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This is a diagram of the seasons. Regardless of the time of day (i.e. Earth 's rotation on its axis), the North Pole will be dark, and the South Pole will be illuminated; see also arctic winter . Figure 3 shows the angle of sunlight striking Earth in the Northern and Southern Hemispheres when Earth's northern axis is tilted away from the Sun ...
Mathematically, an ellipse can be represented by the formula: r = p 1 + ε cos θ , {\displaystyle r={\frac {p}{1+\varepsilon \,\cos \theta }},} where p {\displaystyle p} is the semi-latus rectum , ε is the eccentricity of the ellipse, r is the distance from the Sun to the planet, and θ is the angle to the planet's current position from ...
In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle .
Given the different Sun incidence in different positions in the orbit, it is necessary to define a standard point of the orbit of the planet, to define the planet position in the orbit at each moment of the year w.r.t such point; this point is called with several names: vernal equinox, spring equinox, March equinox, all equivalent, and named considering northern hemisphere seasons.
A rotation can be represented by a unit-length quaternion q = (w, r →) with scalar (real) part w and vector (imaginary) part r →. The rotation can be applied to a 3D vector v → via the formula = + (+). This requires only 15 multiplications and 15 additions to evaluate (or 18 multiplications and 12 additions if the factor of 2 is done via ...
The rotation group is a Lie group of rotations about a fixed point. This (common) fixed point or center is called the center of rotation and is usually identified with the origin. The rotation group is a point stabilizer in a broader group of (orientation-preserving) motions. For a particular rotation: The axis of rotation is a line of its ...
At the equator, the solar rotation period is 24.47 days. This is called the sidereal rotation period, and should not be confused with the synodic rotation period of 26.24 days, which is the time for a fixed feature on the Sun to rotate to the same apparent position as viewed from Earth (the Earth's orbital rotation is in the same direction as the Sun's rotation).
The ancient Greek astronomer Hipparchus noted the apsidal precession of the Moon's orbit (as the revolution of the Moon's apogee with a period of approximately 8.85 years); [4] it is corrected for in the Antikythera Mechanism (circa 80 BCE) (with the supposed value of 8.88 years per full cycle, correct to within 0.34% of current measurements). [5]
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