For doing what you want to do, removing an object from an image, you need an image editor/graphics program along the lines of Photoshop or GIMP.
Aperture is capable of working with such a program to manage the images and to do the initial development of the image from the camera but does not do that type of image manipulation.
I've done some minor manipulation of the type you need using the retouch brush. I set it to "Clone" and then as in Photoshop one performs an option-click to select the area to use as a replacement for the pixels depicting the "persons" you wish to remove. It's a bit tedious but it works within Aperture. I can rarely do this in one movement –– that is to say –– I do it with the opacity set high, then again from a different clone of pixels at a lesser opacity and then a final opacity of pixels than provide a light cover to "polish" the maneuver. I was pleasantly surprised to find the capability with the Aperture App.
If you want a compositing program especially for removing large objects, try Inpaint. It is very good, but not free (about 19 $US). You can download a trial here: http://www.theinpaint.com
It is very simple to use: Just drag the mouse over the area you want to remove and Inpaint will it fill automatically with a texture from your image that fits best into the area you want to clear.
To remove the moon:
Drag the mouse over the region - it will be marked red:
Press the blue "Inpaint" arrow and the region will be replaced by some best fitting texture picked from the image:
Essentially Inpaint does automatically what stanleyd described, but in a way that will work with really large regions to be patched.
But your method is free - built in - and preserves Apertures lossless workflow. For small objects I use it frequently, and it is preferable to using a plug-in. For larger objects inpainting will help, but if the background is cluttered, you may still have to retouch the resulting image afterwards in Aperture. Inpaint picks the txture to use based on statistics - not based on a semantic analysis of the image.
For a really complicated scene you will have to fall back on Frank Caggiano's initial suggestion - use a full graphics compositing program like Gimp or Photoshop.
Too complicated: let Frodo vanish:
Why is it to complicated? Because Inpaint has no notion of "floor" and "wall" and "table". Here a manual fix would be much better. This method usually works best with outdoor scenes and without objects touching or occluding each other.