The program below renders a solar system in three dimensions. Each planet's height above or depth below a reference plane is shown by a perpendicular line that connects it to a grid on the base plane. To see the source code, visit http://thiscouldbebetter.wordpress.com/2013/08/19/visualizing-a-solar-system-with-a-base-plane-and-elevations/.
You can move the camera by using the A, D, S, W, R, and F keys. There’s also a little green square named “Ship” that can be moved from place to place. When you click the ship, a cursor appears. Clicking again fixes the cursor’s position on the XY plane. Clicking yet again fixes the cursor’s Z position, and the ship will start moving toward the specified location.
There’s still some bugs. For one, if you get the camera too close to the base plane’s grid, it will start rendering incorrectly. The solution to that would probably be to clip the lines in the grid against the camera’s viewing, uh, frustum? But I haven’t implemented that yet.