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Other Techniques
Published in C. R. Kitchin, Astrophysical Techniques, 2020
Henceforth in this section, we talk about the position of an object as its position on the celestial sphere and we ignore the differing radial distances that may be involved. We also extend the polar axis, the equatorial and orbital planes of the Earth until these too meet the celestial sphere (Figure 5.1). These intersections are called the ‘celestial North Pole’, the celestial equator, etc. Usually, there is no ambiguity if the ‘celestial’ qualification is omitted, so that they are normally referred to as the North Pole, the equator and so on. The intersections (or nodes) of the ecliptic and the equator are the vernal and autumnal equinoxes. The former is additionally known as the ‘first point of Aries’ (from its position in the sky some two thousand years ago). The ecliptic is also the apparent path of the Sun across the sky during a year and the vernal equinox is defined as the node at which the Sun passes from the Southern to the Northern Hemisphere. This passage occurs within a day of 21 March each year. The position of a star or other object is thus given with respect to these reference points and planes.
Definitions and Terminology
Published in Frank Vignola, Joseph Michalsky, Thomas Stoffel, Solar and Infrared Radiation Measurements, 2019
Frank Vignola, Joseph Michalsky, Thomas Stoffel
The Earth’s axis is tilted approximately 23.44 degrees with respect to the plane of the Earth’s orbit around the Sun. As the Earth moves around the Sun, its rotational axis is fixed if viewed from space (Figure 2.2). In June, the orientation of the axis is such that the Northern Hemisphere is pointed toward the Sun. In December, the Earth’s position is at the opposite end of the orbit around the Sun, and the orientation of the Earth’s axis is such that the Northern Hemisphere is pointed away from the Sun. During the spring and fall equinoxes, the Earth’s axis is perpendicular to a line drawn between the Earth and the Sun. The mean geometric orbit of the Earth around the Sun defines the ecliptic plane. For an eclipse to occur, the orbit of the new (solar) eclipse or full (lunar) eclipse moon has to be very near to the ecliptic plane, hence the name.
Orbit Dynamics and Properties
Published in Yaguang Yang, Spacecraft Modeling, Attitude Determination, and Control Quaternion-based Approach, 2019
Next, we define the X axis of the geocentric inertial coordinate system. It is known that the Earth’s equator plane is not on the same plane as of the ecliptic plane, which is the plane of the Earth orbiting around the Sun. The Earth’s equator plane is inclined to the ecliptic plane at an angle of about 23.5°. The two planes intersect along a line that is called the vernal equinox vector (see Figure 2.5). While the Earth rotates around the Sun, it crosses this line twice a year. The point when Earth cross this line in March is called vernal equinox. The direction from the center of mass of the Sun to the vernal points is defined as the X direction of the geocentric inertial system. The third axis Y completes an orthogonal right-hand system. Both equator and ecliptic planes move slowly because of the force of attraction of astronomical bodies. The coordinate axes may need some corrections over the time.
Error analysis of exterior orientation elements on geolocation for a Moon-based Earth observation optical sensor
Published in International Journal of Digital Earth, 2020
Huadong Guo, Hanlin Ye, Guang Liu, Changyong Dou, Jing Huang
Another peculiar factor is the changing observation angle. Unlike the low Earth orbit satellite, the orbit of the Moon does not have a fixed inclination. As the Earth moves around the Sun, with its rotational axis tilted about 23.5° from the ecliptic plane. The angle between the ecliptic plane and the Earth equator plane changes from 23.5° to −23.5°. The Moon also changes in inclination, with an inclination about 5.15° to the ecliptic plane. In consequence, the maximum inclination of the Moon varies from 18.35° (i.e. 23.5°−5.15°) to 28.65° (i.e. 23.5°+5.15°). This is enough to observe the total Arctic or Antarctic Region. Every about two weeks, the Moon will move from a maximum positive inclination to a maximum negative one. However, the maximum positive or negative inclination is not a coincidence with the apogee or perigee. Thus, there are four specific nodes during one orbital period, which are the apogee, the perigee, the maximum positive inclination, and the maximum negative inclination. Besides, there exists another longer observation period. The orbit of the Moon changes its inclination during the period of 18.6 years. Every 18.6 years, the angle between the orbit of the Moon plane and the Earth equator plane reaches a maximum of 28.65°. 9.3 years later, the angle between the orbit of the Moon plane and the Earth equator reaches its minimum, 18.35°. The nadir points of the Moon-based platform make a circle around the Earth surface. The latitudinal range of the nadir point is about 18.35° to 28.65° and all longitudes of the nadir points can be covered.