Satellite Orbit Tutorial
Mechanical Engineering Dept.
New Mexico State University


Content


About the Program

Satellite Orbit Tutorial is a program to demonstrate: The model used in the program is implemented in ADAMS 2005. so, to run the program, ADAMS 2005 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 ADAMS and import all the model files automatically.


Menu of the Program

  • Setting
    • Control Panel...: Setup the parameters of the program, simulate, animate and analyze the simulation results
    • Exit: Exit the program
  • Help
    • Satellite Orbit Tutorial Help: Launch the help of the program
    • About...: Information about the program


Control Panel

Toolbar

Select: clear the select list.
View Fit: fit model extents into the active view.
Dynamic pick: drag diagonal of desired viewing region
Dynamic zoom: hold Shift key to snap to increment.
Dynamic rotate about XY screen axes
Dynamic translate
Render the view
Set the view orientation to Front or back
Set the view orientation to right or left
Set the view orientation to top or bottom
Set the view to isometric
Analysis the simulation result

Parametersr

Initial Radius:Initial radius of the satellite, from 6500000 to 10000000 (Unit: m)
Initial Velocity:Initial velocity of the satellite, from 0 to 20000 (unit: m/s)
Mass of Satellite:Mass of the satellite, from 100 to 1000 (unit: Kg)

Orbit Transfer

1st Thrust:Magnitude of the 1st thrust force, from -100 to 100 (Unit: N)
A negative sign means the thrust force is in the opposite direction of the satellite's velocity
1st Thrust Start:Start time of the 1st thrust force (unit: s)
1st Thrust Stop:Stop time of the 1st thrust force (unit: s)
2nd Thrust:Magnitude of the 2nd thrust force, from -100 to 100 (Unit: N)
A negative sign means the thrust force is in the opposite direction of the satellite's velocity
2nd Thrust Start:Start time of the 2nd thrust force (unit: s)
2nd Thrust Stop:Stop time of the 2nd thrust force (unit: s)

Simulation

Type:The type of the simulation--dynamic
Duration:The duration of the simulation (unit: s)
Step Size:The step size of the simulation (unit: s)
Start:Start a simulation
Pause:Pause a simulation
Reset:Reset a simulation

Animationr

Cycles:Repeat times of the animation
Frame Increment:Increment of frame for the animation
Start Frame:The start frame of the animation
Forward:Start an animation from the beginning frame to the end frame
Reverse:Start an animation from the end frame to the beginning frame
Stop:Stop the animation
Reset:Reset the animation


Why do the satellites go around the earth

The much-used cannon model (see image below) may prove useful to explain why the satellites go around the earth. Imagine a cannon sitting on top of a (very) tall mountain, which fires a cannonball horizontally. The mountain needs to be very tall so that the cannon will be above the earth¡¯s atmosphere so that we can ignore the effects of air friction on the cannon balls. If the cannon fires its ball with a low initial velocity, the trajectory of the ball will curve downwards and hit the ground (A). As the firing velocity is increased, the cannonball will hit the ground further (B) and further (C) away from the cannon, because while the ball is still falling towards the ground, the ground is curving away from it (see first point, above). If the cannonball is fired with sufficient velocity, the ground will curve away from the ball at the same rate as the ball falls - it is now in orbit (D). The orbit may be circular like (D) or if the firing velocity is increased even more, the orbit may become more (E) and more (F) elliptical. This phenomena happens in the satellites of the earth as well. When the satellites get into their orbit, they have a sufficient velocity such that they can go around the earth.


In-plane satellite orbit transfer

At some point during the lifetime of most satellites, we must change one or more of the orbital elements. For example, we may need to transfer from an initial parking orbit to the final mission orbit, rendezvous with or intercept another satellite, or correct the orbital elements to adjust for the perturbations discussed in the previous section. Most frequently, we must change the orbit altitude (in-plane transfer), plane (orbit-plane transfer), or both. To change the orbit of a satellite, we have to change its velocity vector in magnitude or direction. Most propulsion systems operate for only a short time compared to the orbital period, thus we can treat the orbit transfer as an impulsive change in velocity while the position remains fixed. For this reason, any orbit transfer of the satellite must occur at a point where the old orbit intersects the new orbit. If the orbits do not intersect, we must use an intermediate orbit that intersects both. In this case, the total transfer will require at least two propulsive burns. Orbit-plane transfer is relatively complicated. Now We only focus on in-plane transfer, i.e. changing the orbit altitude.

