masses is greater than 24.96, which is the case for the Earth-Moon system (see (12.127)).
Moon-based Earth observation: scientific concept and potential applications
Published in International Journal of Digital Earth, 2018
Huadong Guo, Guang Liu, Yixing Ding
Fundamentally, climate change depends on Earth’s radiation balance. Observation of both the solar radiation and Earth’s reflection and emission will depend on accurate measurement with space technology. Since the late 1970s, the United States and Europe have launched a number of missions to measure solar and terrestrial radiation, such as NASA’s Active Cavity Radiometer Irradiance Monitor Series programme (ACRIM1, 1980–1989; ACRIM2, 1991–2001; ACRIM3, 2000–present), Earth Radiation Budget Experiment (ERBE, 1984–1994), Clouds and Earth’s Radiant Energy System (CERES, 1997–present), Solar Radiation and Climate Experiment (SORCE, 2003–present) and the French Megha-Tropiques satellite on the Scanner for Radiation Budget (ScaRaB, 2011–present). These missions have greatly improved our understanding of Earth’s energy system. The Deep Space Climate Observatory (DSCOVR), placed at the earth–Sun first Lagrangian point, has been designed to measure the outgoing radiation of the sunlit Earth disk with a constant look angle. But in the outgoing radiation, the reflected shortwave radiation is highly affected by albedo and atmospheric conditions, showing obvious anisotropy. Lack of sampling in space and time is vulnerable to uncertainties. The lunar observatory provides large-scale observation with continuously changing angles, enabling it to calibrate the data of satellites in different orbits at different times. Its most important property is that it can provide a very long-term time series from a single orbit platform. In a year, the time series covers all local times, all seasons (different weather pattern) and all Earth phases for all underlying surfaces (Pallé and Goode 2009; Karalidi et al. 2012). The diversity of the surface-weather-phase combination is beneficial to improving the quality of global energy budget data and to the study of regional energy redistribution and its multi-layer coupling effects. The Moon-based data will also provide a direct connection between the data from space technology and the data from ground-based earthshine measurement series, which span almost one hundred years.