Georgia to Georgia

The flight lasts 11 h 25 min, or 11.417 h, so the distance flown is $875\times 11.417=9990$ km, an arc of $9990/6378=1.566$ rad, or 89.74°, on Earth's surface.

A star south of the zenith is due south when it crosses the meridian, which is its highest point. If it only touches the horizon there, its highest altitude at that place is zero. For a star south of the zenith (1.12) gives $h_{max}=90°-(\phi -\delta )$, which falls as the observer moves north. The star is seen throughout the flight, so $h_{max}$ cannot be negative anywhere on the route, and the place where it is zero must be where it is smallest, the northernmost point N of the route. Setting $h_{max}=0$ gives

At its northernmost point a great circle runs exactly east to west, so it crosses the meridian through N at a right angle. Let P be the North Pole and A be Tbilisi. In the spherical triangle PAN the angle at N is 90°, with sides $PN=90°-{\phi }_{\text{N}}=30.07°$ and $PA=90°-{\phi }_{\text{A}}=48.28°$. For a right-angled spherical triangle (Section 1.5),

The angle at P is the difference in longitude between Tbilisi and N.

The rest of the route is $NB=89.74°-39.74°=50.00°$. Triangle PNB also has a right angle at N, so

The latitude of Atlanta is $90°-56.20°=33.80°\text{ N}$. Atlanta lies west of Tbilisi by $58.93°+67.20°=126.13°$, so its longitude is $41.80°-126.13°=-84.33°$, that is, 84.33° W.