Fixed stars in the context of Inertial frame

Geocentrism is a superseded astronomical model description of the Universe with Earth at the center. It is also known as the geocentric model, often exemplified specifically by the Ptolemaic system. Under most geocentric models, the Sun, the Moon, stars, and planets all orbit Earth. The geocentric model was the predominant description of the cosmos in many European ancient civilizations, such as those of Aristotle in Classical Greece and Ptolemy in Roman Egypt, as well as during the Islamic Golden Age.

Two observations supported the idea that Earth was the center of the Universe. First, from anywhere on Earth, the Sun appears to revolve around Earth once per day. While the Moon and the planets have their own motions, they also appear to revolve around Earth about once per day. The stars appeared to be fixed on a celestial sphere rotating once each day about an axis through the geographical poles of Earth. Second, Earth seems to be unmoving from the perspective of an earthbound observer; it feels solid, stable, and stationary.

A star is a luminous spheroid of plasma held together by self-gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night; their immense distances from Earth make them appear as fixed points of light. The most prominent stars have been categorised into constellations and asterisms, and many of the brightest stars have proper names. Astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations. The observable universe contains an estimated 10 to 10 stars. Only about 4,000 of these stars are visible to the naked eye—all within the Milky Way galaxy.

A star's life begins with the gravitational collapse of a gaseous nebula of material largely comprising hydrogen, helium, and traces of heavier elements. Its total mass mainly determines its evolution and eventual fate. A star shines for most of its active life due to the thermonuclear fusion of hydrogen into helium in its core. This process releases energy that traverses the star's interior and radiates into outer space. At the end of a star's lifetime, fusion ceases and its core becomes a stellar remnant: a white dwarf, a neutron star, or—if it is sufficiently massive—a black hole.

The sky is an unobstructed view upward from the surface of the Earth. It includes the atmosphere and outer space. It may also be considered a place between the ground and outer space, thus distinct from outer space.

In the field of astronomy, the sky is also called the celestial sphere. This is an abstract sphere, concentric to the Earth, on which the Sun, Moon, planets, and stars appear to be drifting. The celestial sphere is conventionally divided into designated areas called constellations.

A tropical year or solar year (or tropical period) is the time that the Sun takes to return to the same position in the sky – as viewed from the Earth or another celestial body of the Solar System – thus completing a full cycle of astronomical seasons. For example, it is the time from vernal equinox to the next vernal equinox, or from summer solstice to the next summer solstice. It is the type of year used by tropical solar calendars.

The tropical year is one type of astronomical year and particular orbital period. Another type is the sidereal year (or sidereal orbital period), which is the time it takes Earth to complete one full orbit around the Sun as measured with respect to the fixed stars, resulting in a duration of 20 minutes longer than the tropical year, because of the precession of the equinoxes.

The ecliptic or ecliptic plane is the orbital plane of Earth around the Sun. It was a central concept in a number of ancient sciences, providing the framework for key measurements in astronomy, astrology and calendar-making.

From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the background of stars – specifically the Zodiac constellations. The planets of the Solar System can also be seen along the ecliptic, because their orbital planes are very close to Earth's. The Moon's orbital plane is also similar to Earth's; the ecliptic is so named because the ancients noted that eclipses only occur when the Moon is crossing it.

In classical physics and special relativity, an inertial frame of reference (also called an inertial space or a Galilean reference frame) is a frame of reference in which objects exhibit inertia: they remain at rest or in uniform motion relative to the frame until acted upon by external forces. In such a frame, the laws of nature can be observed without the need to correct for acceleration.

All frames of reference with zero acceleration are in a state of constant rectilinear motion (straight-line motion) with respect to one another. In such a frame, an object with zero net force acting on it, is perceived to move with a constant velocity, or, equivalently, Newton's first law of motion holds. Such frames are known as inertial. Some physicists, like Isaac Newton, originally thought that one of these frames was absolute — the one approximated by the fixed stars. However, this is not required for the definition, and it is now known that those stars are in fact moving, relative to one another.

Retrograde motion in astronomy is, in general, orbital or rotational motion of an object in the direction opposite the rotation of its primary, that is, the central object (right figure). It may also describe other motions such as precession or nutation of an object's rotational axis. Prograde or direct motion is more normal motion in the same direction as the primary rotates. However, "retrograde" and "prograde" can also refer to an object other than the primary if so described. The direction of rotation is determined by an inertial frame of reference, such as distant fixed stars.

