Final totality: The final total solar eclipse will be in 600 million years time, as the moon will be around 30,400km further from the Earth while the sun’s diameter will be around 5% larger

Total solar eclipses are seen on Earth because of a fortuitous combination of circumstances. But when will be the last, the real final totality?

The final total solar eclipse will be in 600 million years time, as the moon will be around 30,400km further from the Earth while the sun’s diameter will be around 5% larger

Even on Earth, the diversity of eclipses familiar to people today is a temporary (on a geological time scale) phenomenon.
Hundreds of millions of years in the past, the Moon was closer to the Earth and therefore apparently larger, so every solar eclipse was total and there were no annular eclipses.

Solar corona during totality. By M. Druckmüller via NASA

Over a billion years in the future, the Moon will be too far away to fully occlude the Sun, and no total eclipses will occur.
Due to tidal acceleration, the orbit of the Moon around the Earth becomes about 2.2 cm more distant each year.

Total Solar Eclipse from Palu, Indonesia on March 9 2016. via Space.com

It is estimated that, in slightly less than 1.4 billion years, the distance from the Earth to the Moon will have increased by 30,400 km.
During that period, the apparent angular diameter of the Moon will decrease in size, meaning that it will no longer be able to completely cover the Sun’s disk as seen from the Earth. This will be true even when the Moon is at perigee, and the Earth at aphelion.

A solar eclipse like on August 21 2017 across the USA. via Time and Date

Moreover, the Sun is increasing in diameter by about 5% per billion years.
Therefore, the last total solar eclipse on Earth will occur about six hundred million years from now.

http://strangesounds.org/2017/08/final-totality-final-total-solar-eclipse-will-be-in-600-million-years-time-as-the-moon-will-be-around-30400km-further-from-the-earth-while-the-suns-diameter-will-be-around-5-larger.html