According to the International Astronomical Union and famous physicist Johnny Wheeler, you should omit the definite article and capitalize Sun, Moon, and Earth.
From Wheeler's book Spacetime Physics on page 32:
Note: Neither astronomers nor newspapers say "the Venus" or "the Mars." All say simply "Venus" or "Mars." Astronomers follow the same snappy practice for Earth, Moon, and Sun. More and more of the rest of the world now follows -- as we do in this book -- the recommendations of the International Astronomical Union.
The ocean's rise and fall in a never-ending rhythmic cycle bears witness to the tide-driving power of Moon and Sun. In principle those influences are no different from those that cause relative motion of free particles in the vicinity of Earth.