Laotzu dreamed he was drifting unhurriedly over the intricately sculpted surface of a golden planet of. The bas relief showed monkeys engaged in various activities, and at intervals grew potted jasmine. He was in orbit and skimspeed at this planet was slow—five paces in a minute—so that after twenty minutes he had only traveled the length of a city block. Dayside was in bright sunshine and the dream-air, which doesn't interfere with motion, enabled him to smell the jasmine.
After some 50 minutes had passed, Laotzu recognized some monkeys playing the Gamelan and realized that he had made a complete circuit of the planet. Looking at his watch, which told time in Taoist minutes (ten percent shorter than ordinary Earth ones), he saw it had taken 16pi minutes to come full circle around this planet and reflected that it must take 8 minutes to go the length of the planet's radius. This 8 minute radian time or "skimtime" is typical of planets made of solid gold. On pure silver planets the skimtime is 11 minutes, and on planets carved out of jade it is 19 minutes. On planets made of amber the time is around 30 minutes—there being some variation due to the different densities of amber. All planets with the same density have the same skimtime whether they are large or small.
Laotzu thought the planet radius must be 40 paces because that is how far one goes in 8 minutes when one travels five paces a minute. The cube of a planet's radius over the square of its skimtime is an "attractiveness" quantity that summarizes the orbits around it. In this case the radius cubed is 64 thousand cubic paces and the skimtime squared is 64 square minutes. Evidently this planet's attractiveness was 1000 pace3/ minute2, which meant that its mass was a billion talents. (According to the constant ratio in gravity, each cubic pace per square minute—each unit of attractiveness—is worth a million talents of mass. It is the same universal proportion according to which each cubic mile per square minute is worth a quadrillion talents.)
When Laotzu told Confucius his dream, the other sage asked him all sorts of questions about orbits around the planet and Laotzu was always able to answer from his knowledge of the planet's attractivness. To find the speed of a circular orbit at any distance from center, one divides the attractiveness by the distance—it gives the speed squared. Taoists know this, as they do that to find the acceleration of falling at any distance from center, one divides the attractiveness by the square of the distance. When Confucius asked what the circular orbit speed would be 250 paces from center, Laotzu simply divided a thousand pace3/minute2 by 250 paces and got 4 pace2/minute2. That being the square of the orbit speed means that the speed itself would be 2 pace/minute. And when Confucius asked what the acceleration of falling would be 50 paces from center, Laotzu squared 50 and divided a thousand pace3/minute2 by 2500 (pace/minute)2 to get 1/4 pace/minute2. A quarter of a pace per minute per minute.
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note:
Johannes Kepler discovered the attractiveness invariant for the sun. He found a cubic distance over square time quantity that was the same no matter which of the planets he used to calculate it. Attractivenessof central bodies, not their mass, is the quantity used for spacecraft navigation. You can find the attractiveness of the sun listed at this NASA website of astrophysical constants I've copied it verbatim here to show the degree of precision:
1.32712440018 × 1020meter3/second2.
Laotzu just happens to be using paces and minutes instead of NASA's meters and seconds. But their approach to calculating orbit parameters is the same.
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Copyright © 1999, 2002 by Leonard Cottrell. All rights
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