How Do You Find the Orbital Plane Revolution Duration?

You can use STK's Analysis Workbench capability to calculate the duration of an orbital plane revolution around the Earth. This information is important for constellation design of satellites. These instructions show how to create a vector, angle, scalar, and scalar condition as steps toward determining the orbital plane revolution duration.

License Required: For STK 12.2 and earlier, you need a specific license for Analysis Workbench. For STK 12.3 and later, all STK product license types include Analysis Workbench.

Create a LEO satellite

1. From the Insert menu, select New....
2. Select Satellite on the left and Define Properties method on the right.
3. Specify the orbital parameters such that the satellite is in low Earth orbit (LEO).
4. Make sure that the Inclination > 0, because you will be using the line of nodes, and there is no line of nodes for an equatorial satellite orbit.

Create a vector (fixed location along the equatorial plane)

1. In Analysis Workbench, select the Vector Geometry tab.
2. Change the Filter by: field to Primary Central Bodies and select Earth.
3. Click the Create New Vector () button.
4. Set the following values to define a Fixed Vector:
   • Type: Fixed in Axes
   • Name: Longitude_### (enter a Longitude of revisit)
   • Coordinate Type: Spherical
   • Right Ascension: ### deg (enter a Longitude of revisit)
   • Declination: 0 deg
   • Magnitude: 1
   • Reference Axes: Earth Fixed
5. Click OK.

Create an angle (between a fixed vector and the line of nodes)

1. In Analysis Workbench, select the Vector Geometry tab.
2. Select Earth as the Primary Central Body.
3. Click the Create new Angle () button.
4. Set the following values to define a new angle:
   • Type: Between Vectors
   • Name: Between_Vectors
   • From Vector: Earth/Longitude_###
   • To Vector: Satellite/LineOfNodes
5. Click OK.

Create a scalar (using the new custom angle)

1. In Analysis Workbench, select the Calculation tab.
2. Select Earth as the Primary Central Body.
3. Click the Create new Scalar Calculation () button.
4. Set the following values to define a new Scalar:
   • Type: Angle
   • Name: Scalar_Between
   • Input Angle: Earth Between_Vectors
5. Click OK.

Create a condition (to find when the angle is 0 degrees)

1. In Analysis Workbench, select the Calculation tab.
2. Select Earth as the Primary Central Body.
3. Click the Create New Condition () button
4. Set the following values to define a new condition:
   • Type: Scalar Bounds
   • Name: Above_Zero
   • Scalar: Scalar_Between
   • Operation: Above Minimum
   • Minimum: 0.2 deg
5. Click OK.

Generate the report summary

1. In Analysis Workbench, select the Calculation tab,
2. Select Earth as the Primary Central Body.
3. On the right, under My Components, select Above_Zero.
4. Expand the Above_Zero Condition to expose Satisfaction Intervals.
5. Right-click Above_Zero>Satisfaction Intervals and select Report...
6. In the Report, click the Report Units () button to change the time units to hours.

Note: If you do not have three intervals, you will need to increase the Scenario Analysis time.