The period in space is shown as 1.03521, which appears to have enough significant digits but the leading value of 1 is thrown away and left with the Delaunay value of F=1/(1/1.03521-1-1/365.242) =-27.2106. Then the value is closer to what is in the paper. Perhaps one more significant digit is needed after 1.03521_ to resolve this issue. To get to 27.212, the value needs to be 1.035207, which indicates that the value *could have been* rounded up. This is frustrating because the final result has 7 digits, which is more precision than the "period in space" shown.
The other possibility is in what is considered a year. There is the tropical year which is essentially the calendar year 365.242 days. Or the sidereal year which is 365.256 days and the anomalistic year which is 365.2596 days. If one of these other definitions is necessary for the calculation -- for example they do mention sidereal time which is used for a [space-relative reference frame](https://en.wikipedia.org/wiki/Year#Sidereal.2C_tropical.2C_and_anomalistic_years) -- that would be enough slop to close up much of the difference.
Ft = 27.2106*365.242/365.256 = 27.20956 tropical days
This is closer to the 27.20986 days they give.
This book [Space-Time Reference Systems](https://books.google.com/books?hl=en&lr=&id=FhKfr3ZPX6kC&oi=fnd&pg=PR5&ots=F45F0Af2YJ&sig=53Gk5ijEK95YnEaq7SDf61_DSXg#v=onepage&q&f=false) may give some insight.
Sorry for this thread getting too pedantic but that always seems to happen when the result is homing in on a potentially solid match.
This is the difference between using 27.209 days 27.212 days in a QBO fit. The value of 27.209 days results in a correlation improvement, which is marginally noticeable by eye.