Orbital eccentricity in the context of "Conic section"

Apollonius of Perga (Ancient Greek: Ἀπολλώνιος ὁ Περγαῖος Apollṓnios ho Pergaîos; c. 240 BC – c. 190 BC) was an ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the earlier contributions of Euclid and Archimedes on the topic, he brought them to the state prior to the invention of analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today. With his predecessors Euclid and Archimedes, Apollonius is generally considered among the greatest mathematicians of antiquity.

Aside from geometry, Apollonius worked on numerous other topics, including astronomy. Most of this work has not survived, where exceptions are typically fragments referenced by other authors like Pappus of Alexandria. His hypothesis of eccentric orbits to explain the apparently aberrant motion of the planets, commonly believed until the Middle Ages, was superseded during the Renaissance. The Apollonius crater on the Moon is named in his honor.

A comet is an icy, small Solar System body or interstellar object that warms and begins to release gases when passing close to the Sun, a process called outgassing. This produces an extended, gravitationally unbound atmosphere or coma surrounding the nucleus, and sometimes a tail of gas and dust gas blown out from the coma. These phenomena are due to the effects of solar radiation and the outstreaming solar wind plasma acting upon the nucleus of the comet. Comet nuclei range from a few hundred meters to tens of kilometers across and are composed of loose collections of ice, dust, and small rocky particles. The coma may be up to 15 times Earth's diameter, while the tail may stretch beyond one astronomical unit. If sufficiently close and bright, a comet may be seen from Earth without the aid of a telescope and can subtend an arc of up to 30° (60 Moons) across the sky. Comets have been observed and recorded since ancient times by many cultures and religions.

Comets usually have highly eccentric elliptical orbits, and they have a wide range of orbital periods, ranging from several years to potentially several millions of years. Short-period comets originate in the Kuiper belt or its associated scattered disc, which lie beyond the orbit of Neptune. Long-period comets are thought to originate in the Oort cloud, a spherical cloud of icy bodies extending from outside the Kuiper belt to halfway to the nearest star. Long-period comets are set in motion towards the Sun by gravitational perturbations from passing stars and the galactic tide. Hyperbolic comets may pass once through the inner Solar System before being flung to interstellar space. The appearance of a comet is called an apparition.

A low Earth orbit (LEO) is an orbit around Earth with a period of 128 minutes or less (making at least 11.25 orbits per day) and an eccentricity less than 0.25. Most of the artificial objects in outer space are in LEO, peaking in number at an altitude around 800 km (500 mi), while the farthest in LEO, before medium Earth orbit (MEO), have an altitude of 2,000 kilometers, about one-third of the radius of Earth and near the beginning of the inner Van Allen radiation belt.

The term LEO region is used for the area of space below an altitude of 2,000 km (1,200 mi) (about one-third of Earth's radius). Objects in orbits that pass through this zone, even if they have an apogee further out or are sub-orbital, are carefully tracked since they present a collision risk to the many LEO satellites.

A lunar phase or Moon phase is the apparent shape of the Moon's day and night phases of the lunar day as viewed from afar. Because the Moon is tidally locked to Earth, the cycle of phases takes one lunar month and moves across the same side of the Moon, which always faces Earth. In common usage, the four major phases are the new moon, the first quarter, the full moon and the last quarter; the four minor phases are waxing crescent, waxing gibbous, waning gibbous, and waning crescent. A lunar month is the time between successive recurrences of the same phase: due to the eccentricity of the Moon's orbit, this duration is not perfectly constant but averages about 29.5 days.

The appearance of the Moon (its phase) gradually changes over a lunar month as the relative orbital positions of the Moon around Earth, and Earth around the Sun, shift. The visible side of the Moon is sunlit to varying extents, depending on the position of the Moon in its orbit, with the sunlit portion varying from 0% (at new moon) to nearly 100% (at full moon).

Mercury is the first planet from the Sun and the smallest in the Solar System. It is a rocky planet with a trace atmosphere and a surface gravity slightly higher than that of Mars. The surface of Mercury is similar to Earth's Moon, being heavily cratered, with an expansive rupes system generated from thrust faults, and bright ray systems, formed by ejecta. Its largest crater, Caloris Planitia, has a diameter of 1,550 km (960 mi), which is about one-third the diameter of the planet (4,880 km or 3,030 mi). Being the most inferior orbiting planet, it always appears close to the sun in Earth's sky, either as a "morning star" or an "evening star". It is the planet with the highest delta-v required for travel from Earth, as well as to and from the other planets in the Solar System.

