Hey there! it's a good attempt for not having much knowledge of perspective. I think your colours are OK, but be careful about going too much into white or black, or at least try to limit how much and where you are using them.
Shadow construction is fairly complicated, but I've tried to break it down below. If you;re interested in this kind of technical knowledge, I'd suggest picking up both of Scott Robertsons books : "How to draw" , which will teach just about everything related to perspective, and "How to Render" which will use concepts from perspective to cast shadows, draw reflections accurately and so on.
It's been about 2 years since I've worked through this material so it might be slightly, off, but I'll do my best to explain! Also, I didn't go through the entire construction in painting over this, so again, probably off a bit but the theory should be good enough.
For starters, I've taken your image and moved the light source slightly behind the camera and to it's right, off frame.
To construct accurate shadows, you need to know where both your light source and object sit in perspective relative to each other. With that knowledge, you need two things from the light source:
1) A point where the light rays originate from. Lines very similar to a vanishing point in regular perspective will be drawn from this point.
2) A point directly beneath the light source that lies on the same plane as the object youre casting a shadow onto. This point will be used to draw lines that determine the direction of the shadows. Once again, this point will have lines radiating out from it like a vanishing point would in regular perspective.
Heres a diagram to explain it visually. The same lines are also included in my little paintover.
From the object, you now need to do two things with the information you have from the light source.
1) Determine all corners where the Rays of light will intersect. It's as simple as drawing a line from the source of the light through a corner or point on your object. BUT you need to have determined where the light source is first, as we did above.
2) From each of these corners, you need to drop a line down beneath them to reach the floor. It's important that it actually intersects with the floor plane here. Draw a line starting from your shadow direction point that crosses the vertical line you drew from each corner of your object. Eventually, each of these lines will also cross the matching light ray line that was drawn in the previous step.
For each corner and shadow direction pair, you will get an intersection that determines where the shadow ends. Connect these end points and you have the shape of the shadow. Afterwards, it's simply a matter of rendering the object and the shadow it casts appropriately, which is another matter entirely!
You've chosen here a sphere, which is actually one of the more complicated shapes to cast a shadow from. The reason being that it has no corners or obvious edges to use to cast from. You need a deeper understanding of the ellipses that it's made of and how they are used in perspective to construct shadows. Here's an example i did 2 years ago when i was working from the How to Render book, using rectangular forms to find the edges:
For a sphere, you need to find the "Terminator" which is an ellipse that wraps around the sphere and is the edge where the light ray is tangent. Using that ellipse, you can select 4 points that are ideally equally spaced apart, and do the same construction with them where a line is dropped to intersect with the shadow direction lines. I've shown that in the paintover above.
Here's an example for the terminator:
http://farm6.static.flickr.com/5055/5520...c37bf2.jpg
Here it is wthiout the lines:
Hope that helps! Let me know if I can clarify anything