The Neanderthals managed to locate the dead modern human astronauts. They boarded the abandoned ship and found the astronauts' bodies sprawled across the floor. Grunting and growling, they scratched their noggins and ineffectively pondered their next course of action.
Suddenly, their base, primal, untamed instincts took over. They bent down and feasted upon the corpses of the astronauts. NASA had made a serious mistake: they hadn't vetted their new Neanderthal astronauts, and thus failed to learn that they were cannibals.
After the feast was complete, the Neanderthals set their sights to the moon. Several weeks later, they arrived.
One by one, the brave explorers stepped onto the surface of the moon. They planted their favorite stick into the soil.
Then they ate each other and died.