Today, our questions and hypotheses about the Solar System's origin have surpassed our ability to deliver scientific instruments to deep space. The moons of the outer planets, the Trojan and Centaur minor planets, the trans-Neptunian objects (TNO), and distant Kuiper Belt objects (KBO) hold a wealth of information about the primordial conditions that led to the formation of our Solar System. Robotic missions to these objects are needed to make the discoveries, but the lack of deep-space propulsion is impeding this science. Radioisotope electric propulsion (REP) will revolutionize the way we do deep-space planetary science with robotic vehicles, giving them unprecedented mobility. Radioisotope electric generators and lightweight ion thrusters are being developed today which will make possible REP systems with specific power in the range of 5 to 10 W/kg. Studies have shown that this specific power range is sufficient to perform fast rendezvous missions from Earth to the outer Solar System and fast sample return missions. This whitepaper discusses how mobility provided by REP opens up entirely new science opportunities for robotic missions to distant primitive bodies. We also give an overview of REP technology developments and the required next steps to realize REP.