I got a new calculator for my collection today, the HP 9g. It's an odd little thing, with its 35x23 pixel display used for graphing, and a tiny, separate result display. It also stores a couple of scientific constants, such as the newtonian constant of gravitation, G. It gives the value as 6.6725985e-11. It's curious that they give that much precision.

G may be a constant, but it's notoriously hard to measure, because gravity is the weakest of the fundamental forces, and it's impossible to remove the measurement apparatus from the influences of stars and planets or the material of the apparatus itself. Many different experiments have been conducted, from these the people at NIST build a weighted average and publish it as part of their CODATA set of constants. The CODATA values from different years are:

1969: 6.6732(31)

1973: 6.6720(41) - note the increase in uncertainity!

1986: 6.67259(85) - oh, large improvement in accuracy, maybe they were getting a bit cocky there?

1998: 6.673(10) - experiments in the 90s must have been all over the map! Or it's a typo in their publication, which seems very unlikely.

2002: 6.6742(10)

2006: 6.67428(67)

2010: 6.67384(80) - again, note the increase in uncertainity.

2014: 6.67408(31) - published just a couple of months ago.

Btw, a recent

study claims to have found a weird annomaly by statistical analysis: measurements of G increase and decrease by 1.6e-14 (so the 3rd place after the period in the values above) in a 5.9 year cycle. They suggest that G itself doesn't actually change, but that a yet unknown effect influences all measurements. Curious, huh.

A note about the syntax: 6.6732(31) means 6.6732+-0.0031. The two digits inside the parentheses have the same order of magnitude as the last two digits of the given value. If only one digit were given inside the parentheses, it'd have the same order of magnitude as the last digit of the given value.

And now I get to my calculators. By looking at what value they use for G, we get a small glimpse into the development, i.e. whether they took just old code, or went to the trouble of updating the constants. Here's a short list of calculators I tested with their values (just the mantissa, I left out the e-11 exponent)

HP 9g: 6.6725985 - Wtf. Seems the guy who created the table didn't know what the parentheses syntax meant! Otherwise it's the 1986 value.

HP 35s: 6.673 - 1998 value.

HP 48G: 6.67259 - 1986 value.

HP 50G: 6.67259 - 1986 value.

HP Prime: 6.67384 - 2010 value.

TI-85: 6.67259 - 1986 value.

TI-86: 6.67259 - 1986 value.

TI-89 (first gen): 6.67259 - 1986 value.

TI Voyage 200: 6.6742 - 2002 value.

TI-nspire CAS: 6.6742 - 2002 value.

TI-30X Pro: 6.67428 - 2006 value.

Casio fx-991EX: 6.67384 - 2010 value.

Anyway, that was my nerdgasm for today. Thought I'd share