Modern car odometers can record up to a million miles driven. What happens to the odometer reading when a car drives beyond its maximum reading?

Unless the odometer has been tampered with, nothing happens to the odometer reading when a car drives beyond its maximum reading.  It will continue to read and show the mileage the car is covering.  The odometer is simply indicating that the car has reached its useful life and needs to be replaced by the user or owner.

Explanation:

Ordinarily, the odometer is installed to show the car's mileage.  It also indicates when some maintenance and repairs must be carried out.  Attaining the maximum mileage shows that the car is too old for continued maintenance because the car has experienced much wear and tear.  Many of the drive belts and pumps will require replacement if one must continue using the car at this point.  The costs of servicing and repairing the car will skyrocket to uneconomical levels.

light-year  

the distance that light travels in a vacuum in one year, equal to about 9.46 trillion km (5.88 trillion mi). light-years are used in measuring interstellar and intergalactic distances.  

parsec  

a unit of distance used in astronomy, equal to about 3.25 light years (3.08 × 1016 meters).  

parallax  

the apparent angular displacement of a celestial body due to its being observed from the surface instead of from the center of the earth (diurnal parallax or geocentric parallax) or due to its being observed from the earth instead of from the sun (annual parallax or heliocentric parallax)  

absolute magnitude  

the magnitude (brightness) of a celestial object as it would be seen at a standard distance of 10 parsecs.  

apparent magnitude  

the magnitude of a celestial object as it is actually measured from the earth.  

redshift  

an increase in the wavelength of radiation emitted by a celestial body as a consequence of the doppler effect.  

the great thing about your imagination is that it doesn't have to make sense! if i were you i would be stuck in space, no communication with earth travelling around and around, you can only guess how long its been since your communication broke down. you land on an undiscovered planet, you do a scientific investigation examining the elements and conditions. you come across alien lifeforms.  

best of luck!