Difference in Time at Different Altitudes

[Number Six]

I was reading an article recently in (I think) Skeptical Inquirer. It had to do with astrology. Someone had written an article debunking it and of course the astrologers were displeased.

In the study they grouped people whose birth times differed by an average of five minutes. On of the astrologers objections was that five minutes was too wide of a window because even a millionth of a billionth of a second difference mattered greatly. Of course, the article then noted that even if that were true then astrology would be useless because the time of birth is never measured that precisely anyway.

But that aside issue aside, it made me wonder how much more slowly time moves at (say) sea level than at 1 K above sea level. If I understand correctly when you're near a massive object. If you're at sea level then you're closer to the mass of the earth than if you're 1 k above sea level. The difference in time passage would be extremely small, but then again the astrologer did say that a millionth of a billionth of a second mattered and that is pretty small too.

What I'm getting at is if time really matters then altitude at birth would have to be factored it. I know that astrologers do take into account place of birth but I think they take longitude and latitude into account rather than altitude (although I realize that if you take longitude and latitude into account you're implicity taking altitude into account too...I'm just saying that I doubt that the altitude aspect of time passage has ever occurred to them, although it's probably irrelevant to most of them since I'd be that most of them don't think a millionth of a billionth of a second matters).

 

[Skeptical Greg]

Oooooo... I don't know if anyone will take the time to do the math, but I have a feeling that the time difference between the top of Everest and sea level due to gravity, is for all practical purposes immeasurable... ( but calculable ... )

 

[Brian the Snail]

You can the expression

here

which gives a 1 part in 10^13 difference between the surface and 1 km above the surface.

 

[Skeptical Greg]

I found this interesting paper....


The Gravity Field of the Earth -Part 1

Altitude plays a part, but does not account for the density of the Earth under the location being measured for Gravity..

If our Astrologer friends wanted to account for the time difference due to gravity, they would have to have a detailed gravity survey table for the location of birth..

I feel confident that their charts will be just as accurate without the gravity data...

 

[TillEulenspiegel]

Wow! That slicing the bread really thin.
There does exist a time differental between someone at the top of everest and at sea level and thats because they are moving thru space at different speeds , relitive to each other. The amount of difference is so small tho I'm fairly sure it couldn't be measured but you could demonstrate it mathmatically.

The time dilation of the two in relation to stars thousands and millions of light years away is even smaller.

Besides since the inception of the psudo science of astrology the signs ( Taurus, Aries , ect.) have preceeded the model used by ~1, meaning that a Taurus is now an Aries. Bleh

It has been many years since I looked at this subjuct but I don't have the patience anymore to dis-prove this crap and it remains as much a real predictive mechinism as any tea leaf reading or other accompanying voo-doo superstition.

 

[Cleopatra]

Ha!

I am quoting this by memory but it was either Pyrrho or Sextus the first who debunked astrology by pointing to the astrologers of their time that they use of time of birth in the creation of a astrological profile is quite relative since they didn't agree on what was the time of birth. Was is the time of conception, the time that the labour started, the times that the head of the baby appeared or when the whole of the baby was out?

I understand that you relate altitude with the measurement of time but it doesn't really affect what is really important in sketching an astrological profile: the position of the planets on the sky.The difference is minor and it doesn't affect the position of the moon which is the planet that moves faster that the rest 8 planets. Also, it's so minor that it really doesn't affect the ascendant.

 

[patnray]

I remember reading last year that the newest atomic clocks are so accurate that they can measure the difference when one is raised a small distance. Don't remeber the details, but the article was in Scientific American.

 

[epepke]

But that aside issue aside, it made me wonder how much more slowly time moves at (say) sea level than at 1 K above sea level. If I understand correctly when you're near a massive object. If you're at sea level then you're closer to the mass of the earth than if you're 1 k above sea level.

It is only really significantly enough for high-precision applications.

There's an easy way to calculate it, though, without using GR. Drop the observer from that distance, and the velocity when he and/or she passes the second clock by special relativity is the same that you would get by doing the full GR calculations. At these speeds, classical measurement of the acceleration is good enough.

To keep it simple, take gravitational acceleration as 10 m^2/s and the speed of light as 300,000,000. Drop someone for one second, and he and/or she will be going 10 m/s but will have traveled 5 m, so someone dropped 1 km will be going about 2000 m/s. Plug that into gamma, which is sqrt(1-v^2/c^2) to get the time dilation, so it's sqrt(1-2000^2/300,000,000^2), so by my calculator, the ratio would be 0.9999999999777778, or about two parts in a hundred billion.

 

[TillEulenspiegel]

So who do we drop off the mountain? I have a few candidates in mind but maybe we should have a poll

 

[Skeptical Greg]

I remember reading last year that the newest atomic clocks are so accurate that they can measure the difference when one is raised a small distance. Don't remeber the details, but the article was in Scientific American.

According to this..

The latest generation of atomic clocks can keep time with an accuracy equivalent to neither losing or gaining more than 1 second in 20 million years. Its version of a "pendulum" is a natural oscillation frequency of a cesium atom. The second is defined as exactly 9,192,631,770 of these atomic oscillations.

at:
http://www.atomicatomictime.com/nistinfo.html

Could be true, depending on what they mean by ' small '..

I wonder how much change in gravity would be necessary to change the frequency by one HZ?..

 

[epepke]

So who do we drop off the mountain? I have a few candidates in mind but maybe we should have a poll

So do I, but none of them is bright enough to use a stopwatch.