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.
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: $31558149.504 - 31558149.504*sqrt(1-370000^2/299792458^2) \approx 24.035$