‘Every year, the moon moves about 3.8 centimeters (1.5 inches) farther away from Earth. In addition, the sun is slowly growing larger as it fuses hydrogen into helium and consumes its nuclear fuel. The moon has been slowly slipping away from Earth ever since it formed billions of years ago, a time when the moon was closer and larger in the sky. Because it is getting farther away and smaller as viewed by us on Earth, and the sun is getting larger, there is an inevitable day when the moon will become too small in the sky to block the whole sun.
That day is about 600 million years in the future. A paper published by NASA predicts total solar eclipses will end in about 563 million years. However, British astronomer Jean Meeus suggests in his book, More Mathematical Astronomy Morsels, that perturbations in the orbits of the moon and the Earth will result in periods of on-and-off total solar eclipses starting in 620 million years, and the very last one won’t happen until 1.2 billion years from now…’
Source: Popular Mechanics