In the Solar System, the orbits around the Sun of all planets and dwarf planets and most small Solar System bodies, except many comets and few distant objects, are prograde. They orbit around the Sun in the same direction as the sun rotates about its axis, which is counterclockwise when observed from above the Sun's north pole. Except for Venus and Uranus, planetary rotations around their axis are also prograde. Most natural satellites have prograde orbits around their planets. Prograde satellites of Uranus orbit in the direction Uranus rotates, which is retrograde to the Sun. Nearly all regular satellites are tidally locked and thus have prograde rotation. Retrograde satellites are generally small and distant from their planets, except Neptune's satellite Triton, which is large and close. All retrograde satellites are thought to have formed separately before being captured by their planets.

A sidereal year (/saɪˈdɪəri.əl/, US also /sɪ-/; from Latin sidus 'asterism, star'), also called a sidereal orbital period, is the time that Earth or another planetary body takes to orbit the Sun once with respect to the fixed stars.

Hence, for Earth, it is also the time taken for the Sun to return to the same position relative to Earth with respect to the fixed stars after apparently travelling once around the ecliptic.

Sidereal time ("sidereal" pronounced /saɪˈdɪəriəl, sə-/ sy-DEER-ee-əl, sə-) is a system of timekeeping used especially by astronomers. Using sidereal time and the celestial coordinate system, it is easy to locate the positions of celestial objects in the night sky. Sidereal time is a "time scale that is based on Earth's rate of rotation measured relative to the fixed stars". A sidereal day (also known as the sidereal rotation period) represents the time for one rotation about the planet axis relative to the stars.

Viewed from the same location, a star seen at one position in the sky will be seen at the same position on another night at the same time of day (or night), if the day is defined as a sidereal day. This is similar to how the time kept by a sundial (Solar time) can be used to find the location of the Sun. Just as the Sun and Moon appear to rise in the east and set in the west due to the rotation of Earth, so do the stars. Both solar time and sidereal time make use of the regularity of Earth's rotation about its polar axis: solar time is reckoned according to the position of the Sun in the sky while sidereal time is based approximately on the position of the fixed stars on the theoretical celestial sphere.

Proper motion is the angular speed of a celestial object, such as a star, as it moves across the sky. It is an astrometric measure, giving an object's change in angular position over time relative to the center of mass of the Solar System. This parameter is measured relative to the distant stars or a stable reference such as the International Celestial Reference Frame (ICRF). Patterns in proper motion reveal larger structures like stellar streams, the general rotation of the Milky Way disk, and the random motions of stars in the Galactic halo.

The components for proper motion in the equatorial coordinate system (of a given epoch, often J2000.0) are given in the direction of right ascension (μ_α) and of declination (μ_δ). Their combined value is computed as the total proper motion (μ). It has dimensions of angle per time, typically arcseconds per year or milliarcseconds per year.

The southern celestial hemisphere, also called the Southern Sky, is the southern half of the celestial sphere; that is, it lies south of the celestial equator. This arbitrary sphere, on which seemingly fixed stars form constellations, appears to rotate westward around a polar axis as the Earth rotates.

At all times, the entire Southern Sky is visible from the geographic South Pole; less of the Southern Sky is visible the further north the observer is located. The northern counterpart is the northern celestial hemisphere.

The equatorial coordinate system is a celestial coordinate system widely used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the centre of Earth, a fundamental plane consisting of the projection of Earth's equator onto the celestial sphere (forming the celestial equator), a primary direction towards the March equinox, and a right-handed convention.

The origin at the centre of Earth means the coordinates are geocentric, that is, as seen from the centre of Earth as if it were transparent. The fundamental plane and the primary direction mean that the coordinate system, while aligned with Earth's equator and pole, does not rotate with the Earth, but remains relatively fixed against the background stars. A right-handed convention means that coordinates increase northward from and eastward around the fundamental plane.

The celestial spheres, or celestial orbs, were the fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus, and others. In these celestial models, the apparent motions of the fixed stars and planets are accounted for by treating them as embedded in rotating spheres made of an aetherial, transparent fifth element (quintessence), like gems set in orbs. Since it was believed that the fixed stars were unchanging in their positions relative to one another, it was argued that they must be on the surface of a single starry sphere.