leica laser tracker question on measuring sphere

You're measuring a very, very, very small part of a large sphere, and expect it to be reliable? What about the uncertainty in each measuring point? How many points do you measure? What's the uncertainty of your measuring device?

I did an experiment on a circle with three points, with your numbers for radii, and all that's needed to change the diameter ~1in was an error of one micron (0.001 mm) in each of the measuring points...

(code in mm)

STARTUP =ALIGNMENT/START,RECALL:USE_PART_SETUP,LIST=YES
ALIGNMENT/END
MODE/DCC
FORMAT/TEXT,OPTIONS, ,HEADINGS,SYMBOLS, ;NOM,MEAS,TOL,DEV,OUTTOL, ,
LOADPROBE/ALLA
TIP/T1A0B0, SHANKIJK=0, 0, 1, ANGLE=0
PNT1 =FEAT/CONTACT/VECTOR POINT/DEFAULT,POLAR
THEO/<7137.4,0,0>,<-1,0,0>
ACTL/<7137.399,0,0>,<-1,0,0>
TARG/<7137.4[COLOR=#FF0000]-0.001[/COLOR],0,0>,<-1,0,0>
SHOW FEATURE PARAMETERS=NO
SHOW CONTACT PARAMETERS=NO
PNT2 =FEAT/CONTACT/VECTOR POINT/DEFAULT,POLAR
THEO/<7137.4,6.093,0>,<-0.9943509,-0.1061426,0>
ACTL/<7137.401,6.093,0>,<-0.9943509,-0.1061426,0>
TARG/<7137.4[COLOR=#FF0000]+0.001[/COLOR],6.093,0>,<-0.9943509,-0.1061426,0>
SHOW FEATURE PARAMETERS=NO
SHOW CONTACT PARAMETERS=NO
PNT3 =FEAT/CONTACT/VECTOR POINT/DEFAULT,POLAR
THEO/<7137.4,353.907,0>,<-0.9943509,0.1061426,0>
ACTL/<7137.401,353.907,0>,<-0.9943509,0.1061426,0>
TARG/<7137.4[COLOR=#FF0000]+0.001[/COLOR],353.907,0>,<-0.9943509,0.1061426,0>
SHOW FEATURE PARAMETERS=NO
SHOW CONTACT PARAMETERS=NO
CIR1 =FEAT/CIRCLE,CARTESIAN,IN,LEAST_SQR,NO
THEO/<0,0,0>,<0,0,1>,14274.8
ACTL/<-0.354,0,0>,<0,0,1>,[COLOR=#FF0000]14275.506[/COLOR]
CONSTR/CIRCLE,BFRE,2D,PNT1,PNT2,PNT3,,
OUTLIER_REMOVAL/OFF,3
FILTER/OFF,UPR=0

{"data-align":"none","data-size":"full","data-attachmentid":424497}

I see less than 1mm in size error.... (0.706mm to be picky) not an inch.