At the beginning of the space mission (space angle of max. 5%), the measured values (of time and speed) will be almost the same for both sides, but with the increasing time of the flight (increasing speed), the time on Earth will be accelerating more and more from the astronaut’s point of view. Conversely, in the Earth optics, the time and speed of the astronaut will be decelerating. In summary, the time disproportion will be increasing faster.
The above-mentioned schematic shows the unit circle mathematics under uniformly accelerated motion. For an internal astronaut on a space mission, nothing “non-standard” will happen. His speed will increase without limits – linearly with time: By looking into binoculars in the direction of Earth (or by using measuring devices), the astronaut will record that the time on Earth is accelerating in comparison with his time (the ratio is determined by secans in the scheme). Observers from Earth will record the inverse situation in comparison with the astronaut. From their perspective, the astronaut’s clock will experience a slowdown (ratio determined by cosine in the scheme), and the speed will decelerate in the same ratio, measured externally by the astronaut, getting extremely closer to ve = c = 1. more on: