^{2}, or about one part in 200. So why is a standard gravity defined to be a precise value whose significant digits would indicate a precision of one part in a million? Is the quantity 9.80665m/s

^{2}somehow more physically meaningful than 9.8 or 9.81 would be? If not, what quirk of history caused it to be this bizarre value rather than something rounder?

On a related note, it also bothers me when people use that exact number to compute a trajectory, since the added "precision" it imparts is wholly imagined.

In the thread that prompted this one, phlip and I had the following exchange:

skeptical scientist wrote:While we're on the subject, does anyone know why standard gravity is defined to be exactly 9.80665? Is this precise value in any way physically meaningful? If it isn't, why don't we use the much simpler value of 9.8 for standard gravity?

phlip wrote:Probably for the same reason that the speed of light isn't quite 3e8 m/s, and standard atmospheric pressure is over 1e5 Pa... and, for that matter, why an inch isn't 2.5cm... inertia, and the desire not to change a value too much when it gets redefined in terms of something else.

Presumably, when they decided to define standard gravity as a specific value in m/s/s, they just took the previous value for g, however that was defined, rounded it off to more digits than you'd ever really need, and used that.

I don't buy this argument, especially the comparison to the speed of light. Yes, the meter is now defined to be exactly 1/299,792,458 of the distance light travels in vacuum in one second, so one could say that the speed of light is 299,792,458 by definition, and one could rather have defined it to be 300,000,000. But before this was the definition of the meter, the length of a meter was defined by the length of a particular platinum bar held at the International Bureau of Weights and Measures. Also before the speed-of-light-definition of the meter, the speed of light in vacuum had been measured to 4 parts per billion, and was known to be 299,792,458±1 times the length of that platinum bar in a second. So when the meter was defined by a prototype meter bar, the speed of light really was 299,792,458 m/s, and that precise number had physical meaning. When the meter was redefined from the speed of light as opposed to from a prototype, it made sense to keep the same value, so as not to change the length of the meter.

I don't see how a similar argument can be made for a standard gravity. I understand how the number 299,792,458 used for the speed of light is physically meaningful, but I don't understand the physical significance of 9.80665 m/s

^{2}. Moreover, I don't see how it can be physically significant. It can't possibly be the exact force of gravity on the surface of the Earth, since that value varies between 9.78 m/s

^{2}and 9.82 m/s

^{2}based on location. So what, if anything, does it measure?