I agree with you but our duration of observation is in the state where rocket has achieved the required speed and is moving with zero acceleration, so that makes the 2nd option correct. although you are also correct to think that practically it must have accelerated to be where it is.
But how can it affect it ? I mean if the rocket is hypothetically not very far from earth's surface, i.e., within the range of kilometers where effect of altitude on gravitational pull on rocket by earth is not significant,
and the rotation of our earth from which we observe is also not...