Empty the universe of all matter. Place the Earth in that universe sitting in an inertial frame. Take a pair of twins. One twin gets into a space ship and takes off from Earth (t=a). He accelerates rapidly and obtains .9c within a day of Earth's time and then turns off his engines (t=b). He then glides for 4 Earth years. After 3 Earth years 364 earth days (t=c), he starts to decelerate the ship, turns it around and returns to Earth the exact same way he left (1 earth day to decelerate 1 earth day to accelerate). After 4 years, he decelerates for one Earth day as he approaches Earth and then lands the ship 8 years to the day after he took off.
My understanding is that the stay-at-home twin has now aged 8 years. The spaceship twin has aged less than that (about 7 years). If we assume linear acceleration the 4 Earth days of acceleration account for 2 days equivalent of time discrepancy. The remaining 7 years 361 days account for the majority of the discrepancy.
Question 1: Is that analysis correct?
Now, I repeat the experiment, spaceship twin takes off in the spaceship as before, but now as soon as he hits Earth orbit he parks his ship. stay-at-home twin attaches a really big rocket engine to the Earth itself and blasts the planet away from his brother. The distances versus time between the ship and Earth is exactly as before.
I assume now the spaceship twin will have aged 8 years and the Earth twin will have aged about 7 years.
Question 2: Is that correct?
I repeat the experiment one last time. As before the spaceship twin blasts off of Earth. This time however he accelerates to .45c; his brother again attaches the rockets to the Earth and accelerates it .45c. Again they maintain the exact same distance to time relationship.
My guess now is that when the brothers meet they will be the exact same age.
Question 3: Is this correct?
Question 4: In each of these scenarios from t=b to c the systems appear to be exactly equal to one another. The ship and the Earth are receding from one another at .9c. Where is the difference in their situations stored? How would an outside observer differentiate the 3 scenarios?
Question 5: It appears that time dilation, length contraction is really caused by acceleration not velocity. Why does acceleration not show up in the special relativity formulas? Is perhaps velocity in these equations not really velocity, but rather the integral of acceleration?