This idea is for a geoynchronous or geostationary satellite comprised of a simple reflective dish, plus minimal support systems such as gyrostabiliser, energy source, and communication systems.
This is not actually a pinhole camera, but a pinhead camera. The principals and math are the same though.
key calculation for pinhole cameras is given below:
Taking the focal length to be the altitude of geosynchronous orbit of 35,780km and the (inappropriate?) wavelength of light at 550nm, that would imply a disc of under 8m diameter would produce an image focused on the earth's surface.
In addition, cosmic phenomena could be seen from parts of the world not actually pointing at that part of space.
Phenomena not normally visible because of backlighting could also be seen if the mirror is positioned over a dark part of the sky.
Variations may include:
Mirrors of different or variable reflective diameter to reflect other wavelengths.
Mirrors reflecting onto a flat bit of the dark side of the moon.
Advertising beamed images, including advertising on dark parts of the moon.
Wikipedia NASA New Worlds Mission (different; that's an occluder)
Pinhead Mirror USPat4,948,211
Various 007 plots