Postscript — Eine kleine NASA-Tafel

Most of this stuff we don't need in the Fables but I've stuck it in here to have handy because it is not possible to predict what one might want to know in the course of making an imaginary trip.

A NASA website gives the Keplerian attractiveness of the sun, in metric units, as

1.32712440018 × 10²⁰meter³/second².

This is an exquisite degree of precision but they deserve it because they fly probes to Pluto etc. One needs many digits to navigate spacecraft. For precise navigation one does not use the kilogram mass of the sun, which is an inertia and known only to about three decimal place accuracy. One must use the figure for the sun's attractivness which NASA gives in cubicmeters per square seconds with such admirable accuracy.

See their website—http://ssd.jpl.nasa.gov/astro_constants.html —and consult the entry for the "heliocentric gravitational constant".

At the same site there are some "mass ratios" and what they mean by that in this context are attractiveness ratios. A ratio of the Keplerian attractiveness of sun and earth are what they measure, and that this is identical to the ratio of the two inertias is a theoretical assumption still subject to verification. The strict proportionality of inertia to attractiveness is not axiomatic but is something Dicke and others have attempted to verify, so one ought not to interpret one thing as another without comment, though NASA does.

Sun/(Earth+Moon) -----328900.56

Earth/Moon-----81.30059

If they were not navigating probes to other planets, I would not believe this many digits could be meaningful. It would seem like an inflated claim to precision. But they are placing large bets on their accuracy.

EXACT CONVERSION TO SERIOUS UNITS

Our serious Planckian minutes are defined as exactly 54 atomic clock seconds and our paces as exactly 0.54 × 2.99792458 meters. (The metric number 299792458 is exact by definition of meter.) So we can make an exact conversion of the NASA "heliocentric gravitational constant" into our serious units. I will leave off some digits because it would be embarrassing to write them all out.

9.1212795×10²² pace³/minute²
NASA says divide by 328900.56 to get the combined attractiveness of earth and moon. And then multiply that by 81.30059/82.30059 to get earth's. And by 1/82.30059 to get the moon's. All that stuff is based on the figure for the sun

Sun: 9.1212795 ×10²² pace³/minute².
Earth+Moon: 2.77326 ×10¹⁷ pace³/minute².
Earth: 2.73957 ×10¹⁷ pace³/minute².
Moon: 3.36967 ×10¹⁵ pace³/minute².

NASA data is public domain. Discussion copyright 2002 Leonard Cottrell.
Table of Contents

*