Cakecrumbs, who created the amazing Jupiter Cake and Earth Cake, has posted a tutorial (with video) explaining in detail how to bake nested, hemispherical cakes so you can create your own.

Now, as for the equipment required, you will need a set of any three hemisphere tins or bowls that can fit inside one another. Pudding bowls are great for this if you don't want to buy hemisphere pans, though you may need to trim it to make it round (I'll show you how to do that). Any oven-proof ceramic bowls will work fine. If you're using glass as I do, make sure it's oven safe and heat treated. Some glass bowls will say 'heat-resistant' but that only means they won't explode in your dishwasher.

Baking times will vary based on how big your bowls are. I'll give you some guides on that, but do keep a careful eye on your cakes and use your inner baking muse to judge cooking times.