# Celestial mechanics and orbital period

Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. It is a core discipline within space mission design and control. Time of Periapsis Passage, T Longitude of Ascending Node, An orbiting satellite follows an oval shaped path known as an ellipse with the body being orbited, called the primary, located at one of two points called foci. An ellipse is defined to be a curve with the following property: The longest and shortest lines that can be drawn through the center of an ellipse are called the major axis and minor axis, respectively.

The semi-major axis is one-half of the major axis and represents a satellite's mean distance from its primary. Eccentricity is the distance between the foci divided by the length of the major axis and is a number between zero and one.

An eccentricity of zero indicates a circle. Inclination is the angular distance between a satellite's orbital plane and the equator of its primary or the ecliptic plane in the case of heliocentric, or sun centered, orbits. An inclination of zero degrees indicates an orbit about the primary's equator in the same direction as the primary's rotation, a direction called prograde or direct.

An inclination of 90 degrees indicates a polar orbit. An inclination of degrees indicates a retrograde equatorial orbit. A retrograde orbit is one in which a satellite moves in a direction opposite to the rotation of its primary.

Periapsis is the point in an orbit closest to the primary. The opposite of periapsis, the farthest point in an orbit, is called apoapsis. Periapsis and apoapsis are usually modified to apply to the body being orbited, such as perihelion and aphelion for the Sun, perigee and apogee for Earth, perijove and apojove for Jupiter, perilune and apolune for the Moon, etc.

The argument of periapsis is the angular distance between the ascending node and the point of periapsis see Figure 4. The time of periapsis passage is the time in which a satellite moves through its point of periapsis.

Nodes are the points where an orbit crosses a plane, such as a satellite crossing the Earth's equatorial plane.

Orbital period topic. The orbital period is the time a given astronomical object takes to complete one orbit around another object, and applies in astronomy usually to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars. Celestial Mechanics and Orbital Period. 4 April Moon; AE Problems Set No. 1 1. The orbital period of an Earth satellite is min. Find the apogee altitude if the perigee altitude is km. 2. Find the orbital period of a satellite if the perigee and apogee altitudes are km and km, respectively. Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and Newton's law of universal gravitation.

If the satellite crosses the plane going from south to north, the node is the ascending node; if moving from north to south, it is the descending node.

The longitude of the ascending node is the node's celestial longitude. Celestial longitude is analogous to longitude on Earth and is measured in degrees counter-clockwise from zero with zero longitude being in the direction of the vernal equinox.

In general, three observations of an object in orbit are required to calculate the six orbital elements. Two other quantities often used to describe orbits are period and true anomaly. Period, P, is the length of time required for a satellite to complete one orbit.

## Celestial mechanics - Scholarpedia

True anomaly,is the angular distance of a point in an orbit past the point of periapsis, measured in degrees. Types Of Orbits For a spacecraft to achieve Earth orbit, it must be launched to an elevation above the Earth's atmosphere and accelerated to orbital velocity. The most energy efficient orbit, that is one that requires the least amount of propellant, is a direct low inclination orbit.

To achieve such an orbit, a spacecraft is launched in an eastward direction from a site near the Earth's equator. The advantage being that the rotational speed of the Earth contributes to the spacecraft's final orbital speed. At the United States' launch site in Cape Canaveral Launching a spacecraft in a direction other than east, or from a site far from the equator, results in an orbit of higher inclination.

High inclination orbits are less able to take advantage of the initial speed provided by the Earth's rotation, thus the launch vehicle must provide a greater part, or all, of the energy required to attain orbital velocity. Although high inclination orbits are less energy efficient, they do have advantages over equatorial orbits for certain applications.

Below we describe several types of orbits and the advantages of each: Geosynchronous orbits GEO are circular orbits around the Earth having a period of 24 hours. A geosynchronous orbit with an inclination of zero degrees is called a geostationary orbit.

A spacecraft in a geostationary orbit appears to hang motionless above one position on the Earth's equator. For this reason, they are ideal for some types of communication and meteorological satellites. A spacecraft in an inclined geosynchronous orbit will appear to follow a regular figure-8 pattern in the sky once every orbit.

To attain geosynchronous orbit, a spacecraft is first launched into an elliptical orbit with an apogee of 35, km 22, miles called a geosynchronous transfer orbit GTO.mental concepts of orbital mechanics and provides the necessary foundation to enable have an orbital period equal to the earth’s rotational period (approximately 24 hours).

This allows a sat- moon and sun revolving around the earth while the rest of the celestial bodies re-volved around the sun. German astronomer Johannes Kepler. Celestial mechanics. Celestial mechanics is a branch of astronomy that studies the movement of bodies in outer space. Using a mathematical theory, it explains the observed motion of the planets and allows us to predict their future movements. Orbital mechanics, also called flight mechanics, is the study of the motions of artificial satellites and space vehicles moving under the influence of forces such as gravity, atmospheric drag, thrust, etc.

Orbital mechanics is a modern offshoot of celestial mechanics which is the study of the motions of natural celestial bodies such as the moon and planets.

mental concepts of orbital mechanics and provides the necessary foundation to enable have an orbital period equal to the earth’s rotational period (approximately 24 hours). This allows a sat- moon and sun revolving around the earth while the rest of the celestial bodies re-volved around the sun.

German astronomer Johannes Kepler. Orbital period topic. The orbital period is the time a given astronomical object takes to complete one orbit around another object, and applies in astronomy usually to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars.

Celestial Mechanics and Orbital Period. 4 April Moon; AE Problems Set No. 1 1. The orbital period of an Earth satellite is min. Find the apogee altitude if the perigee altitude is km. 2. Find the orbital period of a satellite if the perigee and apogee altitudes are km and km, respectively.

Celestial Mechanics and Orbital Period - New York Essays