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If you're a sci-fi writer like me, then you've probably come across a sticky problem at some point or other - calculating orbital characteristics.

There are online calculators you can use which are excellent, although a little fiddly if you want the results in both metric and imperial. Another problem with them is they only calculate orbits around specific bodies, usually Earth.

I've written a program called Orbital Calculator (notice the huge lack of imagination there). It can calculate orbital characteristics around almost any gravitational mass. You can add new masses to the database, and satellites too, for easy recall. You can also export/import these to share with friends. It comes with 27 solar system masses (the Sun, all 8 planets, 16 moons and two asteroids).

Adding a new mass is easy, so you can add a real exoplanet or an imaginary one. All you need is its radius and mass - mass is expressed in terms of Earth masses (for example, Venus is 0.815 Earth masses). To calculate an orbit, select the mass, state how far above the surface the satellite is (in km or miles) and calculate. An example of the output:

Orbiting Object: ISS (International Space Station)
Planet: Earth
Character: Roughly Circular
Orbit Type: Equatorial
Perigee: 401.1 km = 249.231 miles
Apogee: 408 km = 253.519 miles
Mean Elevation: 404 km = 251 miles
Average Speed: 27,583 km per hour = 17,140 mph = 7,662 meters per second
Period: 0.06 days = 1.54 hours = 92.65 mins = 5,559 seconds

On-screen, this is nicely tabulated and can be sent to the clipboard.

The program is free, runs on Windows and is portable (meaning it doesn't need to be installed and can run off a USB stick).
http://philip-p-ide.uk/orbital-calculator/