It is given that the angular size of the Sun as viewed from Earth is $0.533^\circ$, the distance of the Moon from Earth at perigee is $3.633\times 10^5$ km, and the mean radius of the Moon is $1737.1$ km.
Suppose that the perigee of the Moon is receding from Earth at a uniform rate of $4$ cm/year. Estimate how long it will take to reach "final totality" (i.e. when we can no longer observe total solar eclipse on Earth).