How often does Mars's orbit come within range of Earth's orbit for a nuclear powered space ship to travel?

Most Mars missions are planned using the most fuel-efficient orbit possible: a Hohmann transfer. This is a highly elliptical orbit around the Sun whose perihelion (closest point to the Sun) corresponds with Earth's orbit and whose aphelion (farthest point from the Sun) corresponds with Mars's orbit. These transfers are more efficient because you can use the planets' orbital velocity to assist you. Unfortunately, a Hohmann transfer to Mars takes 7 to 8 months. When you factor in the two-way travel time and the amount of time the astronauts will spend on the surface of Mars, that's more than a year and a half away from Earth. Hohmann launch windows open up about every 25 months due to the relative movements of Earth and Mars.

If you have a more powerful rocket, like a nuclear rocket, the travel time is shorter. You have more frequent launch windows because you don't have to wait for the planets to orient themselves and give you the most advantageous start. Some scientists think that a nuclear rocket could reach Mars in 4 months, which could shorten the entire trip time to less than 1 year. Anything you can do that reduces the astronauts' time in space is a good thing.

I hope that helps. Good luck!