If I'm not mistaken, you can simply Cut or Copy the grouped frames (from your first screenshot), and Place Into a circle shape.
You're right, this should really be done in Illustrator BUT... if I'm understanding your question correctly, maybe you are going about this backwards. Instead of making a "hole" in space to reveal a planet, do just the opposite by trying the following:
- Copy your Group of Gradient-filled objects.
- Draw a circle with the Ellipse tool (L) by clicking and dragging with the tool while holding down the Shift key.
- With your circle selected, go to Edit > Paste Into to paste the Gradient-ifilled objects inside your circular Frame.
Your Gradient will work like a graphic inside of a Frame. You can click on the Content Grabber in the center of the Frame to moved your Grouped Gradient object around within the Frame. You can also move the planet Frame around as a unit, put it in front of any background and even add a Glow to it in the Effects panel.
Hope this helps!
I feel silly for not thinking of this, thank you both!