Excellent job. I designed a project using a sphere. I will have to search for the wood of the right size so I did a test of something similar with smaller wood. The final project will be larger and more ornate. This one is about 18" tall with a 3" mirror in it.
There are some good videos on youtube that show turning sphere's. I have collected photos of a bunch of different sphere turning jigs and will eventually build one. I'm going to build a nice one out of metal but they can be built quite easily out of wood.
the method I use is to first turn a cylinder. The cut the width to match the diameter of the cylinder. Then turn it close to round and draw a line on the center. Cut the tenons off and mount it between 2 cones so the line you drew runs through the center of the cones. Then just carefully turn away the shadow area so it's round. Draw another line and mount it so neither line runs through the cones. Turn the shadow away. In theory you should now have a round sphere.
What I find usually goes wrong is the cones that you use as a jam chuck may not be accurate enough or are too large or too small to properly support the area you just turned. You can usually tell this because the shadow area will extend all the way to the cones. This usually happens on the first rotation anyway but after the first one the shadow area should ideally be smaller and smaller and more toward the center. My first spheres started out one size and ended up about 1/2" smaller or more. Now I usually end up taking off just an 1/8 or 1/4"
Hope this helps someone. They are fun to turn.