Applicants must meet the following minimum requirements before submitting an application.
Astronaut Candidate (Non-Piloting background)

1. Bachelor’s degree from an accredited institution in engineering, biological science, physical science, or mathematics. Quality of academic preparation is important.

2. Degree must be followed by at least 3 years of related, progressively responsible, professional experience or at least 1,000 pilot-in-command time in jet aircraft. An advanced degree is desirable and may be substituted for experience as follows: master’s degree = 1 year of experience, doctoral degree = 3 years of experience. Teaching experience, including experience at the K - 12 levels, is considered to be qualifying experience for the Astronaut Candidate position; therefore, educators are encouraged to apply.

3. Ability to pass the NASA long-duration space flight physical, which includes the following specific requirements:

   • Distant and near visual acuity: Must be correctable to 20/20, each eye
   • The refractive surgical procedures of the eye, PRK and LASIK, are allowed, providing at least 1 year has passed since the date of the procedure with no permanent adverse after effects. For those applicants under final consideration, an operative report on the surgical procedure will be requested.
   • Blood pressure not to exceed 140/90 measured in a sitting position
   • Standing height between 62 and 75 inches

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The reason for number 1: astronauts are scientists, and their job chiefly consists of running experiments in a microgravity environment
The reason for number 2: Being an astronaut isn't exactly an easy job, especially if something goes wrong. They want responsible people (though, note, you don't need a PhD; it's just considered equivalent to experience)
The reason for number 3: You need healthy people who can do their job and fit inside the spacecraft.

Of course, those are just the requirements that have to be met before you start training, but it's probably less restrictive than you think. Also, I believe all astronauts are expected to learn Russian.