Today in ASL I ... (Day to day ASL doings)

Philippe D.

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Actually, 30 months seems not that small - it's something like 1 in 10^8 (the Earth's age is roughly 100 millions times that). I would have thought relativistic effects would be way smaller than this at this scale - meaning, even in the presence of the Earth's mass. But then, my last relativity course was in high school 30 years ago, at a time when I could barely understand the statement "at low speeds, this gives you back Newton's law".
 

Justiciar

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My knowledge of Special Relativity is mathematically rudimentary, but good enough for Government Work as they say, my knowledge of General Relativity is mathematically non existent, but I guess that for anyone familiar with GR math, such a calculation could be done during a short commuter bus ride home or even during a TV ad break.

.....
Sheldon was just bored then.
 

Paul M. Weir

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Actually, 30 months seems not that small - it's something like 1 in 10^8 (the Earth's age is roughly 100 millions times that). I would have thought relativistic effects would be way smaller than this at this scale - meaning, even in the presence of the Earth's mass. But then, my last relativity course was in high school 30 years ago, at a time when I could barely understand the statement "at low speeds, this gives you back Newton's law".
Earth's age ~ 4 billion years = 4*10^9 Y / 2.5 Y (IE 30 months) = 1.6*10^9 times the 30 month period.

Now that you bring it up, for special relativity the Lagrange thingy equation 1/√(1-v²/c²) is the distortion (about my SR knowledge limit also). Let's see what speed would be required for the same effect. Let D(istortion) be the ratio of the rate ticking of the moving clock compared to that of the observer's clock, v the velocity and c the speed of light.

D = 1/√(1-v²/c²)
D = 1/(1-1.6*10^-9) = 1/√(1-v²/c²)
√(1-v²/c²) = 1-1.6*10^-9 = 0.9999999984
1-v²/c² = 0.99999999680000000256
v²/c² = 1 - 0.99999999680000000256 = 0.00000000319999999744
v/c = 5.6568542472296384949572544786157e-5
v ~ 16958.8 m/s or 37935.8 mph

The escape velocity from earth is ~ 11186 m/s and v is about 1.52 times that (~ π/2 ?)

So that figure of 30 months sees very, very plausible to me.
 

hongkongwargamer

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Paul, you had me at “4 billion”...


Earth's age ~ 4 billion years = 4*10^9 Y / 2.5 Y (IE 30 months) = 1.6*10^9 times the 30 month period.

Now that you bring it up, for special relativity the Lagrange thingy equation 1/√(1-v²/c²) is the distortion (about my SR knowledge limit also). Let's see what speed would be required for the same effect. Let D(istortion) be the ratio of the rate ticking of the moving clock compared to that of the observer's clock, v the velocity and c the speed of light.

D = 1/√(1-v²/c²)
D = 1/(1-1.6*10^-9) = 1/√(1-v²/c²)
√(1-v²/c²) = 1-1.6*10^-9 = 0.9999999984
1-v²/c² = 0.99999999680000000256
v²/c² = 1 - 0.99999999680000000256 = 0.00000000319999999744
v/c = 5.6568542472296384949572544786157e-5
v ~ 16958.8 m/s or 37935.8 mph

The escape velocity from earth is ~ 11186 m/s and v is about 1.52 times that (~ π/2 ?)

So that figure of 30 months sees very, very plausible to me.
 

Philippe D.

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Earth's age ~ 4 billion years = 4*10^9 Y / 2.5 Y (IE 30 months) = 1.6*10^9 times the 30 month period.
Yeah, I was off by a factor of about 10 - I read "months" and counted "years", that's about correct.

The escape velocity from earth is ~ 11186 m/s and v is about 1.52 times that (~ π/2 ?)

So that figure of 30 months sees very, very plausible to me.
I'm unable to check your calculations, never learned enough about relativity for this - but escape velocity on earch is pretty high compared to the speed of its surface, right? (lateral speed at the equator, compared to the earth's center, is about 40.000km per 24h, so that's what? 500m/s? (but I suppose the question is how much the presence of mass distorts time - and that's something I have no intuition of)
 

Paul M. Weir

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4*10^4 km/day ~ 463 m/s, but either that or 500 m/s << 11186 m/s by about a factor of 24.

I would hope that escape velocity is much, much higher, otherwise everything at the equator would drift/fly off into space, including air!

Don't forget that escape velocity is not only enough to get you into orbit beyond the atmosphere, but if earth was the only body in a static universe, it would allow you to disappear to infinity.

I have no more idea than you of how much mass distorts space or time, but I had a hunch that the 30 month mass induced difference would be of the same order of magnitude, at least, as escape velocity induced difference, turning out closer (1.52 x) than I expected.

One effect is that the adjustments necessary to make GPS accurate require allowance for both earth mass and orbital velocity, the mass speeding up the satellite's clock and the velocity slowing the satellite's clock, the velocity element being the larger effect. (compared to an earth based clock)
 
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4*10^4 km/day ~ 463 m/s, but either that or 500 m/s << 11186 m/s by about a factor of 24.

I would hope that escape velocity is much, much higher, otherwise everything at the equator would drift/fly off into space, including air!

Don't forget that escape velocity is not only enough to get you into orbit beyond the atmosphere, but if earth was the only body in a static universe, it would allow you to disappear to infinity.

I have no more idea than you of how much mass distorts space or time, but I had a hunch that the 30 month mass induced difference would be of the same order of magnitude, at least, as escape velocity induced difference, turning out closer (1.52 x) than I expected.

One effect is that the adjustments necessary to make GPS accurate require allowance for both earth mass and orbital velocity, the mass speeding up the satellite's clock and the velocity slowing the satellite's clock, the velocity element being the larger effect. (compared to an earth based clock)
But what is the airspeed velocity of an unladen swallow?
 

Yuri0352

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I've been relaxing by solo playing the two-part PTO scenario OB9 Unhappy Trails. I would highly recommend this scenario as an introduction to the PTO for the newer players. Could easily be played during an evening by experienced players as well.
 

von Marwitz

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D = 1/√(1-v²/c²)
D = 1/(1-1.6*10^-9) = 1/√(1-v²/c²)
√(1-v²/c²) = 1-1.6*10^-9 = 0.9999999984
1-v²/c² = 0.99999999680000000256
v²/c² = 1 - 0.99999999680000000256 = 0.00000000319999999744
v/c = 5.6568542472296384949572544786157e-5
v ~ 16958.8 m/s or 37935.8 mph

The escape velocity from earth is ~ 11186 m/s and v is about 1.52 times that (~ π/2 ?)

So that figure of 30 months sees very, very plausible to me.
I just knew it would just be a matter of time until this happened. Gotta love this forum... :D

von Marwitz
 
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Over the weekend I've finally re-sorted my utility counters into a third box.
The counters were getting too congested.
Also cut up some cork gasket material to make bricks/debris for modeling projects, all while listening to Two Half Squads episodes.