Copyright (c) 2000 Steve Meyers 

Orbit is played on an empty 16x16 square board:

TURN - On each turn, each player drops a stone into an empty cell.
A player may pass his turn (if both players pass, the game ends)
PIE RULE - One player drops two black stones and one white stone. The other player decides which color to play. 
CONNECTION - Two friendly stones are connected if they are orthogonally adjacent or diagonally adjacent.
ORBIT - An orbit is a connected set of stones which completely encircles one or more cells.
When an orbit is formed, any enemy stones within the orbit are removed from the board, and it is thereafter prohibited for the opponent to play within that orbit.
HALF-ORBIT - A half-orbit is a connected set of stones which, together with one side of the board, completely encircles one or more cells. 
When a half-orbit is formed, it is thereafter prohibited for the opponent to play within that half-orbit (but enemy stones inside are not captured).
ENDGAME - At the end of the game, any stones that cannot avoid capture are automatically removed from the board. 
There is often the existence of some shared territory (cells where both players are prohibited from playing).
GOAL - Wins the player with more territory, meaning the number of empty cells he controls exclusively (there are no points for shared territory, captured stones or stones onboard.).
Some examples

In the top left corner, black is not forbidden to drop, since white does not have a half-orbit (the stones connect two adjacent edges rather than a single edge to itself).

On the left side, if White plays the marked stone, he will create a half-orbit, forbidding black to place any stone within (and securing that territory), but the black stone is not captured.

In the bottom, white manages to create an orbit (by dropping the marked white stone) and thus captures two black stones and secures that territory!

Some words from the author: there is no Ko in Orbit, the reason being it is prohibited to play within an opposing structure. For the same reason, "invasion" is not possible in the usual sense --- however, a portion of or all of your opponent's structure can sometimes be destroyed, meaning that it is now permissible to play within it since it no longer exists. (BTW, it is permissible but never advantageous to play within one of your own orbits).

More information can be seen at Meyers' website.