a lovely project... so earth like ... they will be nice to take on the ship to remember it...
you might need some thicker rods or wire to keep it's shape if it was big.. particularly on the bottom 1/2 of it.
how big are you figureing you'd make it..
another thought is to use the rigid styrofoam broken up into pieces... rots love it as there's cracks and fizures in the foam.. it holds a bit of water and the roots grow into it quite well.. I use it in me planters and find the roots growing through it all the time I even saw a passiflora in a foam planter that had it's roots growing through the 1 1/4" foam in dozens of places.. broken up in my pots it anchors the roots to this big burried lump that has to pull it's self through the soil to dislocate the plant.. like a deadman ....where you'd burry a log with a rope attached to secure a tent in sand or snow.. in the sphere it would hold some water for the roots and also help anchor them.. the peanuts are almost sealed on the surface and aren't made up out of lots of tiny spheres pressed together with cracks like the other foam
you coul save on the plants if you had alot of it blue.. and recreated the continents.. I should do one.. thanks