Deep space exploration is a large topic which includes learning about space in and beyond our solar system and asteroid mining. Asteroid mining is the idea that you gather asteroids which are material rich and bring them to Earth’s rotation. Once this is done you send up mining equipment into space to mine the materials and send them back to Earth.
Deep space exploration has already been done but only Voyager 1 and 2 and New Horizons are operational. Voyager 1 is the fastest moving probe but in order to go further faster we need to send probes with nuclear thermal propulsion (NTP) systems. By using NTP systems we can accelerate probes at a faster rate for longer periods of time. The result would be a smaller nuclear reactor that would have a slow rate of fission so it could build up speed for a longer amount of time.
Asteroid mining rocket would be a combination of a rocket heading to Mars and a rocket heading to deep space. This would end up making a rocket with a large reactor but with a slow rate of fission. The reason behind this is combination because a larger reactor is needed to go a set amount of distance comfortably while a slow fission would be used because there are no time constraints. If you used a faster fission you would need to decelerate more in order to obtain the asteroid and take it to Earth.