The correct answer is option 3: Newton`s theory of gravitation.
An annular solar eclipse occurs when the Moon is at a further distance from the Earth, causing it to appear smaller in the sky. As a result, during an annular solar eclipse, the Moon does not completely block out the Sun, leaving a ring of sunlight visible around the Moon.
The duration of annularity refers to the length of time during which the ring of sunlight is visible. In this case, the duration was approximately 12 minutes.
The prediction that such a long annular duration will not occur until the year 3043 is based on Newton`s theory of gravitation. This theory describes the motion of celestial bodies, including the Moon and the Earth, and allows scientists to make accurate predictions about celestial events such as eclipses.
By using mathematical calculations based on Newton`s theory of gravitation, scientists can determine the positions and distances of the Moon and the Earth at different times in the future. This enables them to predict when and how long annular eclipses will occur.
Therefore, the prediction of a long annular duration not occurring until 3043 is possible due to the application of Newton`s theory of gravitation.