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erics
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Suppose you have two ships departing from Earth at the same time, Ship #1 and Ship #2. Both ships depart Earth in the year 2000, both in the same direction from earth, and both Ships return to Earth in the year 2020, so 20 Earth Years for BOTH ships...
Ship #2 does something somewhat different from Ship #1, you'll see
From Earth's Reference Frame:
Ship #1 Cruises at a Velocity of 86.6025% of C, which is a Lorentz Factor of 2... for half the 20-year duration... then the ship returns to Earth. Based on Twin Paradox, the ship's clock ticks half of 20 years... so the ship ages 10 years.
Ship #2 Cruises at the same velocity as Ship #1, but only for the first 6 Earth Years of time.
Between Years 7 thru 10:
After 6 years time, Ship #2 gains additional velocity and passes ahead of Ship #1 at a Velocity of 98.7433% of C with respect to Earth (Lorentz Factor of exactly 7).
Then at some point in time, Ship #2 de-accelerates to 0 km/h with respect to Earth and waits patiently for Ship #1 to catch up to Ship #2. Ship #1 catches up to Ship #2 after 10 Earth Years Time.
Note Ship #1's Reference Frame Between
But based on U - V / (1 + U*-V), the Ship #2 was moving ahead of Ship #1 at 86.6025 of C, Lorentz Factor of 2... and then would have appeared to head back towards ship #1 also at 86.6025% of C.
After 10 Earth Years:
Both Ship #1 and Ship #2 return to Earth side by side at 86.6025% of C with respect to Earth, arriving home to Earth in the year 2020...
Now looking at Years 7 thru 10, however much Ship #1 was aging, Ship #2 would be aging half as much, because with respect to Ship #1's frame of reference, Ship #2 accelerated to Lorentz Factor 2 speed... then moved back towards ship #1 at Lorentz Factor 2 speed (while ship #2 was moving 0 with respect to Earth it was moving backwards with respect to Ship #1)...
Based on the same logic as the Twin Paradox... this would result in a situation where Ship #2 aged one year less than Ship #1, because during the 4 Earth Years Ship #2 parted from Ship #1... Ship #1 would age 2 years and Ship #1 would have aged half of that... 1 years less aging than Ship #2... or is this wrong?
During years 7 thru 10, Ship #1 did not exert any force as it kept its contant cruising velocity. The same would hold true for Earth... eventhough they were traveling at different velocities.
So here is what gets confusing to me.
From Ship #1's Reference Frame:
It would appear that between Earth years 7-10, Ship #2 spent 50% of the time moving farther away from Ship #1, and 50% of the time moving back towards Ship #1... for with respect to the ship... the relative speed of Ship #2 was 86.6025% of C
From the Earth's Reference Frame:
I would appear that between Earth years 7-10, Ship #2 spent much more time moving away from Ship #1 compared to the time it took Ship #1 to catch back up to Ship #2.
Ship #2 would have appeared to move 98.7433% of C away from Earth while Ship #1 was cruising at 86.6025% of C away from Earth... a velocity difference of only 12.1408% of C...! Then when Ship #2 stopped moving and waited for Ship #1 to catch up, this would have appeared to be a movement of 86.6025% of C for BOTH Earth and the ship...
so what's confusing to me is given the Earth AND Ship #1 are not accelerating/deacclerating since only Ship #2 is exerting force and shifting in speeds...
Why does it make sense relativity wise that Earth and Ship #1 would disagree on the PERCENTAGE of duration it took Ship #2 to move farther away from Ship #1... VS. the percentage of duration the ship #1 was moving closer to Ship #2...?
Can someone explain this discrepancy or correct me if my assumptions are incorrect?
Thanks!
Ship #2 does something somewhat different from Ship #1, you'll see
From Earth's Reference Frame:
Ship #1 Cruises at a Velocity of 86.6025% of C, which is a Lorentz Factor of 2... for half the 20-year duration... then the ship returns to Earth. Based on Twin Paradox, the ship's clock ticks half of 20 years... so the ship ages 10 years.
Ship #2 Cruises at the same velocity as Ship #1, but only for the first 6 Earth Years of time.
Between Years 7 thru 10:
After 6 years time, Ship #2 gains additional velocity and passes ahead of Ship #1 at a Velocity of 98.7433% of C with respect to Earth (Lorentz Factor of exactly 7).
Then at some point in time, Ship #2 de-accelerates to 0 km/h with respect to Earth and waits patiently for Ship #1 to catch up to Ship #2. Ship #1 catches up to Ship #2 after 10 Earth Years Time.
Note Ship #1's Reference Frame Between
But based on U - V / (1 + U*-V), the Ship #2 was moving ahead of Ship #1 at 86.6025 of C, Lorentz Factor of 2... and then would have appeared to head back towards ship #1 also at 86.6025% of C.
After 10 Earth Years:
Both Ship #1 and Ship #2 return to Earth side by side at 86.6025% of C with respect to Earth, arriving home to Earth in the year 2020...
Now looking at Years 7 thru 10, however much Ship #1 was aging, Ship #2 would be aging half as much, because with respect to Ship #1's frame of reference, Ship #2 accelerated to Lorentz Factor 2 speed... then moved back towards ship #1 at Lorentz Factor 2 speed (while ship #2 was moving 0 with respect to Earth it was moving backwards with respect to Ship #1)...
Based on the same logic as the Twin Paradox... this would result in a situation where Ship #2 aged one year less than Ship #1, because during the 4 Earth Years Ship #2 parted from Ship #1... Ship #1 would age 2 years and Ship #1 would have aged half of that... 1 years less aging than Ship #2... or is this wrong?
During years 7 thru 10, Ship #1 did not exert any force as it kept its contant cruising velocity. The same would hold true for Earth... eventhough they were traveling at different velocities.
So here is what gets confusing to me.
From Ship #1's Reference Frame:
It would appear that between Earth years 7-10, Ship #2 spent 50% of the time moving farther away from Ship #1, and 50% of the time moving back towards Ship #1... for with respect to the ship... the relative speed of Ship #2 was 86.6025% of C
From the Earth's Reference Frame:
I would appear that between Earth years 7-10, Ship #2 spent much more time moving away from Ship #1 compared to the time it took Ship #1 to catch back up to Ship #2.
Ship #2 would have appeared to move 98.7433% of C away from Earth while Ship #1 was cruising at 86.6025% of C away from Earth... a velocity difference of only 12.1408% of C...! Then when Ship #2 stopped moving and waited for Ship #1 to catch up, this would have appeared to be a movement of 86.6025% of C for BOTH Earth and the ship...
so what's confusing to me is given the Earth AND Ship #1 are not accelerating/deacclerating since only Ship #2 is exerting force and shifting in speeds...
Why does it make sense relativity wise that Earth and Ship #1 would disagree on the PERCENTAGE of duration it took Ship #2 to move farther away from Ship #1... VS. the percentage of duration the ship #1 was moving closer to Ship #2...?
Can someone explain this discrepancy or correct me if my assumptions are incorrect?
Thanks!