Think of a bowling ball that has rolled to the center of a trampoline. I would like to depict that in Illustrator, except the trampoline would be a grid that conforms to the weight of the bowling ball (the planet in the example below).
Found an interesting option in this video.
Start by creating a grid with the Rectangular Grid or Polar Grid tool.
Click Object > Envelope Distort > Make with Mesh
Add some perspective with the Effect > 3D > Rotate and adjust to your liking.
Move the points from the Mesh grid (not your original grid) until you get the desired effect. Go back and tweak the settings in the Rectangular grid and Envelope Distort tools if the result is still not good enough.
This is my final result after just a few minutes doing what I just described: