Nature Fables 2: distance and mass of sun

The Distance to the Sun

One morning the Emperor called Laotzu into his presence and questioned him concerning the distance to the sun.

"Sage," said the Emperor, "you have explained to me that the earth's orbit speed around the sun is one thousand miles per minute. Indeed it was by squaring this speed twice in succession, the other day, that you reckoned for me the weight of the sun. But tell me, how many miles distant is the sun?"

"Long life to your Majesty, the Son of Heaven! Has it not been established that the year shall have 365 and a quarter days and the day shall have 1600 minutes, in accordance with your Imperial decree? May the humblest of your subjects then multiply these to find the number of minutes in a year?" The Emperor nodded augustly.

"Behold then, your Majesty," said Laotzu, "I shall divide the minutes in a year by 2 pi, to get the number of minutes it takes for the earth to go the length of an orbit radius—1/2pi of its full circuit. The Ancients called this the radian arctime of the earth's orbit and reckoned it as 93 thousand minutes."

"Yes," agreed the Emperor, "I have heard of this 93 thousand minutes. It is 58 days, as may be inferred, even by a barbarian, from the Imperial calendar."

"The Son of Heaven himself tells us the distance to the sun!" declared Laotzu, "for the earth travels one thousand miles in each of those minutes. And so, in the 93 thousand minutes it takes to go the length of its orbit radius, the earth travels 93 million miles."

The Emperor beckoned to an advisor, with whom he spoke inaudibly for a moment, and who then came to where the sage waited and said, "His Majesty wishes to know the mass of the sun!" At the Emperor's bidding, the advisor then disappeared into an alcove from which he returned leading a full-grown white Samoyed on a leash. The mass of this Samoyed was believed by foreigners to be 48 of their pounds, and had been declared the standard of mass throughout the land inside the Wall.

Laotzu squared the earth's speed (10⁶mile²/minute²) and multiplied by the earth's distance (93 million miles) to get 93 × 10¹² mile³/minute². Each of those units was worth a quadrillion times the mass of the white Samoyed (10¹⁵ being the sage's proportion for gravity.) In this way he found that the mass of the sun was 93 × 10²⁷ times the mass of the dog.