Thanks for the calculation.  I also consulted the formula in the Condon

Report (Bantam ed. p. 190;  or on the Web at National Capital Area Skeptics

website) which might be more accessible for some who have problems downloading a

PDF (or analyzing the algebra).  And I got a magnitude of -2.1 from the CR's

formula which is even less bright than the mag -4.6 you got for a 73-ft (22 m)

balloon at 140 miles (225 km).  I agree that just like Venus it is almost

invisible in the daytime sky. 

I am not sure where you got the 73 by 129 ft figures from but I suspect that

if the balloon plastic envelope is 73 ft that the 129 is the total length with

both balloon and cable/package thus the latter is 56 ft long (73 + 56 = 129

ft). 

Your 1970 satellite analysis report from North American Rockwell (PDF p. 9),

based on 22,000 observations of satellites including the Echo balloon

satellites, gives the formula:

m = -26.58 - 2.5log[AYF/R^2]

where A is cross-sectional area of the object (pi times radius squared for a

sphere or circular flat plate), Y is the reflectivity (assume 100% for maximum

conceivable even though that is impossible), F is the phase factor depending

on sun-observer-object angle and they give a table of formulas to calculate it

on p. 10 (but the maximum would be 0.21), and R is the slant range to the

object.  Use consistent units throughout for A and R (if meters then don't use

kilometers anywhere else in the formula, if you use feet don't use miles

elsewhere, etc.).  . 

The Condon Report formula is:

m = -7.16 - 5logD +5logR,

where D is diameter of object, R is slant range, again use consistent units

for both D and R. 

I do know an optical physicist interested in UFO's, indeed the leading

expert, Dr Bruce Maccabee, and I'm "cc-ing" him here if he should have any comments.

 

Bottom line:  No way the 70-foot Skyhook between Nashville and Columbia could

be seen to the naked eye 140 miles away at Godman Tower or by Mantell and his

wingmen or by various civilians calling in to Kentucky State Police about a

250-300-foot disc traveling W at a "pretty fast clip," which is the report that

triggered the alert at Godman at 1 PM that day (plus others, still being

sorted out).