How to lower opacity of PART of a path (ellipse)

Hello! I have a transparent globe situation and I have some ellipses surrounding it to make them look as if they're orbiting. Because the globe is transparent, I need to lower the opacity of the "back half" of the orbiting ellipses so it looks as if they're on the other side of the globe.

As you can see, these are just ellipses drawn on top of the globe. What type of tool can I use in illustrator to depict the depth I'm looking for?

In Photoshop, I would just apply a mask and use the brush tool with a grey color. In Illustrator, I was hoping there would be an opacity tool for the eraser.

Please help! Thank you.