Satellite Orbit Design
Mechanical Engineering Dept.
New Mexico State University


Content


About the Program

Satellite Orbit Design is a program to demonstrate how the orbit of the satellite is described using the classical (Keplerian) coordinate. The program is implemented in Matlab 6.5. So, to run the program, Matlab 6.5 must be installed in the computer.


Run the Program

To run the program, just double click the MS-DOS batch file named "run.bat", which will launch Matlab and the program itself automatically.


Main Window

The main window provides a interface for defining satellite orbits and editing the properties of previously defined orbits.

Orbital Elements

Element nameDescription
Perigee AltitudeDefault Value: 1000Km. A suitable perigee altitude should be chosen so that the orbit does not intercept with the earth.
Apogee AltitudeDefault Value: 10000Km. Apogee altitude should be greater of equal to perigee altitude.
Mean AnomalyDefault Value: 0 degree. Mean Anomaly should be from 0 to 360 degrees.
InclinationDefault Value: 0 degree. Inclination should be from 0 to 180 degrees.
Argument of PerigeeDefault Value: 0 degree. Argument of Perigee should be from 0 to 360 degrees.
RAANDefault Value: 0 degree. RAAN should be from 0 to 360 degrees.

Orbit Epoch

Epoch Data nameDescription
Start DayDefault Value: current day. Start Day should be a number from 1 to 31.
Start MonthDefault Value: current month. Start Month should be a number from 1 to 12.
Start YearDefault Value: current month. Start Year should be a number from 1801 to 2099.
Step SizeDefault Value: 2 minutes. Step Size should be greater than zero minute.
Propagate DurationDefault Value: 1 day. Propagate Duration should be greater than zero day.

Buttons

Button nameDescription
AnimationLaunch the animation window.
HelpDisplay the help file.
QuitQuit the program and Matlab.


Animation Window

The animation window provides a interface for animating the movement of the satellite in its orbit defined by the parameters in the main window.

Keys to control the animation
Key PressDescription
mouse button down and moverotate 3D view.
szoom out in three dimensions.
Szoom in three dimensions.
xpan the data to negative x direction.
ypan the data to negative y direction.
zpan the data to negative z direction.
Xpan the data to positive x direction.
Ypan the data to positive y direction.
Zpan the data to positive z direction.
t or Ttop view.
f or Ffront view.
l or Lleft view.
i or Iisometric view.
r or Rreplay the animation.
v or Vtoggle the ECI frame.
c or Cclose the animation window.
h or Htoggle the help message.


Satellite Orbit Description

Orbit epoch and orbital elements are used to accurately describe the orbit of a satellite in space and time. Orbit epoch is the time at which the established orbital elements are true. Many different types of orbital elements may be used to describe the shape and size of an orbit and the location of the satellite. There is a standard type of orbital elements called the Keplerian elements that are most used and most useful. The Keplerian orbital elements define an orbital ellipse around the Earth, orient it three dimensionally, and place the satellite along the ellipse in time. In Keplerian mechanics, all orbits are ellipses.

Orbit Epoch

Orbit epoch is the time at which the established orbital elements are true. The first thing one need to define an orbit is orbit epoch at which the Keplerian Elements were defined. In this program, orbit epoch is defined as the following:

ParameterDescription
Start DayThe satellite's start date that we are interested.
Start MonthThe satellite's start month that we are interested.
Start YearThe satellite's start year that we are interested.
Step SizeThe interval between calculated output points.
Propagate DurationThe satellite's time period that we are interested.

Perigee Altitude & Apogee Altitude

Since an orbit usually has an elliptical shape, the satellite will be closer to the Earth at one point than at another. The point where the satellite is the closest to the Earth is called the perigee. The point where the satellite is the furthest from the Earth is called the apogee. Perigee altitude and apogee altitude are measured from the "surface" of the Earth to the points of minimum and maximum radius in the orbit respectively. The surface of the Earth is modeled as a sphere whose radius equals the equatorial radius of the Earth.

Mean Anomaly

The mean anomaly tells you where the satellite is in its orbital path. It is defined as the angle from the eccentricity vector to a position vector where the satellite would be if it were always moving at its average angular rate. The mean anomaly ranges from 0 to 360 degrees. The mean anomaly is referenced to the perigee. If the satellite were at the perigee, the mean anomaly would be 0. In the following figure, the mean anomaly is the angle z-c-y, where the point y is defined such that the circular sector area z-c-y is equal to the elliptic sector area z-s-p, scaled up by the ratio of the major to minor axes of the ellipse.

Inclination

The orbit ellipse lies in a plane, and this plane forms an angle with the plane of the equator. This angle is called the inclination. Think of it as the tilt between the orbit and the equator. The inclination ranges from 0 to 180 degrees. Inclinations of near 0 degrees are called equatorial orbits, and those near 90 degrees are called polar orbits. By convention, orbits that go the same way as the Earth rotates (counter-clockwise from above) have inclinations of 0 to 90 degrees. Satellites that orbit retrograde, opposite to the rotation of the Earth, have inclinations great than 90 degrees. For example, if the orbit went exactly around the equator from left to right, then the inclination would be 0. And a satellite with an inclination of 180 degrees is in an equatorial orbit going east to west.

Arguement of Perigee

Now that the orbital plane is oriented in space, then the position of the orbital ellipse in the orbital plane must be defined. This parameter is called the argument of perigee and is the angle between the major axis and line of nodes. The perigee is the point on the orbit that satellite is closest to the Earth. On the opposite side of the orbit, the satellite is at its farthest point from the Earth called the apogee. The line through the apogee and perigee is called the major axis; it is the long axis of the ellipse. The angle between the major axis and the line of nodes is the argument of perigee. This is measured in the plane of the orbit. It ranges from 0 to 360 degrees, and is 0 degrees when the perigee is at the ascending node and 180 degrees when the satellite is farthest from the Earth when it rises up over the equator.

RAAN

RAAN (Right Ascension of Ascending Node) is probably one of the most difficult of the elements to describe. The intersection of the orbit plane and the equatorial plane is called the line of nodes. The point where the satellite's orbit crosses the equator going south to north is called the ascending node. The one on the opposite side of the Earth, where the satellite passes into the Southern Hemisphere is called the descending node. Now since the Earth rotates, you need to specify a fixed object in space. Right ascension is an angle measured in the equatorial plane from a fixed point in space, called the point of Ares (which is also the same location as the vernal equinox). The angle, from the center of the Earth, between Aries and the ascending node is called the right ascension of ascending node.


Example

Choosing different values for the orbital elements, you will get different orbits. The two orbital elements, apogee altitude and perigee altitude, describe the size and shape of the orbit. The three elements, inclination, argument of the perigee and RAAN describe the orientation of the orbit. And the orbital element, mean anomaly, describes the location of the satellite.

For example:

  • Let the perigee altitude equals 1000 km and the apogee altitude equals 1000 km, you will get circular orbit.
  • Let the perigee altitude equals 1000 km and the apogee altitude equals 10000 km, you will get elliptic orbit.
  • Let the inclination equals 30 deg, you will get an orbit, whose orbital plane inclines 30 deg with respect to the equatorial plane of the earth.
  • Let the mean anomaly equals 180 deg, the satellite will starts from the apogee for the animation.