Time Machine - One way of course.

Considering the feasibility of a time accelerator

Spinning pods/missiles for you and a friend

I've often considered the possibility of accelerating someone to relativistic speeds in order to slow their experience of time relative to the rest of earth. The serious issue would seem to be that it would require huge amounts of energy to accelerate to those speeds, and even worse, to slow down and come back to earth.

A simplified solution might be to revolve someone, ideally a pair of someones (this is the kind of trip best taken with a friend) up to relativist speeds. This gives the advantage that you do not have to travel as far from earth, and supplies could be delivered to the center of revolution to some kind of tether keeping the two objects together.

​So lets check the math.

In order for this trip to be a decent use of time, you need a good return on your invested time. I would want at least a ten times speed acceleration. Trade 3 years to skip 30 earth years. So this sets our desired speed.

Our other constraint on this journey is the maximum force exerted on a travelers body. Since this will be a long trip, I will set this at 3G - 3x earth's gravity, which will probably still suck for your internal organs.

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Speed
So how fast do we need to be moving to get this back to the future-esque effect?

Damn. 0.995c is very close to the speed of light. For comparison, the crew of Apollo 10 reached almost 40000kph on their return voyage from the moon,  the fastest any human has ever traveled. We want to travel about 27000 times that fast!

Acceleration
Lets get up to speed. Again, we will limit the acceleration to 3G to make some attempt at keeping this passenger alive. 
​Total time to get up to speed is 117.5 days. Not bad! Kind of like a really long roller coaster ride.

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Energy
Okay, we know what we have to do; accelerate someone up to .995 times the speed of light. This will require energy. Significant amounts of energy. Let's use the current state of the art, a high power ion engine. Their efficiency is around 60-80%, but lets call it a nice round 100% for now.

We can see that just the kinetic energy involved would be 4x10^20 J. That would require an average power input of 40 TeraWatts. Hmmmm, that's really getting up there. The average global power production is only 2.4 TW. Maybe you have some friends in high places that are willing to amp up global power 17 times and give you ALL OF IT. You only need it for 117 days right?
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Physical Size
You borrowed the power, you know what to do with it and how long it will take. So how long does this tether between you and your friend need to be? It would be 6x10^15m or 0.6 light years across.

Shit, that's about 40 000 000 Astronomical Units (AU), which is 40 million times the distance from the earth to the sun. A 20cm cable would be about 5x10^13 cubic meters. But good news! there is in fact enough aluminum in the earth to make a cable that size!

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Conclusion
Unfortunately, it looks like no one will be taking any trips to the future for at least a while. The size and power requirements of the device are immense, and it would take technology well beyond ours just to get the raw materials off of earth.

However it is something fun to think about. Perhaps some day we can overcome the maximum force issue that causes the device to be so large, and we will have new sources of power that will make these numbers seem smaller. Until then, this will remain a thought experiment.