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Ignoring the influence of other Solar System bodies, Earth's orbit, also called Earth's revolution, is an ellipse with the Earth–Sun barycenter as one focus with a current eccentricity of 0.0167. Since this value is close to zero, the center of the orbit is relatively close to the center of the Sun (relative to the size of the orbit).
Knowledge of the location of Earth has been shaped by 400 years of telescopic observations, and has expanded radically since the start of the 20th century. Initially, Earth was believed to be the center of the Universe , which consisted only of those planets visible with the naked eye and an outlying sphere of fixed stars . [ 1 ]
Earth's rotation axis moves with respect to the fixed stars (inertial space); the components of this motion are precession and nutation. It also moves with respect to Earth's crust; this is called polar motion. Precession is a rotation of Earth's rotation axis, caused primarily by external torques from the gravity of the Sun, Moon and other bodies.
The Earth's radius is the distance from Earth's center to its surface, about 6,371 km (3,959 mi). While "radius" normally is a characteristic of perfect spheres, the Earth deviates from spherical by only a third of a percent, sufficiently close to treat it as a sphere in many contexts and justifying the term "the radius of the Earth".
For positions on the Earth or other solid celestial body, the reference plane is usually taken to be the plane perpendicular to the axis of rotation. Instead of the radial distance r geographers commonly use altitude above or below some local reference surface ( vertical datum ), which, for example, may be the mean sea level .
That’s only the apparent path if your presumption is that the earth and stars are stationary and the sun is revolving around the earth. It’s been quite a while since that was the first thought that entered one’s mind as the explanation for the sun’s movement across the sky, so that isn’t a description that quickly conveys the desired ...
The inverse problem for earth sections is: given two points, and on the surface of the reference ellipsoid, find the length, , of the short arc of a spheroid section from to and also find the departure and arrival azimuths (angle from true north) of that curve, and .
Due to forces that the Sun and Moon exert, Earth's equatorial plane moves with respect to the celestial sphere. Earth rotates while the ECI coordinate system does not. Earth-centered inertial (ECI) coordinate frames have their origins at the center of mass of Earth and are fixed with respect to the stars. [1] "