It hit me as I was watching...
Kirk orders the Enterprise be put into an orbit that'll keep it beyond the range of Ecos detection devices (which I'll assume were along the lines of radar).
Hmmm...
Those same "detection devices" noted the Enterprise heading toward the planet from a GOOD ways off, and allowed VERY long range missles to be directed at the ship.
How far away from the planet did Kirk expect the ship to orbit?
Kirk orders the Enterprise be put into an orbit that'll keep it beyond the range of Ecos detection devices (which I'll assume were along the lines of radar).
Hmmm...
Those same "detection devices" noted the Enterprise heading toward the planet from a GOOD ways off, and allowed VERY long range missles to be directed at the ship.
How far away from the planet did Kirk expect the ship to orbit?