Main Content

Satellite Communications
Toolbox
`satelliteScenario`

object provides the ability to model and visualize satellites in orbit, compute access with
ground stations, and visualize and analyze communication links. This topic provides an
overview of the technical terms frequently encountered in scenario visualization.

A geodetic system uses coordinates
(*lat*,*lon*,*h*) to represent
position relative to a reference ellipsoid. All geodetic coordinates in satellite scenario
use the WGS 84 as the reference ellipsoid. The coordinate origin of WGS 84 is located at
the center of mass of the Earth.

*lat*is the latitude, which originates at the equator. More specifically, the latitude of a point is the angle a normal to the ellipsoid at that point makes with the equatorial plane, which contains the center and equator of the ellipsoid. An angle of latitude is in the range [–90°, 90°]. Positive latitudes correspond to north and negative latitudes correspond to south.*lon*is the longitude, which originates at the prime meridian. More specifically, the longitude of a point is the angle that a plane containing the ellipsoid center and the meridian containing that point makes with the plane containing the ellipsoid center and prime meridian. Positive longitudes are measured in a counterclockwise direction from a vantage point above the North Pole. Typically, longitude is in the range [–180°, 180°] or [0°, 360°].*h*is the ellipsoidal height, which is measured along a normal of the reference spheroid.

An Earth-centered Earth-fixed (ECEF) system uses Cartesian coordinates
(*X*,*Y*,*Z*) to represent
position relative to the center of the reference ellipsoid. The distance between the
center of the ellipsoid and the center of the Earth depends on the reference ellipsoid.
Satellite scenario uses the WGS 84 reference ellipsoid, whose center coincides with the
center of mass of the Earth.

The positive

*X*-axis intersects the surface of the ellipsoid at 0° latitude and 0° longitude, where the equator meets the prime meridian.The positive

*Y*-axis intersects the surface of the ellipsoid at 0° latitude and 90° longitude.The positive

*Z*-axis intersects the surface of the ellipsoid at 90° latitude.

^{[1]}

To describe a point in space, you need a frame of reference that does not rotate with
respect to the stars. The *Geocentric Celestial Reference Frame
(GCRF)*, with the origin at the center of the Earth and orthogonal vectors
**I**, **J**, and **K**, is used as the frame of reference while adding `Satellite`

objects to a `satelliteScenario`

object. The fundamental plane is the **IJ** - plane, which is closely aligned with the equator with a small offset
that changes over time because of precession and nutation of the rotation axis of the
Earth. When orbital elements are used to add satellites to the satellite scenario, they
are assumed to be defined in the geocentric celestial reference frame.

When referring to the position, velocity, acceleration, orientation, and angular
velocity, you must always mention the coordinate system in which these quantities are
expressed. Global systems such as GCRF and geodetic systems describe the position of an
object using a triplet of coordinates. Local systems such as NED and *Azimuth
Elevation Range* (AER) systems require two triplets of coordinates: one
triplet describes the location of the origin, and the other triplet describes the location
of the object with respect to the origin.

A NED system uses Cartesian coordinates
(*xNorth*,*yEast*,*zDown*) to
represent position relative to a local origin. The local origin is described by geodetic
coordinates (*lat0*,*lon0*,*h0*).
Typically, the local origin of an NED system is above the surface of the Earth.

The positive

*xNorth*-axis points north along the meridian of longitude containing*lon0*.The positive

*yEast*-axis points east along the parallel of latitude containing*lat0*.The positive

*zDown*-axis points south along the ellipsoid normal.

An NED coordinate system is commonly used to specify location relative to a moving satellite. In this case, the coordinates are not fixed to the frame of the satellite, but to the point on the surface of the WGS 84 ellipsoid corresponding to the latitude and longitude of the satellite.

Three lines run through a satellite and intersect at right angles at the center of mass of the satellite. These axes are fixed with respect to the satellite, and are used to define the orientation of the satellite with respect to the NED frame. The orientation is defined by rotations in the following sequence:

Rotation about the

*yaw*axis by the yaw angle.Rotation about the

*pitch*axis by the pitch angle.Rotation about the

*roll*axis by the roll angle.

The yaw, pitch, and roll angles have positive clockwise directions when looking in the positive direction of the axes. Unless otherwise specified, by default the Satellite Communications Toolbox uses the yaw-pitch-roll rotation order for these angles.

An AER system uses spherical coordinates
(*az*,*elev*,*range*) to
represent position relative to a local origin. The local origin is described by geodetic
coordinates (*lat0*,*lon0*,*h0*).
Azimuth, elevation, and slant ranges are dependent on a local Cartesian system (for
example, an NED system) with origin centered at the center of mass of the
satellite.

*az*is the azimuth, which is the clockwise angle in the (*xEast*)(*yNorth*) - plane from the positive*yNorth*-axis to the projection of the object into the plane.*elev*is the elevation, which is the angle from the (*xEast*)(*yNorth*) - plane to the object.*range*is the slant range, which is the Euclidean distance between the object and the local origin.

Orbital elements are parameters required to uniquely identify a specific orbit. Uniquely
defining an orbit and the position of a satellite within satellite orbit requires at least
six parameters. Three of the parameters describe what the orbital plane looks like and the
position of the satellite in the ellipse. The other three parameters describe how that plane
is oriented in the celestial inertial reference frame and the location of the satellite in
that plane. These six parameters are called the *Keplerian elements* or
*orbital elements*.

