We need the resources of the solar system so that we can afford interstellar travel.
The NERVA rocket technology is reviewed in detail by Geoffrey Landis.
Russia did some more advanced nuclear thermal rocket work.
Look at bimodal nuclear thermal rocket for a mission to Callisto (Jupiter moon outside of the deadly radiation belt).
About 2.5 years each way.
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Brian Wang is a Futurist Thought Leader and a popular Science blogger with 1 million readers per month. His blog Nextbigfuture.com is ranked #1 Science News Blog. It covers many disruptive technology and trends including Space, Robotics, Artificial Intelligence, Medicine, Anti-aging Biotechnology, and Nanotechnology.
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