Monday, March 06, 2006

 

Keeping Time

Okay, so now I'm confused. I've been working on questions of time-keeping and time-scales for the space opera, and thought I had it licked, until I remembered that Earth's orbit is an ellipse, and not a circle. As a result, seasonal shifts in the Earth's orbital speed and distance from the sun, which puts it deeper into the sun's gravitational well, mean that terrestrial clocks actually tick slower at some times of the year than others. Right?

So if you're a near-future space man, hanging out on a mining station in the Asteroid Belt, communicating back and forth with your corporate bosses on Earth, does your chronometer--oh, hell, let's just call it a "clock"--have some sort of integrated logic to compensate for the differing clock-speeds as the Earth moves around in it's orbit? (And I'm assuming here that the asteroid in question orbits in a perfect circle, and so doesn't have any changes due to relativistic effects itself.) You're already going to be a few minutes "behind" your boss, in any radio communication, given the lag of several light-minutes between the Earth and the Belt, so simultaneity is already a pretty tricky concept, but what I can't work out is whether there's any cumulative effect from the different clock-speeds, or whether it all evens out when the Earth-clocks "speed-up" again.

How does NASA handle this, when programming or communicating with robotic probes sent out to the outer planets? As the probes move further out into the sun's gravity well, don't their clock-speeds change, as well? Since a lot of the maneuvers have to be performed at extremely precise moments, how do the programmers compensate?

I wish my skills at mathematics weren't so horrible. I sometimes brush near understanding the concepts in physics, but the ability to grasp the underlying formulae and calculations are just completely beyond me.

Comments:
The clocks don't tick slower or faster. They change with respect to an outside obsever. It's all relative, only the speed of light is constant.
The seasons are not due to the distance from the sun, they are caused by the tilt of earth's axis.
Earth's orbit is an elipse, but almost close to a perfect circle when compared to the dimensions. Any effects due to the proximity of the sun would probably be negligible, and only measureable with an atomic clock.
 
Pat, but doesn't General Relativity say that, if you have two observers, each with a clock, one of them deep in a gravity well and the other farther out, that from the perspective of both the lower clock would be running slower than the higher one? That's really the time dilation I'm thinking about, here. Even if the differences are measureable only by really precise atomic clocks, it seems to me that it would impact the timing of precise manuevers. Or wouldn't it?
 
I'm not a physicist, only an engineer . . .

It's relative. You have to assume one clock is not moving at all. Then, to the observer who is not moving, the other clock, wehter at the bottom of a gravity well or moving at 0.9c is the one that looks funky. The person moving 0.9c or at the bottom of a gravity well, his clock looks fine. It's the other guy's clock that isn't working.

As for timing precice manuevers, any effect would probably be too small. I just fliped through a book on astrodynamics, and couldn't find any mention of considering realativist effects. Remember, the ship making the manuever has its own clock, and it looks OK to them!

Pat
 
Time dilation is absolute in the sense that, when you bring the clocks back together to compare them, everyone will agree on which one of the clocks has been running slower than the other.

However, the differences are not going to be significant for orbital manuevers. The launch windows for interplanetary probes are measured in days or weeks. Changes of a fraction of a second won't matter.
 
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