New Metric Fables: Apollo and the black hole

Apollo and the black hole

When the sun and its planets had just been made the people and animals were disappointed by one detail. The contractors had left a black hole where Jupiter should have been, as a place-holder. The Jovian moons, which some animals with their sharp eyes could see, were going around the black hole (which had the same mass as the planet which should have been there) instead of a brilliant visible thing.

So the people and animals made a great outcry unto the Lord Apollo Maker of the Universe and called on him to get himself over to the solar system and correct the oversight.

There was a glorious arpeggio of plucked lyre strings and Apollo appeared. He examined the contract and agreed there had been an error. Instead of a black hole, there was supposed to be a gas giant planet with a mass he had specified should be 10²⁶ billets. But unfortunately the contractors had already been paid off and had vanished back into the untold from whence they came—it was too late to get them to fix the problem.

However, said the god, there was a band of gypsies traveling through this part of the galaxy trading planets for black holes. They had a bag of surplus planets of various sizes, for which they had no use, and they were looking to trade them for black holes. Being compact and indistinguishable from universe to universe, black holes were used as currency in many of the places gypsies traveled.

Whether or not the gypsies could help you, said the god, depended on whether the gypsies happened to be carrying in their bag a planet of exactly the same mass as your black hole. If so, then it was legal for them to swap. The Jovian moons could continue orbiting the swapped-in planet just as they had been orbiting the swapped-out black hole. The moons wouldn't know the difference and everything would be all right.

Among the animals there was a parrot who knew how to deduce the mass of a central body from things in orbit. The parrot was suspicious of contractors and wanted to check to see what the mass of the black hole actually was. The parrot observed that one of the moons was in 900,000 mile radius circular orbit (around the invisible thing at the center). He and a falcon with very sharp eyesight had been watching that moon and they had determined that its radian arctime (1/2 pi of a full circuit) was 2700 minutes. The parrot did a little arithmetic, cubing the radius and dividing by the square of the time, and said that the attractiveness of the hole must indeed be 10²⁰ finger³/trice². Since there is a 10^-6 ratio of attractiveness to inertia, the mass of the black hole was indeed 10²⁶ billets. Therefore, decided the parrot, if the gypsies had a planet of that mass which they could swap in, then everything would be fine.

Apollo felt responsible for the error so he made it his business to consult the gypsies. He found them sitting around the campfire with their bag of planets telling metric-system stories. They laughed tolerantly at the god and said they didn't rate planets by billets they rated them by the size of the black hole you could swap them for. Show us the halfradius of the black hole, they said, and we'll see if we have a planet we can swap for it. Apollo was not versed in these matters (he considered himself a musician and only created universes as a sideline) but fortunately he had brought the parrot along.

Just divide the attractivess by the square of the speed of light, said the parrot. 10²⁰ finger³/trice² divided by 10¹⁸ finger²/trice² (which the parrot had learned from Ole Roemer was the square of the speed of light) is one hundred fingerwidths: a distance of one pace. The halfradius of the black hole we have to swap is one pace! said the parrot. Ask them, it urged impatiently, if they have a planet to match. It turned out that the gypsies did.

The next evening the people and animals were waiting to see and they watched Jupiter rise in the heavens, very bright, with its little moons twinkling around it which some of the animals could see with their sharp eyes.

ORIGINALLY THE STORY WAS TOLD IN DIFFERENT UNITS like this:

So the people and animals made a great outcry unto the Lord Apollo Maker of the Universe and called on him to get himself over to the solar system and correct the oversight.

There was a glorious arpeggio of plucked lyre strings and Apollo appeared. He examined the contract and agreed there had been an error. Instead of a black hole, there was supposed to be a gas giant planet with a mass he had specified should be 10²⁰ quads. But unfortunately the contractors had already been paid off and had vanished back into the untold from whence they came—it was too late to get the problem corrected.

Among the animals there was a parrot who knew how to deduce the mass of a central body from things in orbit. The parrot was suspicious of contractors and wanted to check to see what the mass of the black hole actually was. The parrot observed that one of the moons was in 900,000 mile radius circular orbit (around the invisible thing at the center). He and a falcon with very sharp eyesight had been watching that one of the moons and they had determined that its radian arctime (1/2 pi of a full circuit) was 2700 minutes. The parrot did a little arithmetic, cubing the radius and dividing by the square of the time, and said that the attractiveness of the hole must indeed be 10²⁰ pace³/minute². Since there is a unitary ratio of attractiveness and inertia, the mass of the black hole was indeed 10²⁰ quads. Therefore, decided the parrot, if the gypsies had a planet of that mass which they could swap in, then everything would be fine.

Apollo felt partly responsible so he made it his business to consult the gypsies. He found them sitting around the campfire with their bag of planets telling metric-system stories. They laughed tolerantly at the god and said they didn't rate planets by quads they rated them by the size of the black hole you could swap them for. Show us the halfradius of the black hole, they said, and we'll see if we have a planet we can swap for it. Apollo was not up on these matters (he considered himself a musician and only made universes as a sideline) but fortunately he had brought the parrot along.

Just divide the attractivess by the square of the speed of light, said the parrot. 10²⁰ pace³/minute² divided by 10²⁰ pace²/minute² (which the parrot had learned from Ole Roemer was the square of the speed of light) is one pace. The halfradius of the black hole we have to swap is one pace. Ask them, urged the parrot, if they have a planet to match! It turned out that the gypsies did.