In this diagram, the *orbital plane* (yellow) intersects a
*reference plane* (gray). For Earth-orbiting satellites, the
reference plane is usually the IJ - plane of the GCRF.

These two elements define the shape and size of the ellipse:

Eccentricity (e) — Shape of the ellipse, describing how elongated it is compared to a circle.

Semimajor axis (a) — Sum of the

*periapsis*and*apoapsis*distances divided by two. Periapsis is the point at which an orbiting object is closest to the center of mass of the body it is orbiting. Apoapsis is the point at which an orbiting object is farthest away from the center of mass of the body it is orbiting. For classic two-body orbits, the semimajor axis is the distance between the centers of the bodies.

These two elements define the orientation of the orbital plane in which the ellipse is embedded:

Inclination (i) — Vertical tilt of the ellipse with respect to the reference plane, measured at the

*ascending node*. The ascending node is the location where the orbit passes upward through the reference plane (the green angle*i*in the diagram). The tilt angle is measured perpendicular to the line of intersection between orbital plane and the reference plane. Any three points on an ellipse defines the ellipse orbital plane.Starting with an equatorial orbit, the orbital plane can be tilted up. The angle it is tilted up from the equator is referred to as the

*inclination angle*,*i*, in the range [0,180]. Because the center of the Earth must always be in the orbital plane, the point in the orbit where the satellite passes the equator on its way up north-bound through the orbit is the ascending node, and the point where the satellite passes the equator on its way down south-bound is the*descending node*. Drawing a line through these two points on the equator defines the*line of nodes*.Right ascension of ascending node (Ω) — Horizontal orientation of the ascending node of the ellipse (where the orbit passes upward through the reference plane) with respect to I-axis of the reference frame.

The rotation of the right ascension of the ascending node (RAAN) can be any number between 0 and 360°.

The remaining two elements are:

Argument of periapsis (ω) — Orientation of the ellipse in the orbital plane, as an angle measured from the ascending node to the periapsis in the range [0,360).

True Anomaly (v) — Position of the orbiting body along the ellipse at a specific time. The position of the satellite on the path is measured counterclockwise from the periapsis and is called the

*true anomaly*, ν, in the range [0,360).

The Satellite Communications
Toolbox
`satellite`

function accepts a TLE file as a possible input to initialize the
satellite. To download TLE files, see the Space track website.

A TLE set is a data format encoding a list of orbital elements of an Earth orbiting
object for a given point in time, the *epoch*. Orbital
element parameters can be encoded as text in a variety of formats. The most common format is
the NASA/NORAD TLE format. In this format, each satellite has three lines: the first line
contains the name of the satellite, and the next two lines are the standard two lines of
elements.

Data for each satellite consists of three lines, as this example shows.

Satellite 1 1 25544U 98067A 04236.56031392 .00020137 00000-0 16538-3 0 9993 2 25544 51.6335 344.7760 0007976 126.2523 325.9359 15.70406856328906

Line 1 is a eleven-character satellite name.

Line 2 and 3 are the standard TLE set format identical to that used by NORAD and NASA.

**Column****Description**Example 1 Line Number

`1`

3 — 7 Satellite Number

`25544`

8 Elset Classification

`U`

10 — 17 International Designator

`98067A`

19 — 32 Element Set Epoch (UTC)

`04236.56031392`

34 — 43 First derivative of the Mean Motion with respect to time

`.00020137`

45 — 52 Second derivative of the Mean Motion with respect to Time (decimal point assumed)

`00000-0`

54 — 61 BSTAR Drag Term.

`16538-3`

63 Element set type

`0`

65 — 68 Element number

`999`

69 Check Sum (Modulo 10)

`3`

This table describes the columns in Line 3.

**Column****Description**Examples 1 Line Number of Element Data

`2`

3 — 7 Satellite Number

`25544`

9 — 16 Inclination [Degrees]

`51.6335`

18 — 25 Right Ascension of the Ascending Node [Degrees]

`344.7760`

27 — 33 Eccentricity (Leading decimal point assumed)

`0007976`

35 — 42 Argument of Perigee [Degrees]

`126.2523`

44 — 51 Mean Anomaly [Degrees]

`325.9359`

53 — 63 Mean Motion [Revs per day]

`15.70406856`

64 — 68 Revolution number at epoch [Revs]

`32890`

69 Check Sum (Modulo 10)

`6`

Depending on the application and object orbit, the data derived from TLEs older than 30 days can become unreliable. Orbital positions can be calculated from TLEs by using the SGP4 and SDP4 algorithms.

[1] “HSF - Orbital Elements.” Accessed November 30, 2020. https://spaceflight.nasa.gov/realdata/elements/graphs.html.

[2] “CelesTrak: ‘FAQs: Two-Line Element Set Format,” March 26, 2016. https://web.archive.org/web/20160326061740/http://celestrak.com/columns/v04n03/.

- Multi-Hop Satellite Communications Link Between Two Ground Stations
- Satellite Constellation Access to a Ground Station
- Comparison of Orbit Propagators
- Modeling Satellite Constellations Using Ephemeris Data
- Estimate GNSS Receiver Position with Simulated Satellite Constellations
- Model, Visualize, and Analyze Satellite Scenario
- Satellite Scenario Basics

^{[1]} Alignment of boundaries and region labels are a presentation of the feature provided by the
data vendors and do not imply endorsement by MathWorks^{®}.