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1. Create a curve with your object at the center; scale it to size
2. Create an empty at the center of the curve
3. (in object mode) select camera, shift-select curve, ctrl+p, and “Follow curve”

Of course, the camera will just kinda stare in some direction. You need to add a “Track-to” modifier, which behaves weirdly.

1. Select the camera
2. Constraints -> Add Object Constraint -> Track To
3. Select the target
4. Adjust “To” to be -Y, and Up to by Y

Tada!

Blender file: http://logrit.com/media/uploads/camera_circle.blend