Mercury's sidereal year (88.0 Earth days) and sidereal day (58.65 Earth days) are in a 3:2 ratio, in a spin–orbit resonance. Consequently, one solar day (sunrise to sunrise) on Mercury lasts for around 176 Earth days: twice the planet's sidereal year. This means that one side of Mercury will remain in sunlight for one Mercurian year of 88 Earth days; while during the next orbit, that side will be in darkness all the time until the next sunrise after another 88 Earth days. Above the planet's surface is an extremely tenuous exosphere and a faint magnetic field just strong enough to deflect solar winds. Combined with its high orbital eccentricity, the planet's surface has widely varying sunlight intensity and temperature, with the equatorial regions ranging from −170 °C (−270 °F) at night to 420 °C (790 °F) during sunlight. Due to its very small axial tilt, the planet's poles are permanently shadowed. This strongly suggests that water ice could be present in the craters.

The dwarf planet Haumea has two known moons, Hiʻiaka and Namaka, named after Hawaiian goddesses. These small moons were discovered in 2005, from observations of Haumea made at the large telescopes of the W. M. Keck Observatory in Hawaii.

Haumea's moons are unusual in a number of ways. They are thought to be part of its extended collisional family, which formed billions of years ago from icy debris after a large impact disrupted Haumea's ice mantle. Hiʻiaka, the larger, outermost moon, has large amounts of pure water ice on its surface, which is rare among Kuiper belt objects. Namaka, about one tenth the mass, has an orbit with surprising dynamics: it is unusually eccentric and appears to be greatly influenced by both the elongated shape of Haumea and by the larger satellite.

Gonggong (minor-planet designation: 225088 Gonggong) is a dwarf planet and a member of the scattered disc beyond Neptune. It has a highly eccentric and inclined orbit during which it ranges from 33–101 astronomical units (4.9–15.1 billion kilometers; 3.1–9.4 billion miles) from the Sun. As of 2019, its distance from the Sun is 88 AU (13.2×10^ km; 8.2×10^ mi), and it is the sixth-farthest known Solar System object. According to the Deep Ecliptic Survey, Gonggong is in a 3:10 orbital resonance with Neptune, in which it completes three orbits around the Sun for every ten orbits completed by Neptune. Gonggong was discovered in July 2007 by American astronomers Megan Schwamb, Michael Brown, and David Rabinowitz at the Palomar Observatory, and the discovery was announced in January 2009.

At approximately 1,230 km (760 mi) in diameter, Gonggong is similar in size to Pluto's moon Charon, making it the fifth-largest known trans-Neptunian object (apart possibly from Charon). It may be sufficiently massive to be in hydrostatic equilibrium and therefore a dwarf planet. Gonggong's large mass makes retention of a tenuous atmosphere of methane just possible, though such an atmosphere would slowly escape into space. The object is named after Gònggōng, a Chinese water god responsible for chaos, floods and the tilt of the Earth. The name was chosen by its discoverers in 2019, when they hosted an online poll for the general public to help choose a name for the object, and the name Gonggong won.

Eris (minor-planet designation: 136199 Eris) is the most massive and second-largest known dwarf planet in the Solar System. It is a trans-Neptunian object (TNO) in the scattered disk and has a high-eccentricity orbit. Eris was discovered in January 2005 by a Palomar Observatory–based team led by Mike Brown and verified later that year. It was named in September 2006 after the Greco–Roman goddess of strife and discord. Eris is the ninth-most massive known object orbiting the Sun and the sixteenth-most massive in the Solar System (counting moons). It is also the largest known object in the Solar System that has not been visited by a spacecraft. Eris has been measured at 2,326 ± 12 kilometres (1,445 ± 7 mi) in diameter; its mass is 0.28% that of the Earth and 27% greater than that of Pluto, although Pluto is slightly larger by volume. Both Eris and Pluto have a surface area that is comparable to that of Russia or South America.

Eris has one large known moon, Dysnomia. In February 2016, Eris's distance from the Sun was 96.3 AU (14.41 billion km; 8.95 billion mi), more than three times that of Neptune or Pluto. With the exception of long-period comets, Eris and Dysnomia were the most distant known natural objects in the Solar System until the discovery of 2018 AG37 and 2018 VG18 in 2018.

The scattered disc (or scattered disk) is a distant circumstellar disc in the Solar System that is sparsely populated by icy small Solar System bodies, which are a subset of the broader family of trans-Neptunian objects. The scattered-disc objects (SDOs) have orbital eccentricities ranging as high as 0.8, inclinations as high as 40°, and perihelia greater than 30 astronomical units (4.5×10 km; 2.8×10 mi). These extreme orbits are thought to be the result of gravitational "scattering" by the gas giants, and the objects continue to be subject to perturbation by the planet Neptune.

Although the closest scattered-disc objects approach the Sun at about 30–35 AU, their orbits can extend well beyond 100 AU. This makes scattered disc objects among the coldest and most distant known objects in the Solar System. The innermost portion of the scattered disc overlaps with a torus-shaped region of orbiting objects traditionally called the Kuiper belt, but its outer limits reach much farther away from the Sun and farther above and below the ecliptic than the Kuiper belt proper.