Reduce a single solar observation and convert it to a grid azimuth in NAD $83(2011)$ Maine East Mercator. The occupied point is Q$,$ and the backsight point is $4.$ The geodetic coordinates of point Q are latitude

$4$

$4$

$$

$5$

$4$

$$

$06\mathrm{.}5655$

$2$

$$

$$

$44$

$$

$54$

$$

$06\mathrm{.}56552$

$$

N$,$ longitude

$6$

$8$

$$

$4$

$0$

$$

$04\mathrm{.}6576$

$1$

$$

$$

$68$

$$

$40$

$$

$04\mathrm{.}65761$

$$

W$,$ with an ellipsoidal height of $33\mathrm{.}2950$ feet. The scale factor at point Q is $0\mathrm{.}9999021631,$ and the convergence angle is

$$

$0$

$$

$0$

$7$

$$

$0$

$7$

$$

$$

$0$

$$

$07$

$$

$07$

$$

$.$ Point $4$ has a latitude of

$4$

$4$

$$

$5$

$4$

$$

$06\mathrm{.}4129$

$8$

$$

$$

$44$

$$

$54$

$$

$06\mathrm{.}41298$

$$

N$,$ longitude

$6$

$8$

$$

$4$

$0$

$$

$09\mathrm{.}6804$

$0$

$$

$$

$68$

$$

$40$

$$

$09\mathrm{.}68040$

$$

W$,$ an ellipsoidal height of $32\mathrm{.}3590$ feet, a scale factor of $0\mathrm{.}9999021988,$ and a convergence angle of

$$

$0$

$$

$0$

$7$

$$

$1$

$0$

$$

$$

$0$

$$

$07$

$$

$10$

$$

$.$ The plane coordinates for point Q are Northing $450287\mathrm{.}5860$ feet and Easting $940731\mathrm{.}6510$ feet, while point $4$ has Northing $450272\mathrm{.}8900$ feet and Easting $940370\mathrm{.}1190$ feet. The GHA of the Sun at $0$ hours UTC is

$18$

$2$

$$

$2$

$6$

$$

$12.$

$6$

$$

$$

$182$

$$

$26$

$$

$12\mathrm{.}6$

$$

and at $24$ hours UTC is

$18$

$2$

$$

$3$

$1$

$$

$07.$

$1$

$$

$$

$182$

$$

$31$

$$

$07\mathrm{.}1$

$$

$.$ The declination at $0$ hours UTC is

$$

$2$

$$

$3$

$4$

$$

$42.$

$3$

$$

$$

$2$

$$

$34$

$$

$42\mathrm{.}3$

$$

and at $24$ hours UTC is

$$

$2$

$$

$5$

$8$

$$

$0.$

$6$

$$

$$

$2$

$$

$58$

$$

$0\mathrm{.}6$

$$

$.$ The initial circle reading on the backsight is

$15$

$9$

$$

$3$

$0$

$$

$15.$

$0$

$$

$$

$159$

$$

$30$

$$

$15\mathrm{.}0$

$$

with an observation of the Sun at $8$:$16$:$38$ AM EDT, corresponding to $12$:$16$:$27$ UTC. Use this information to compute the grid azimuth and compare it to the azimuth derived from the RTK GPS coordinates in the Maine East survey feet.