This issue is a result of your graphics card failing to support the higher level of advanced graphic rendering required for the high resolution planetary maps.
There is an option in File ---> Preferences ---> Shaders ---> Advanced Planet Rendering <--- turn this off. Then the planets and moons will then be visible.
What graphics card do you have?
In Windows 7/Vista--->Start---> Control Panel---> System---> Device Manager---> Display adapters <--- what it says here will be the graphics card.
Affected Cards:
ATI Radeon X1900 Series
ATI Radeon X1600 Series
ATI Mobility Radeon HD 5450 Series
ATI Mobility Radeon HD 4200 Series
ATI Radeon HD 5700 Series
ATI Radeon HD 3200
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