Chang'e 3 now on the Lunar surface has imaged the Earth. Is it possible for that same camera to take a time exposure and show us the stars?
Looking through this image archive, they haven't taken photos where stars are the main subject. All photos in that archive were done in daylight.
I've removed the processed photo - I found 2 bright pixels in the shadowed region of the Earth, so those can't possibly be stars.
The majority of power provided by the RTG is used for the heaters and a small fraction is used to sustain the lander's Lunar Night Sleep Mode in which all systems except for crucial control and housekeeping systems are shut down.
I tried to find out a bit more about the camera:
Three panoramic cameras are installed on the lander, facing different directions to allow the lander to acquire images of the lunar terrain surrounding the landing site and take photos of the rover as it departs the landing site. The cameras can take still images as well as video. Exact technical details for the cameras were not released. (emphasis mine)
Camera technology tested on previous missions that is employed on Chang’e 3 include auto-exposure, focus adjustments, high-speed compression of color imagery and static gray image, and sub-sampling methods.
I also found a paper (PDF) that analyzes the performance of the cameras on Yutu in more detail. It doesn't mention exposure times specifically. It does say the camera has both manual and automatic exposure modes. The PDF contains a few graphs that show camera performance, these have an X-axis marked 0-1200 with a label of "0.5 ms". I think that means the X-axis shows an exposure time of 0-0.6 seconds, but I'm not entirely sure. If this is true, the camera has been designed to use exposures of up to 0.6 s, which sounds long enough to see a few stars.
The archive itself is here but is available in Chinese only.