North pole is point P.
Albany is point A.
Tallahassee is point T.
The moon is over point M.
Line (arc) PA is 90 minus the latitude of Albany.
Line (arc) PT is 90 minus the latitude of Tallahassee.
Angle APT is the difference in longitudes of the two cities.
Find line AT and angle PAT:
AT=acos(cos(PT)*cos(PA)+sin(PT)*sin(PA)*cos(APT))
PAT=acos((cos(PT)-cos(PA)*cos(AT))/(sin(PA)*sin(AT)))
These come out as
AT = 14.8286706264398°
PAT = 142.024005446739°
The great circle toward the moon is at right angle to that connecting Albany to Tallahassee, so angle PAM is 90° plus the supPlement of angle PAT, or 270-PAT. Side (arc) AM is 90°, so the distance from the pole to the sublunar point, or PM, is given from
PM=acos(cos(PA)*cos(AM)+sin(PA)*sin(AM)*cos(PAM))
and the complement of this is the declination. These come out
PM = 116.9081137328°
dec = -26.9081137327996°
So, removing the excess precision, the moon is at 26.9° South. This is outside the tropics, which is possible as the moon's orbital plane is tilted about 5° from that of the Earth's around the sun. During the course of an 18.6-year cycle, this can add to or take away from the sun's 23.45° excursions from the equator, to give the Moon's monthly excursions. |
