HELIOCENTRIC and GEOCENTRIC Systems
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Heliocentric Systems, Geocentric Systems, # Frame of reference
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HELIOCENTRIC and GEOCENTRIC Systems
- 1. HELIOCENTRIC vs GEOCENTRIC Systems #frame of reference A PRESENTATION BY – PAWAN RAMA MALI
- 5. Apparent motion of Mars against "fixed" stars 5 1 2 3 4 5 6 7 1 2 3 4 5 67 Earth Mars * * * * * * January July Retrograde Motion of Planets Planets sometimes appear to loop back - retrograde motion Loops are called "epicycles"
- 7. Frame of reference • Required for performing survey operations. • Also known as control points or stations • These points are determined with respect to certain coordinate systems. • Defined by its axes and origin .
- 8. P (x, y) X Y x y O (X, Y, Z) P O X Y Z Y X Z Coordinate System
- 9. Geocentric frame of reference Greenwich Meridian Equator Earth Surface X Y Z (X, Y, Z) X Y Z
- 10. Geocentric frame of reference Greenwich Meridian Equator Earth Surface X Y Z P h ),,( h
- 11. Celestial frame of reference
- 20. CELESTIA
- 21. ThankYou THE END
Editor's Notes
- The ancient Greeks observed the sky and noticed that the moon, sun, and stars seemed to move in a circle around the Earth. It seemed that the Earth was not moving and everything in the heavens revolved around the Earth. As it turned out, it was very difficult to prove that the planets did not revolve around the Earth without leaving the planet.
- Ancient Greeks such as Aristotle believed that the universe was perfect and finite, with the Earth at the exact center. This is the geocentric theory, which stated, the planets, moon, sun, and stars revolve around the Earth. In AD 140 the Greek astronomer Ptolemy revised the geocentric model to explain all the planetary motions. His model had the planets move in little circles that also moved in bigger circles. This belief persisted for about 1500 years
- In the early 1500’s the polish astronomer Copernicus suggested that the Sun, not Earth, was the center of the solar system and the planets revolved around it. This is the Heliocentric Theory
- Earth overtakes slow outer planet so the outer planet appears to slow down, move in reverse, and then move forward again with respect to the fixed stars
- In the heliocentric model, apparent retrograde motion of the planets is a direct consequence of the Earth’s motion
- The frame of reference are required for performing survey operations. These points are known as control points or stations The coordinates of these points are determined with respect to certain coordinate systems. The coordinate systems are defined by its axes and origin .
- The geocentric Cartesian Coordinate system is often called Earth Centered, Earth fixed (ECEF) or Conventional Terrestrial Reference System (CTRS). This system is defined as: Origin of coordinate system is placed at the centre of earth Z axis aligned to the axis of rotation of earth which has the direction of the conventional International origin for polar motion (CIO). The X axis passes through the intersection of primary plane (equatorial plane) and plane containing the Greenwich meridian
- Geodetic latitude () of a point on the surface of the earth is the angle between ellipsoidal normal passing through the point and equatorial plane, positive to north. Geodetic Longitude () is the angle between the prime meridian (Greenwich meridian) and the meridian plane passing through the point (observer’s meridian), positive to the east. Ellipsoidal height (h) of a point on the surface of the earth is the distance measured from the ellipsoid to the point along ellipsoidal normal passing through the point.
- In astronomy, a celestial coordinate system is a system for specifying positions of celestial objects: satellites, planets, stars, galaxies, and so on. Coordinate systemscan specify a position in 3-dimensional space, or merely the direction of the object on the celestial sphere, if its distance is not known or not important. The coordinate systems are implemented in either spherical coordinates or rectangular coordinates. Spherical coordinates, projected on the celestial sphere, are analogous to the geographic coordinate system used on the surface of the Earth. These differ in their choice of fundamental plane, which divides the celestial sphere into two equal hemispheres along a great circle. Rectangular coordinates, in appropriate units, are simply the cartesian equivalent of the spherical coordinates, with the same fundamental (x,y) plane and primary (x-axis) direction. Each coordinate system is named for its choice of fundamental plane.
- The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane. It is expressed in terms of altitude (or elevation) angle and azimuth. There are two independent horizontal angular coordinates: Altitude (Alt), sometimes referred to as elevation, is the angle between the object and the observer's local horizon. For visible objects it is an angle between 0 degrees to 90 degrees. Alternatively, zenith distance, the distance from directly overhead (i.e. the zenith) may be used instead of altitude. The zenith distance is the complement of altitude (i.e. 90°-altitude). Azimuth (Az), that is the angle of the object around the horizon, usually measured from the north increasing towards the east.
- The equatorial coordinate system is a widely used celestial coordinate system used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the center of the Earth, a fundamental plane consisting of the projection of the Earth's equator onto the celestial sphere (forming the celestial equator), a primary direction towards the vernal equinox, and a right-handed convention.[1][2] The equatorial coordinate system in spherical coordinates. The fundamental plane is formed by projection of the Earth's equator onto the celestial sphere, forming the celestial equator (blue). The primary direction is established by projecting the Earth's orbit onto the celestial sphere, forming the ecliptic (red), and setting up the ascending node of the ecliptic on the celestial equator, the vernal equinox. Right ascensions are measured eastward along the celestial equator from the equinox, and declinations are measured positive northward from the celestial equator - two such coordinate pairs are shown here. Projections of the Earth's north and south geographic poles form the north and south celestial poles, respectively. The origin at the center of the Earth means the coordinates are geocentric, that is, as seen from the center of the Earth as if it were transparent.[3] The fundamental plane and the primary direction mean that the coordinate system, while aligned with the Earth's equator and pole, does not rotate with the Earth, but remains relatively fixed against the background stars.
