>>The Earth around which you are orbiting is stationary with respect
>>to spacetime
>
> You mean there's a fixed reference for space and time?

You mean there isn't ? ;-)

Everything is/has its own reference

Take the well-known travelling clock example. A clock which is
moving passes time slower than one which is moving less fast.
Which is true because the clocks in GPS satellites need constant
correction. The satellites are moving relatively fast compared with
the reference of interest - us

Applying that to your paradox, an object orbiting The Earth will
age more slowly. If The Earth was orbiting the object then The
Earth would age more slowly

If they were orbiting each other equally (like binary stars or black
holes do) then they would not appear, to each other, to be ageing
unequally, if they were moving at the same speed. However, to a
slower-moving observer they would be ageing equally more slowly
than the observer

Any two objects connected orbitally perturb each other and change
the apparent passage of time. A satellite steals gravitational energy
from The Earth *, which in turn wobbles only ever so ever so slightly,
due to the enormous mass difference between a satellite and The
Earth. An elliptical orbit of a satellite will cause The Earth to=20
alternately
accelerate and deccelerate minutely, causing temporal fluctuations

* energy stealing is the principal behind slingshotting spacecraft and
one method of detecting exoplanets and other companion objects=20

--=20
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