Elliptic orbit in the context of Escape trajectory

In celestial mechanics, an orbit is the curved trajectory of an object under the influence of an attracting force. Known as an orbital revolution, examples include the trajectory of a planet around a star, a natural satellite around a planet, or an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.

For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital motion.

In astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic (escape orbit or capture orbit), and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the Galaxy.

Heliocentrism (also known as the heliocentric model) is a superseded astronomical model in which Earth and planets orbit around the Sun at the center of the universe. Historically, heliocentrism was opposed to geocentrism, which placed Earth at the center. The notion that Earth revolves around the Sun had been proposed as early as the 3rd century BC by Aristarchus of Samos, who had been influenced by a concept presented by Philolaus of Croton (c. 470 – 385 BC). In the 5th century BC the Greek philosophers Philolaus and Hicetas had the thought on different occasions that Earth was spherical and revolving around a "mystical" central fire, and that this fire regulated the universe. In medieval Europe, however, Aristarchus' heliocentrism attracted little attention—possibly because of the loss of scientific works of the Hellenistic period.

It was not until the 16th century that a mathematical model of a heliocentric system was presented by the Renaissance mathematician, astronomer, and Catholic cleric, Nicolaus Copernicus, leading to the Copernican Revolution. In the following century, Johannes Kepler introduced elliptical orbits, and Galileo Galilei presented supporting observations made using a telescope.

Greenwich Mean Time (GMT) is the local mean time at the Royal Observatory in Greenwich, London, counted from midnight. At different times in the past, it has been calculated in different ways, including being calculated from noon; as a consequence, it cannot be used to specify a particular time unless a context is given. The term "GMT" is also used as one of the names for the time zone UTC+00:00 and, in UK law, is the basis for civil time in the United Kingdom.

Because of Earth's uneven angular velocity in its elliptical orbit and its axial tilt, noon (12:00:00) GMT is rarely the exact moment the Sun crosses the Greenwich Meridian and reaches its highest point in the sky there. This event may occur up to 16 minutes before or after noon GMT, a discrepancy described by the equation of time. Noon GMT is the annual average (the arithmetic mean) moment of this event, which accounts for the word "mean" in "Greenwich Mean Time".

A solar equinox is a moment in time when the Sun appears directly above the equator, rather than to its north or south. On the day of the equinox, the Sun appears to rise directly east and set directly west. This occurs twice each year, around 20 March and 23 September.

An equinox is equivalently defined as the time when the plane of Earth's equator passes through the geometric center of the Sun's disk. This is also the moment when Earth's rotation axis is directly perpendicular to the Sun-Earth line, tilting neither toward nor away from the Sun. In modern times, since the Moon (and to a lesser extent the planets) causes Earth's orbit to vary slightly from a perfect ellipse, the equinox is officially defined by the Sun's more regular ecliptic longitude rather than by its declination. The instants of the equinoxes are currently defined to be when the apparent geocentric longitude of the Sun is 0° and 180°.

In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity (e) equal to 1 and is an unbound orbit that is exactly on the border between elliptical and hyperbolic. When moving away from the source it is called an escape orbit, otherwise a capture orbit. It is also sometimes referred to as a ${\displaystyle C_{3}=0}$ orbit (see Characteristic energy).

Under standard assumptions a body traveling along an escape orbit will coast along a parabolic trajectory to infinity, with velocity relative to the central body tending to zero, and therefore will never return. Parabolic trajectories are minimum-energy escape trajectories, separating positive-energy hyperbolic trajectories from negative-energy elliptic orbits.

In celestial mechanics, apsidal precession (or apsidal advance) is the precession (gradual rotation) of the line connecting the apsides (line of apsides) of an astronomical body's orbit. The apsides are the orbital points farthest (apoapsis) and closest (periapsis) from its primary body. The apsidal precession is the first time derivative of the argument of periapsis, one of the six main orbital elements of an orbit. Apsidal precession is considered positive when the orbit's axis rotates in the same direction as the orbital motion. An apsidal period is the time interval required for an orbit to precess through 360°, which takes the Earth about 112,000 years and the Moon about 8.85 years.

In space mission design, a geostationary transfer orbit (GTO) or geosynchronous transfer orbit is a highly elliptical type of geocentric orbit, usually with a perigee as low as low Earth orbit (LEO) and an apogee as high as geostationary orbit (GEO). Satellites that are destined for geosynchronous orbit (GSO) or GEO are often put into a GTO as an intermediate step for reaching their final orbit. Manufacturers of launch vehicles often advertise the amount of payload the vehicle can put into GTO.

In celestial mechanics, the mean anomaly is the fraction of an elliptical orbit's period that has elapsed since the orbiting body passed periapsis, expressed as an angle which can be used in calculating the position of that body in the classical two-body problem. It is the angular distance from the pericenter which a fictitious body would have if it moved in a circular orbit, with constant speed, in the same orbital period as the actual body in its elliptical orbit.