Close. Of course Eve and Adam agree on the number of Earth day-nights that have happened between Eve's departure and return. Eve sees all of the Earth-clocks as running slow. That includes the Earth's spin. She thinks it takes more than 24 hours, as defined by her wristwatch. So she thinks the spinning Earth and Adam and his clocks are all slow by some shared factor, about (1/(1+gR/c
2)), where g is the gravitational acceleration at the earth's surface, R is the radius, and c is the speed of light. That's (1- 6.7*10
-10). There's no real problem or even complication here.
Mike W.
(published on 02/13/2011)