Efficient massive heightmap storage

I am working on a project that creates procedural solar systems with planets with a radius of about 12720 units. I use a Noise function to generate the terrain + Quad Tree for the LOD. My goal is to store the generated heightmap for the player to edit as he sees fit. A big problem with that is the amount of storage it takes up to have 11 levels of detail of meshes 32 vertex wide. To achieve a diecent detail on a player level it's about 4^11*16 vertexes i need to store just for one side of a cubed sphere. For the entire planet it will be about 4^11*16*6 vertexes. I did some testing and writing the float heightmap , as a 32bit color to a texture, the whole map took about 384 MB. I can live with that for just one planet, but i have over a 100 planets. What can i do to bring down storage to a more realistic level.