Cartesian Doubt
Cognito il Sum
The question is vague - When we say "destroy" do we we mean melting the surface beyond all recognition, or do we we mean launching every bit of Earth Mass into orbit ?
In regards to A.) then yes .... Michio Kaku's recent Physics of the imposable series, claims you can scar a planet beyond all recognition, by melting the Core - Well withing Superman's power levels, destroying destroying that Shadow moon, Moving the Moon with Wonder Woman, and Green Lantern, require a far superior energy output.
http://www.scientificamerican.com/article.cfm?id=star-wars-science-death-star
In regards to B.) ... No way !!!!! Not because Superman doesn't have the physical potential, but because the Sun does even come close to giving out enough energy.
http://rikdad.blogspot.com/2009/04/how-strong-is-superman.html
This being the Key Quote :
"The bad news is, for Superman to push a planet with the force described above, he would have to burn up 2 quintillion tons of matter each second. "
This is Trillion times more energy than the Sun gives off a second - Even if you take Superman's ability to store Sunlight energy, it would still take over 30, 000 years (and that's if he absorbs ALL the Sun's energy - Killing everyone on earth in the process) to absorb enough energy to move the Earth for a second.
So Yes I think Superman can "destroy" a planet. But there's no way he can DESTROY a planet. Planet Destroying, i.e. moving the entire mass out of orbit is IMO a truly Sky Father level feat. We talking about the manipulation of energies beyond the out put of a Star.