The Besselian elements are a set of values used to calculate and predict the local circumstances of

occultation An occultation is an event that occurs when one object is hidden from the observer by another object that passes between them. The term is often used in astronomy, but can also refer to any situation in which an object in the foreground blocks ...

s for an observer on Earth. This method is particularly used for

solar eclipses A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby obscuring the view of the Sun from a small part of the Earth, totally or partially. Such an alignment occurs during an eclipse season, approximately every six mont ...

, but is also applied for occultations of

star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...

s or

planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...

s by the

Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

and

transit Transit may refer to: Arts and entertainment Film * ''Transit'' (1979 film), a 1979 Israeli film * ''Transit'' (2005 film), a film produced by MTV and Staying-Alive about four people in countries in the world * ''Transit'' (2006 film), a 2006 ...

s of

Venus Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never fa ...

Mercury Mercury commonly refers to: * Mercury (planet), the nearest planet to the Sun * Mercury (element), a metallic chemical element with the symbol Hg * Mercury (mythology), a Roman god Mercury or The Mercury may also refer to: Companies * Merc ...

. In addition, for

lunar eclipse A lunar eclipse occurs when the Moon moves into the Earth's shadow. Such alignment occurs during an eclipse season, approximately every six months, during the full moon phase, when the Moon's orbital plane is closest to the plane of the Earth ...

s a similar method is used, in which the shadow is cast on the Moon instead of the Earth. For solar eclipses, the Besselian elements are used to calculate the path of the umbra and penumbra on the Earth's surface, and hence the circumstances of the eclipse at a specific location. This method was developed in the 1820s by the German mathematician and astronomer,

Friedrich Wilhelm Bessel Friedrich Wilhelm Bessel (; 22 July 1784 – 17 March 1846) was a German astronomer, mathematician, physicist, and geodesist. He was the first astronomer who determined reliable values for the distance from the sun to another star by the method ...

, and later improved by

William Chauvenet William Chauvenet (24 May 1820 in Milford, Pennsylvania – 13 December 1870 in St. Paul, Minnesota) was a professor of mathematics, astronomy, navigation, and surveying who was instrumental in the establishment of the U.S. Naval Academy at Annapo ...

. The basic concept is that Besselian elements describe the movement of the shadow cast by the occulting body – for solar eclipses this is the shadow of the Moon – on a specifically chosen plane, called the ''fundamental plane''. This is the geocentric, normal plane of the shadow axis. In other words, it is the plane through the Earth's center that is perpendicular to the line through the centers of the occulting and the occulted bodies. One advantage, among others, of choosing this plane is that the outline of the shadow on it is always a circle, and there is no perspective distortion. Comparatively few values are needed to accurately describe the movement of the shadow on the fundamental plane. Based on this, the next step is to

project A project is any undertaking, carried out individually or collaboratively and possibly involving research or design, that is carefully planned to achieve a particular goal. An alternative view sees a project managerially as a sequence of even ...

the shadow cone on to the Earth's surface, taking into account the

figure of the Earth Figure of the Earth is a Jargon, term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. A Spherical Earth, sphere is a well-k ...

, its

rotation Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...

, and the observer's

latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...

longitude Longitude (, ) is a geographic coordinate that specifies the east–west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter l ...

and

elevation The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface (see Geodetic datum § Vert ...

. Although the Besselian elements determine the overall geometry of an eclipse, which ''longitudes'' on the earth's surface will experience an eclipse are determined by the earth's rotation. A variable called ΔT measures how much that rotation has slowed over time and must also be taken into account when predicting local eclipse circumstances.

References

Further reading