I believe there is not yet a kind of "ruler" function to measure the distance between two objects. You can only view the distance between an object and another when placing it down from the object menu.
Here's what I suggest you do. It's a roundabout way, but it works. Say you want to measure the distance between two planets A and B that have already been placed down. Get another planet from the object menu but do not place it down; only hover it. I'll call this planet C. Hover C next to planet A, real close. When you drag an object onto the simulation but do not place it down, a ruler is automatically generated. So, you can indirectly measure the distance between A and B by placing C right next to A, whereupon a ruler would be generated that measures the distance from C to B. But since C is right next to A, the distance between C and B is pretty much the same as the distance between A and B. Once you've finished measuring the distance, you can just delete C.