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where is the orbital inclination, is the eccentricity, is mean motion in degrees per day, is the perturbing factor, is the radius of the Earth, is the semimajor axis, and ˙ is in degrees per day. To avoid this expenditure of fuel, the Tundra orbit uses an inclination of 63.4°, for which the factor ( 4 − 5 sin 2 i ) {\displaystyle (4-5 ...
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets, satellites, and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal gravitation .
Every object in a 2-body ballistic trajectory has a constant specific orbital energy equal to the sum of its specific kinetic and specific potential energy: = = =, where = is the standard gravitational parameter of the massive body with mass , and is the radial distance from its center. As an object in an escape trajectory moves outward, its ...
A highly elliptical orbit (HEO) is an elliptic orbit with high eccentricity, usually referring to one around Earth.Examples of inclined HEO orbits include Molniya orbits, named after the Molniya Soviet communication satellites which used them, and Tundra orbits.
The argument of periapsis (also called argument of perifocus or argument of pericenter), symbolized as ω , is one of the orbital elements of an orbiting body. Parametrically, ω is the angle from the body's ascending node to its periapsis , measured in the direction of motion.
The longitude of the ascending node, also known as the right ascension of the ascending node, is one of the orbital elements used to specify the orbit of an object in space. Denoted with the symbol Ω , it is the angle from a specified reference direction, called the origin of longitude , to the direction of the ascending node (☊), as ...
Final v s, θ s and r must match the requirements of the target orbit as determined by orbital mechanics (see Orbital flight, above), where final v s is usually the required periapsis (or circular) velocity, and final θ s is 90 degrees. A powered descent analysis would use the same procedure, with reverse boundary conditions.
The ITN is based around a series of orbital paths predicted by chaos theory and the restricted three-body problem leading to and from the orbits around the Lagrange points – points in space where the gravity between various bodies balances with the centrifugal force of an object there.