Sat Tel GK

[cheshunt]

21d  Method of determining the position of a body by the distance and direction of its travel 4 and 9            - E - D  and 3 blanks K  5 blanks 

31d  Relating to the lens of the eye and being convex on both sides. -  -  -  T  -  C  -  L  -  R    Looks like something OCULAR

12a  The formal act of adding to one's own territory by conquest or appropriation.  4 blanks T 1 blank T 3 blanks.

[ST]

21d dead reckoning

31d Lenticular

12a Annexation

[cheshunt]

Many thanks ST  I have heard of Dead Reckoning, now I know what it means.  Glad you were not put off by a wrong letter in 15a, I started to write Chartres in the wrong place.

[ghs]

21d     DEAD RECKONING

31d     LENTICULAR

15a (not 12 as quoted)   ANNEXATION