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This HP Prime program demonstrates how to calculate the orbital periods of an Earth satellite.

The user can define the classical orbital elements of the satellite starting at line 35 of the source code. The attached zip archive contains a PDF document that explains the different orbital periods of a satellite.

Here's an example

////////////////////////////////////
// define classical orbital elements
////////////////////////////////////

// semimajor axis (kilometers; semimajor axis > 0)

sma := 8000.0;

// orbital eccentricity (non-dimensional; 0 <= eccentricity < 1)

ecc := 0.015;

// orbital inclination (degrees; 0 <= inclination <= 180)

inc := 28.5;

// argument of perigee (degrees; 0 <= argument of perigee <= 360)

argper := 270.0;

// true anomaly (degrees; 0 <= true anomaly <= 360)

tanom := 30.0;