Travel to the moon is impossible because astronauts could not possibly survive the levels of radiation in the Van Allen belts and in outer space.
The Van Allen belts are belts of electrons and high-energy ions trapped in our magnetic field, as pictured to the left. Radiation exposure is a very serious concern when traveling into outer space, but the radiation dosage involved in a trip to the moon is not as intense as many might think. The biological efficiency of a radiation dose is measured in rems. It would take a dose of about 100-200 rems for a person to experience adverse reaction. NASA was able to keep the radiation exposure low through the Van Allen belts by traveling underneath the belts through the belts at a high speed (Bara). The astronauts were exposed to about one rem traveling through the Van Allen belts, which is not likely to cause significant immediate effects, as it is about the average exposure per year for a person residing on Earth ("Moon Hoax"). The bigger concern was the possibility of a solar flare during the Apollo missions, but, luckily, there weren't any large solar flares during that time.
Each astronaut also carried a personal radiation dosimeter and three passive dosimeters during the mission to be analyzed upon their return (Bara).
http://lasp.colorado.edu/strv/vanallen_strv.html