We think of two very similar scenarios:

1. Two twins are hoovering with their spacecrafts at an earthlike distance A from the Sun and with no velocity with respect to the Sun. Then one of the twins suddenly accelerates to 100 km per second in some direction. He is now the accelerated twin. After a while when he reaches a Plutolike distance from the Sun B the accelerated twin stops so the two twins are at rest with respect to each other. Then both takes off at 100 km/s and meets in the middle and stops and compare their clocks. They agree that less time have elapsed for the twin that has been travelling at an accelerated speed for a longer period of time.

2. Two twins are flying their spacecrafts in parallel just next to each other at 100 km/s with respect to the Sun. Suddenly, at an earthlike distance A from the Sun, one of the twins accelerates by 100 km/s so that he now is at rest in relation to the Sun . He is now the accelerated twin. The other twin happily flies on at constant velocity in his inertial reference frame until he reaches a Plutolike distance from the sun B where he suddenly accelerates by 100 km/s in the same direction that his twin accelerated. The two twins are now at rest with respect to each other and the Sun. Then both takes off at 100 km/s and meets in the middle and stops and compare their clocks. Now what will their clocks show? Will the clock of the twin that did not accelerate until he reached B show more or less elapsed time than his twin that started off by accelerating?

We ignore the fact that thet have spent time at different gravitational potential and care only of the effect of velocity on time.

Related Other Physics Topics News on Phys.org
Oops, should have been posted in the relativity forum...