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**a - the semi-major axis**

**angular momentum vector - h
- the resulting cross product of the postion and velocity vectors which
is a constant. h is normal to the orbit
plane. The angle between the primary body's polar axis and h
is the inclination.**

**apogee - the farthest point on an orbit from
the earth**

**apoapsis - the farthest point on an orbit
from the primary body. For earth orbits apoapsis is called apogee.**

**apparent solar day - solar day**

**argument of perigee - ,
-a COE, the angle from the longitude
of the ascending node to perigee for earth orbits**

**argument of periapsis - ,
- the generic term for the COE that is defined as the
angle from the ascending node
to the closest point the orbit makes with the primary body, for earth orbitsthis term is called the argument of perigee**

**ascending node** - **the point on the
orbit where the spacecraft crosses the equatorial plane moving from the
southern hemisphere to the northern hemisphere. 180 degrees from the ascending
node is the descending node.**

**ballistic coefficient - a measure of how
aerodynamic a satellite is for computing drag effects and perturbations.**

**classical orbital elements - six
terms that define an orbit: a , e
, i , ,
, **

**COEs - C lassical
O rbital E lement s**

**conic sections - the family of curves created
by passing planes through two right circular cones. These include circles,
ellipses, parabolas, and hyperbolas. These curves
are the only possible orbits an object can take in a two body problem.**

**coordinate systems - three orthonormal unit vectors which serve as
an origin for completely and uniquely defining a body's position in three
dimensions. see ECI, ECEF, J2000, MEME, METE, MOD, TOD**

**descending node - the point in the orbit
where the spacecraft crosses the equatorial plane
moving from the northern hemisphere to the southern hemisphere. 180 degrees
from the descending node is the ascending node.**

**DU - D istance U nits - the mean equatorial
radius of the primary body, for earth orbits one DU is equal to one earth
radii.**

**e -eccentricity**

**ECI - Earth Center Inertial**

**ECEF - Earth Centered Earth Fixed**

**Earth Centered Inertial - ECI - a coordinate system in which the
primary or I axis is directed towards the First Point of Aries and the
rotational rate of the earth is NOT taken into account.**

**Earth Centered Earth Fixed - ECEF - a coordinate system in which
the primary or I axis is tied to the Prime Meridian and
the rotational rate of the earth IS taken into account.**

**earth radii - ER - the mean distance from the
center of the earth to the surface - 6378.137 kilometers or 1 **

**eccentric anomaly** - **the angle between
two points on an ellipse measured from a focus**.

**eccentricity - a measure of how circular
(or elliptical) an orbit is**

**ecliptic - the orbital plane of the earth about the sun. The ecliptic
does not lie in the same plane as the equator. The equatorial plane is
inclined to the ecliptic by 23.5 degrees - the earth's axial tilt. The
orbits of the planets and moon are within a few degrees of the ecliptic
plane.**

**ellipse - the conic section
defined by passing a plane through a right circular cylinder at angle between
0 and 90 degrees. Most orbits to a first order approximation are ellipses.**

**ER - earth radii **

**equatorial plane - the projection of the
earth's equator out into space. The equatorial plane is inclined 23.5 degrees
to the ecliptic.**

**First Point of Aries - -
arbitrary direction in which the inertial I axis points for the Solar System.2000 years ago on the vernal equinox the sun rose
in the constellation Aries. The zodical sign for Aries is
and for historical reasons the symbol of the Ram continues to be used to
define the principle axis in celestial coordinate systems.**

**flight path angle - -
the angle between the velocity vector and the local horizon. In aeronautics
this is called the angle of attack.**

**GEO - geostationary or geosynchronous orbits**

**geostationary - an orbit whose orbit
lies in the equatorial plane (inclination
= 0) and whose period is equal to the rotational
rate of the earth. Geostationary satellites' groundtracks
are points.**

**geosynchronous - an orbit whose period
is equal to the rotational rate of the earth
but is inclined to the equatorial plane. Geosynchronous satellites' groundtracks
are figure eight shaped. **

**Greenwich Meridian - the Prime
Meridian**

*h - *the angular
momentum vector

**HEO - Highly Eliptical Orbit**

**i - inclination**

**inclination - the angle between the orbit
plane and the equator of the primary body, for earth orbits the inclination
is equal to the highest lattitude that the spacecraft's ground
track crosses.**

**Julian Date - the basis of time for astrodynamics.
The number of days since 12:00 on 1 January 4713 B.C. The Julian Day for
1 January 2000 at noon is 2451545.0. Julian Days are measured from noon
to noon so that astronomers can have all of their observations during the
same day.**

**Kepler's Laws of
Planetary Motion - named for Johannes Kepler who determined the following
three laws of two body motion:**

**LEO - Low Earth Orbit**

**longitude of the ascending
node - , - the angle between the
Greenwich Meridian and the ascending
node. LAN realtes the orbits orientation to the Prime Meridian. RAAN
relates the orbits orientation relative to the stars.**

**M - mean anomaly**

**MEO - Medium Earth Orbit**

**mean anomaly - an expression containing the eccentric
anomaly, E, and used to determine time of flight calculations based on
Kepler's Second Law. It is also the angle between
perigee and a point on a circle circumscribing the ellipse (orbit). Mean
anomaly is equal to E and at
periapsis (all equal 0 degrees) and **

**at apoapsis (all equal 180 degrees). **

**Molniya - HEO**

**nadir - the point directly below in the direction
of the center of the earth. For spacecraft the arbitrarily defined 'down'
direction. This is usually defined as the direction pointing toward the
center of the primary body. Opposite of nadir is zenith.**

**orbit - the path traced out by a body moving
about a primary body. Keplerian orbits follow conic
sections.**

**orbit plane - the plane defined by the motion
of an object about a primary body. The position
and velocity vectors lie withing the orbital plane while the angular momentum
vector is a right angles to the orbital plane.**

**periapsis - the closest point in an orbit
to the primary body. For earth orbits periapsis is known as perigee.**

**perigee - the closest point on an orbit to
the earth.**

**period - the time required for one body to orbit
the primary body. The period is related to the semi-major axis as defined
by Kepler's Third Law.**

**primary body - the object which is the gravitational
center of the system. The sun is the primary body for the Solar System
and the earth is the primary body for almost all satellite operaitons.**

**Prime Meridian - the line of longitude that runs
through Greenwich, England and from which longitude is **

**measured east or west. 180 degrees from the Prime Meridian lies the
International Date Line.**

**quaternions - a mathematics that allows for the rotation of vectors
in three dimensions without the problems of singularities associated with
Euler Angles.**

**RAAN - Right Ascension of the Ascending Node**

**radius - the distance from the center of a circle
or sphere to its edge. The distance from the center of the earth to the
surface is 1 DU.**

**Right Ascension of the Ascending Node - the angle between the ascending
node and the First Point of Aries. RAAN relates the orbits orientation
relative to the stars. LAN realtes the orbits orientation to the Prime
Meridian.**

**rotational rate - the time it takes for
a body to rotate once about a particular axis. The rotational rate for
the earth is 1 solar day.**

**selen - a prefix meaning "of or pertaining to the Moon"**

**semi-major axis - one half the distance
across the longest line through an ellipse, for
circular orbits the semi-major axis is the radius
of the circle, the semimajor axis is usually measured in km or DU**

**solar day (apparent) - the time between two successive
overhead transits of the sun for a given line of longitude. A solar day
is shorter than a sidereal day.**

**TOD - True of Date**

**true anomaly - ,
- the angular distance from periapsis to the actual
position of the satellite in its orbit.**

**is
equal to E and M at periapsis (all equal 0 degrees) and at apoapsis (all
equal 180 degrees). **

**True of Date - TOD - the most accurate coordinate system used
to define a body's position relative to the center of the Earth. This coordinate
system incorporates the earth's rotation, UTC corrections, precession,
nutation, and polar wander.**

**two body problem - the simplest orbit which includes the primary
body and the body in question. NO other forces are included
in the calculation. Kepler's Laws are based on solving for the two body
problem. These solutions are conic sections.**

**vernal equinox - the first day of spring. The
day in which the sun appears to move from the southern hemisphere to the
northern hemisphere. The apparent ascending node
of the sun as viewed from earth. This occurs around 21 March. On this day
the earth is aligned with .**

**WGS 84 - World Geodetic
Survey**

**World Geodetic Survey - the survey conducted
by the Defense Mapping Agency in 1984 that includes a standardized set
of constants and a potential model for the earth to degree and order 41.**

**zenith - the point directly overhead. For spacecraft
this arbitrarily defined as 'up' and away from the primary body. The opposite
of zenith is nadir.**