The earth rotates around its “earth axis” at the north and south poles every day. One rotation is one day and one night, and 15° per hour. The earth is revolving around the sun while it is rotating, and one revolution is one year. The inclination of the normal line between the earth’s rotation axis and the orbital plane (also known as the ecliptic plane) is 23~27′, and the direction of the rotation axis of the earth is always the same when the earth revolves. different, thus forming the change of seasons.
(1) Geographical coordinates and celestial coordinates
1) Geographical coordinates are a coordinate system that indicates a certain position on the earth’s surface, with the earth as the basic circle, the earth’s center as the origin, and the earth’s axis as the central axis, with longitude and latitude to represent the position of a certain point on the earth’s surface. The two focal points of the earth’s axis and the earth’s surface in geographic coordinates are called the north and south poles, and the great circle passing through the earth’s center and perpendicular to the earth’s axis is called the earth’s equatorial plane. The equatorial plane divides the earth into the northern and southern hemispheres. A circular line parallel to the equator at any point on the earth is called the latitude line. The angle between the vertical line pointing to the center of the earth at any point on the latitude line and the equatorial plane is called the latitude of the latitude line, denoted as φ. At any point on the earth, a circular plane perpendicular to the equator is made through the north and south poles. The circular line is called the longitude line of geographical coordinates, also called the meridian. The international meridian where the Greenwich Observatory is located is 0° longitude, and is called This meridian is the prime meridian, and the angle between the plane where other meridians lie and the plane of the prime meridian is called the longitude of the meridian.
2) Celestial coordinates are a coordinate system that expresses the position of the sun relative to the observer from a human perspective. The celestial sphere is an imaginary sphere introduced from the perspective of human observation in order to study the position and motion of celestial bodies, on which the sun performs periodic motion. Generally, a large sphere with the center of the earth as the center and the average distance between the sun and the earth as the radius. The celestial coordinates are divided into several coordinate systems according to the different reference planes. Among them, the horizon coordinate system and the hour-angle coordinate system are mostly used in photovoltaic applications. Some specific physical quantities in celestial coordinates are as follows.
(2) Zenith and nadir: The line connecting from any observation point on the earth to the center of the earth, extending upward to the intersection of the celestial sphere is called the zenith, which is directly above the observer, and the celestial sphere is opposite to the zenith. The point of symmetry is called the nadir, which is directly below the observer.
(3) Horizon: The great circular plane that passes through the center of the earth and is perpendicular to the line connecting the zenith and nadir is called the horizon, and the horizon is parallel to the tangential plane of the earth where the observer is located.
(4) The north and south celestial poles: The intersection of the earth’s terrestrial axis with the celestial sphere after extending infinitely at both ends is called the north and south celestial poles.
(5) Sky axis: The axis connecting the north and south celestial poles is called the sky axis.
(6) The celestial equator: a plane perpendicular to the celestial axis is made through the center of the earth, and the great circle formed on the celestial sphere is called the celestial equator, which is an imaginary large circle.
(7) Horizon meridian, celestial meridian: The circular line perpendicular to the horizon from the zenith is called the horizon meridian, and the circular line connecting the north and south celestial poles perpendicular to the celestial equator is called the celestial meridian.
(8) Declination δ: The angle between the line connecting the earth’s center and the sun and the celestial equator is called declination, which is an angle variable that reflects the law of the earth’s revolution around the sun, with one year as the change cycle. Declination is an important parameter in photovoltaic calculations.
(9) Hour angle τ: The angle between the line connecting the sun and the center of the earth and the celestial meridian is called the solar hour angle τ. At noon time τ=0°, τ is negative in the morning, τ is positive in the afternoon, and τ corresponds to ±180° in one day and night.
(10) Solar zenith angle: The angle between the line connecting the center of the earth and the sun and the line connecting the center of the earth and the zenith is called the zenith angle of the sun.
(11) Solar altitude angle αs: The angle between the line connecting the center of the earth and the sun and the ground plane is called the solar altitude angle.
(12) Sun azimuth angle γ: refers to the angle between the projection of the sun’s rays on the ground plane and the local longitude. The variation range of the sun azimuth angle is ±180°, the azimuth angle due to the south is 0°, and the azimuth angle is 0° when rotated clockwise to the west. A positive value, a negative value for a counterclockwise rotation to the east.
(13) Horizon coordinate system and hour angle coordinate system
1) Horizon coordinate system: a celestial coordinate system with the ground plane as the basic circle, the zenith as the basic point, and the intersection of the celestial meridian and the ground plane as the origin. The position of the sun in the horizon coordinate system is demarcated by the two angles of the sun’s altitude and the sun’s azimuth.
2) Hour-angle coordinate system: a coordinate system with the celestial equator as the basic circle, the north celestial pole as the basic point, and the intersection of the celestial equator and the celestial meridian as the origin, also known as the equatorial coordinate system. The position of the sun in the equatorial coordinate system is demarcated by two angles, the hour angle and the declination.
In the calculation of photovoltaics, it is generally necessary to combine these two coordinate systems so that the sun altitude and azimuth angle of any observation point can be easily obtained.