Picture a globe lying on its side, "north" pole to the right. (It's our planet, and we'll position it the way we like.) You will be mapping the X and Y axes of the starting image to latitude and longitude on the globe, so that what was a horizontal row of pixels follows a line of longitude. The defaults exactly cover the hemisphere facing you, from longitude 180 degrees (top) to 0 degrees (bottom) and latitude -90 (left) to latitude 90 (right). By changing them you can map the image to a piece of the hemisphere or wrap it clear around the globe.
The next entry is for a radius factor that controls the over-all size of the globe. All the rest of the entries are the same as in the landscape projection. You may want less surface roughness for a plausible look, unless you prefer small worlds with big topography, a la "The Little Prince."
WARNING: When the "construction" process begins at the edge of the globe (default) or behind it, it's plotting points that will be hidden by subsequent points as the process sweeps around the sphere toward you. Our nifty hidden-point algorithms "know" this, and the first few dozen lines may be invisible unless a high mountain happens to poke over the horizon. If you start a spherical projection and the screen stays black, wait for a while (a longer while for higher resolution or fill type 6) to see if points start to appear. Would we lie to you? If you're still waiting hours later, first check that the power's still on, then consider a faster system.