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.
The main window provides a interface for defining satellite orbits and editing the properties of previously defined orbits.
Element name Description
Perigee Altitude Default Value: 1000Km. A suitable perigee altitude should be chosen so that the orbit does not intercept with the earth.
Apogee Altitude Default Value: 10000Km. Apogee altitude should be greater of equal to perigee altitude.
Mean Anomaly Default Value: 0 degree. Mean Anomaly should be from 0 to 360 degrees.
Inclination Default Value: 0 degree. Inclination should be from 0 to 180 degrees.
Argument of Perigee Default Value: 0 degree. Argument of Perigee should be from 0 to 360 degrees.
RAAN Default Value: 0 degree. RAAN should be from 0 to 360 degrees.
Epoch Data name Description
Start Day Default Value: current day. Start Day should be a number from 1 to 31.
Start Month Default Value: current month. Start Month should be a number from 1 to 12.
Start Year Default Value: current month. Start Year should be a number from 1801 to 2099.
Step Size Default Value: 2 minutes. Step Size should be greater than zero minute.
Propagate Duration Default Value: 1 day. Propagate Duration should be greater than zero day.
Button name Description
Animation Launch the animation window.
Help Display the help file.
Quit Quit the program and Matlab.
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 Press Description
mouse button down and move rotate 3D view.
s zoom out in three dimensions.
S zoom in three dimensions.
x pan the data to negative x direction.
y pan the data to negative y direction.
z pan the data to negative z direction.
X pan the data to positive x direction.
Y pan the data to positive y direction.
Z pan the data to positive z direction.
t or T top view.
f or F front view.
l or L left view.
i or I isometric view.
r or R replay the animation.
v or V toggle the ECI frame.
c or C close the animation window.
h or H toggle 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 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:
Start Day The satellite's start date that we are interested.
Start Month The satellite's start month that we are interested.
Start Year The satellite's start year that we are interested.
Step Size The interval between calculated output points.
Propagate Duration The 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.
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.
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 (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.
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.