Co ordinates in Space Time

Suppose we have an "origin" in SpaceTime.

It emits regular pulses of light .

From this origin (O) 2 objects(A and B) are sent in orthogonal directions (A traveling 4/3 times faster than B) and at all times they use measuring equipment (light emitters and receivers) to measure their current distance from O and also each other.

After a predetermined length of time (the same length of time measured by both A and B) both A and B measure their distance from each other and also O.

If A measures (a multiple of)4 light seconds to O and B measures (the same multiple of ) 3 light seconds to O is it the case that both A and B will measure (the same multiple of ) 5 light seconds to each other in the absence of any massive bodies causing a local gravitational field?

Is this what is meant by Space Time being **flat** in the absence of gravity?

And if 5 light seconds is **not **measured does this show that __Space Time has in fact been curved__ by the presence of a massive body?

If there are no mistakes here ,can I pat myself on the back?:)

EDIT:I now realize that the relative motions of A and B and O complicates(=messes up) the calculation but can I factor them out and make them (unrealistically) stationary wrt each other) at the moment of measurement?

Do my "flat" and "curved" descriptions now hold?