The most common type of in-plane orbit transfer changes the size and energy of an orbit, usually from a low-altitude parking orbit to a higher-altitude mission orbit such as a geosynchronous orbit. Because the initial and final orbits do not intersect, the maneuver requires a transfer orbit. The above figure represents a Hohmann transfer orbit. In this case, the transfer orbit's ellipse is tangent to both the initial and final orbits at the transfer orbit's perigee and apogee respectively. The orbits are tangential, so the velocity vectors are collinear, and the Hohmann transfer represents the most fuel-efficient transfer between two circular, coplanar orbits. When transferring from a smaller orbit to a larger orbit, the change in velocity is applied in the direction of motion; when transferring from a larger orbit to a smaller, the change of velocity is opposite to the direction of motion.

The total change in velocity required for the orbit transfer is the sum of the velocity changes at perigee and apogee of the transfer ellipse. Since the velocity vectors are collinear, the velocity changes are just the differences in magnitudes of the velocities in each orbit. If we know the initial and final orbits, rA and rB, we can calculate the total velocity change using the following equations:


Exmaples

Example 1: Satellites falling down the earth

The satellite will fall down to the earth if its velocity is too small. Let's do this example step by step:
  1. Run the program by double click the file "run.bat".
  2. Open the control panel from the menu "Setting -> Control Panel...".
  3. Choose a small initial satellite velocity, say, 7000m/s, from the Parameters tab by slide or click the middle slider.
  4. To have a better view, click form the toolbar.
  5. Click the Simulation tab and then press the Start button to start a simulation using the default the simulation parameters. You will see that the simulation will stop soon due to the satellite's hitting to the earth
  6. Click the Animation tab and then press the Forward button to start a forward animation. You will see the trajectory of the satellite as the white line shown in the following figure:

Example 2: Satellites go around the earth

The satellite will go around the earth if it has suitable velocity. Let's do this example step by step:
  1. Run the program by double click the file "run.bat".
  2. Open the control panel from the menu "Setting -> Control Panel...".
  3. Using the default initial satellite velocity, 8000m/s.
  4. To have a better view, click form the toolbar.
  5. Click the Simulation tab and then press the Start button to start a simulation using the default the simulation parameters. You will see that the satellite will go around the earth instead of falling down to the earth.
  6. Click the Animation tab and then press the Forward button to start a forward animation. You will see the elliptic trajectory of the satellite as the white line shown in the following figure:

Example 3: Satellites go away from the earth

The satellite will go away from the earth if its velocity is large enough. Let's do this example step by step:
  1. Run the program by double click the file "run.bat"
  2. Open the control panel from the menu "Setting -> Control Panel...".
  3. Choose a small initial satellite velocity, say, 15000m/s, from the Parameters tab by slide or click the middle slider.
  4. To have a better view, click form the toolbar.
  5. Click the Simulation tab and then press the Start button to start a simulation using the default the simulation parameters. You will see that the satellite will go away from the earth and never come back.
  6. Click the Animation tab and then press the Forward button to start a forward animation. You will see the elliptic trajectory of the satellite as the white line shown in the following figure:

Example 4: One thrust orbit transfer

The satellite will change its orbit due to the thrust. Let's do this example step by step:
  1. Run the program by double click the file "run.bat"
  2. Open the control panel from the menu "Setting -> Control Panel...".
  3. Click the Orbit Transfer tab, set the thrust force to be 100N, set the start and stop time to be 10600th second and 10700th second respectively.
  4. To have a better view, click form the toolbar.
  5. Click the Simulation tab, set the duration to be 20000 seconds and then press the start button. Wait to the stop of simulation.
  6. Click the Animation tab and then press the Forward button to start a forward animation. You will see how the satellite changes its orbit. The following figure is the trajectory of the satellite:

Note: How to determine the start and stop time of the thrust in a simulation:
  1. Run a simulation first.
  2. Use the start frame slider on the Animation tab to locate the point where you want to give the satellite a thrust.
  3. Get the simulation time from the top-left corner of the main window.

Example 5: Two thrusts orbit transfer

The satellite will change its orbit to a completely different one due to the two thrust. Let's do this example step by step:
  1. Run the program by double click the file "run.bat"
  2. Open the control panel from the menu "Setting -> Control Panel...".
  3. Click the Orbit Transfer tab, set the thrusts as shown in the following figure.
  4. To have a better view, click form the toolbar.
  5. Click the Simulation tab, set the duration to be 30000 seconds and then press the start button. Wait to the stop of simulation.
  6. Click the Animation tab and then press the Forward button to start a forward animation. You will see how the satellite changes its orbit. The following figure is the trajectory of the satellite:

Note: How to use more than two thrusts in one simulation:
  1. Run a two thrust simulation first. Do NOT press the Reset button on the simulation tab after the simulation.
  2. Set up your other thrusts and continue your previous simulation again by press the start button on the simulation tab.
  3. If you need more thrusts, repeat the above two steps.