- As seen from above the Earth's north pole, a star'slocal hour angle (LHA) for an observer near New York (red). Also depicted are the star's right ascension and Greenwich hour angle (GHA), the local mean sidereal time (LMST) and Greenwich mean sidereal time(GMST). The symbol ʏ identifies the vernal equinoxdirection. Right ascension (symbol α, abbreviated RA) measures the angular distance of an object eastward along the celestial equator from the vernal equinox to the hour circle passing through the object. The vernal equinox point is one of the two where the ecliptic intersects the celestial equator. Declination (symbol δ, abbreviated dec) measures the angular distance of an object perpendicular to the celestial equator, positive to the north, negative to the south. Alternatively to right ascension, hour angle (abbreviated HA or LHA, local hour angle), a left-handed system, measures the angular distance of an object westward along the celestial equator from the observer's meridian to the hour circle passing through the object.
- The ecliptic coordinate system is a celestial coordinate system commonly used for representing the positions and orbits of Solar System objects. Because most planets (except Mercury), and many small solar system bodies have orbits with small inclinations to the ecliptic, it is convenient to use it as the fundamental plane. The system's origin can be either the center of the Sun or the center of the Earth, its primary direction is towards the vernal (northbound) equinox, and it has a right-handed convention. It may be implemented in spherical coordinates or rectangular coordinates
- Here the origin is at the center of the Sun, its fundamental plane in the plane of the ecliptic, its primary direction (the x axis) toward the vernal equinox, that is, the place where the Sun crosses the celestial equator in a northward direction in its annual apparent circuit around the Heliocentric ecliptic coordinates. A right-handed convention specifies a y axis 90° to the east in the fundamental plane; the z axis points toward the north ecliptic pole. The reference frame is relatively stationary, aligned with the vernal equinox.
- The galactic coordinate system is a celestial coordinate system in spherical coordinates, with the Sun as its center, the primary direction aligned with the approximate center of the Milky Way galaxy, and the fundamental plane approximately in the galactic plane. It uses the right-handed convention, meaning that coordinates are positive toward the north and toward the east in the fundamental plane
- The galactic coordinates use theSun as the origin. Galactic longitude (l) is measured with primary direction from the Sun to the center of the galaxy in the galactic plane, while the galactic latitude (b) measures the angle of the object above the galactic plane.
- Supergalactic coordinates are coordinates in a spherical coordinate system which was designed to have its equator aligned with the supergalactic plane, a major structure in the local universe formed by the preferential distribution of nearby galaxy clusters (such as the Virgo cluster, the GrBy convention, supergalactic latitude and supergalactic longitude are usually denoted by SGB and SGL, respectively, by analogy to b and l conventionally used for galactic coordinates. The zero point for supergalactic longitude is defined by the intersection of this plane with the galactic plane.eat Attractor and the Pisces-Perseus supercluster) towards a (two-dimensional) plane.
- There are a number of rectangular variants of equatorial coordinates. All have: The origin at the center of the Earth. The fundamental plane in the plane of the Earth's equator. The primary direction (the x axis) toward the vernal equinox, that is, the place where the Sun crosses the celestial equator in a northward direction in its annual apparent circuit around the ecliptic. A right-handed convention, specifying a y axis 90° to the east in the fundamental plane and a z axis along the north polar axis. The reference frames do not rotate with the Earth (in contrast to Earth-Centered, Earth-Fixed frames), remaining always directed toward the equinox, and drifting over time with the motions of precession and nutation. In astronomy:[14] The position of the Sun is often specified in the geocentric equatorial rectangular coordinates X, Y, Z and a fourth distance coordinate, R (=√X² + Y² + Z²), in units of the astronomical unit. The positions of the planets and other Solar System bodies are often specified in the geocentric equatorial rectangular coordinates ξ, η, ζ and a fourth distance coordinate, Δ (=√ξ² + η² + ζ²), in units of the astronomical unit. In astrodynamics:[15] The positions of artificial Earth satellites are specified in geocentric equatorial coordinates, also known as geocentric equatorial inertial (GEI), Earth-centered inertial (ECI), and conventional inertial system (CIS), all of which are equivalent in definition to the astronomical geocentric equatorial rectangular frames, above. In the geocentric equatorial frame, the x, y and z axes are often designated I, J and K, respectively, or the frame's basis is specified by the unit vectors , and . The Geocentric Celestial Reference Frame (GCRF) is the geocentric equivalent of the International Celestial Reference Frame (ICRF). Its primary direction is the equinox of J2000.0, and does not move withprecession and nutation, but it is otherwise equivalent to the above systems. Heliocentric equatorial coordinates[edit] In astronomy, there is also a heliocentric rectangular variant of equatorial coordinates, designated x, y, z, which has: The origin at the center of the Sun. The fundamental plane in the plane of the Earth's equator. The primary direction (the x axis) toward the vernal equinox. A right-handed convention, specifying a y axis 90° to the east in the fundamental plane and a z axis along Earth's north polar axis.