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If I understand special relativity correctly, when we accelerate an object around earth (or back and forth to another planet), the clock on the projectile will slow down and thus effectively time would be slower and the people on the projectile couldn't get as much done (as they have less time) relative to earth time.

specialrelativity

This got me thinking about the reverse situation. Is it possible for us (as humanity) to increase time relative to earth? [Akin to Dragon Ball's Hyperbolic time chamber]

If we manage to stop the earth rotating around the sun [$\approx 29.78km/sec$] (without falling into it) we would save $\approx 0.156$ seconds per year!

If we manage to just stop orbiting the earth [$\approx 46 m/s$] we would save $\approx 38$ microseconds per year.

If we manage to stop rotating around the milky way [$\approx 220 km/s$] we would save $\approx 8.5$ seconds per year.

If we manage to stop rotating relative to the cosmic microwave background [$\approx 370 km/s$] we would save $\approx 24$ seconds per year.

So my question is this. Is my reasoning correct (I only know special relativity) and is there any other ways or more effective ways we could increase time relative to earth (I'm not familiar with general relativity)?

Even with numbers like this it might be something worth striving for one day in the face of, well, the end of our universe.

ADDENDUM:

Time dilation equation: $\Delta t' = \frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}$

where $\Delta t$ is the time of the clock standing still and $\Delta t'$ is the time of the clock moving.

Solving the equation from the perspective of the the stationary earth $\Delta t = \Delta t' \cdot \sqrt{1-\frac{v^2}{c^2}}$

$31558149.504*\sqrt{1-29780^2/299792458^2} \approx 3.1558149.348..$ and subtracting it from the time $31558149.504-3.1558149.348 \approx 0.156$ we would save 0.156 seconds!!

where:
delta t' = 31558149..504 = 24*60*60*365.25636 = seconds in a year/orbit
v = 29780 m/s = average meters per second of earth orbit
c = 299792458 m/s = light speed in m/s
31557600 = seconds/year = seconds/orbit

Similarly, for the sun: $31558149.504 - 31558149.504*sqrt(1-220000^2/299792458^2) \approx 8.497$

Similarly, for the cosmic microwave radiation: $31558149.504 - 31558149.504*sqrt(1-370000^2/299792458^2) \approx 24.035$

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The important point to remember is that by performing all these miracles to change the movement of the Earth you are only changing our time relative to someone else's. We wouldn't notice the difference.

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  • $\begingroup$ Let's say you copy earth and one keeps on orbiting and the other stays at the point. The sun will explode in say 1 billion years. Then the people on the still earth have more time to prepare for it, no? $\endgroup$ – Kevin De Keyser May 18 at 10:22
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No. Your proper (wristwatch) time can go a lot slower than "earth time" if you travel quickly & return, but there is no mechanism that can make your proper time elapse faster than earth time (which is itself not much less than the maximum; free-fall time).

Doing nothing (free-fall in outer space) gives you the maximum possible rate of elapsed time. Travelling, or being in a gravity well can decrease that rate below the maximum, but it cannot be increased.

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There is only one way to make time go faster for you. If you stay one year in outer space, far away from matter that can cause spacetime to curve, your time will go faster than the time on Earth (the "amount of time" will increase). so if you stayed for a while between the Milky Way and Andromeda, there will have more time passed for you than for people on Earth. It won't be much though. Check out this question.

One more thing. If the blue sphere in your animation represents the sun (and the red one the Earth), then time on the blue sphere will go slower than time on the red sphere (even if the red sphere has a velocity wrt the blue sphere).

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  • $\begingroup$ I want time to go slower though. $\endgroup$ – Kevin De Keyser May 18 at 10:20
  • $\begingroup$ @KevinDeKeyser Then you must accelerate away from Earth, travel a while with increasing (or constant 0 speed (say that you can reach half the speed of light), reverse your velocity, turn back on Earth, and then you will see that you haven't aged as much as the people on Earth. Shall I give another answer? $\endgroup$ – Deschele Schilder May 18 at 10:54

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