Costumes are "Men Into Space" leftovers

I just caught this movie on MST3K and noticed that the costumes (Helmets and backpacks but not the space suits) and sets (Space ship exteriors and planet surface) look straight from "Men Into Space". Considering that MIS was made in 1960 and TPP was made in 1961, what are the chances these elements were 'recycled"? All through the early scenes I kept expecting Col. McCauley to show up and set things straight!