How Accurate is Accurate Enough?
04-11-2021, 02:47 PM (This post was last modified: 04-11-2021 04:03 PM by Dave Shaffer.)
Post: #2
 Dave Shaffer Member Posts: 57 Joined: Dec 2013
RE: How Accurate is Accurate Enough?
(04-11-2021 01:15 PM)Chumango Wrote:  Are there real-life calculations where 10, 12, 14 digits are actually required? Or is it a matter of getting more digits and accuracy because we can? Just curious.

Yep!

I used to support a NASA geodesy program. That program is now measuring relative locations all over the earth to a millimeter or so (https://en.wikipedia.org/wiki/Internatio...ms_Service). In round numbers, the earth is about 12,740 km in diameter - 10^7 meters. So, 1 mm precision requires parts in 10^11 calculations. All our analysis programs used quadruple precision calculations.

These (NASA and other) systems use hydrogen maser time standards - we worry about stability here at parts in 10^15 - 10^16 (and can measure at that level!). And, current precision in atomic time keeping laboratory standards approaches parts in 10^18!! With such clocks, you can measure the effects of gravity on a clock by comparing clock rates at the bottom and top of tall buildings.
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 Messages In This Thread How Accurate is Accurate Enough? - Chumango - 04-11-2021, 01:15 PM RE: How Accurate is Accurate Enough? - Dave Shaffer - 04-11-2021 02:47 PM RE: How Accurate is Accurate Enough? - lrdheat - 04-11-2021, 02:50 PM RE: How Accurate is Accurate Enough? - Chumango - 04-11-2021, 03:00 PM RE: How Accurate is Accurate Enough? - ttw - 04-11-2021, 03:12 PM RE: How Accurate is Accurate Enough? - Dave Britten - 04-11-2021, 05:29 PM RE: How Accurate is Accurate Enough? - toml_12953 - 04-11-2021, 07:26 PM RE: How Accurate is Accurate Enough? - Paul Dale - 04-14-2021, 10:30 AM RE: How Accurate is Accurate Enough? - Garth Wilson - 04-11-2021, 07:50 PM RE: How Accurate is Accurate Enough? - cyrille de brĂ©bisson - 04-14-2021, 07:15 AM

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