Science Feature: Accuracy

The first article in a fascinating series which will include the entire solar system

by John W. Campbell, Jr. (pages 96-99 of June 1936's Astounding Stories)

PRACTICALLY no statement made in this series will be exactly accurate, perhaps a tenth will be inaccurate to the point of virtual uselessness, and at least a twentieth will be wholly wrong. But that is the fault of lack of preparation, and lack of time to study the subject. Men have had less than one full century to use telescopes with the necessary accuracy.

In astronomy, time is so immensely important because errors and displacements become cumulative and hence observable. Pluto was discovered because over a period of years systematic mapping of the heavens by photography had been carried out, and finally enough time had elapsed so that the cumulative displacement of Pluto's slow motion in its orbit built up and added till it became a visible difference between a plate several years old and a comparatively recent plate. Time is important.

Accuracy is important; by it a theory may stand or fall. Newton's theory of gravitation was right but inaccurate. But it took cumulative work over years to detect the slight difference Einstein's law expresses.

In 500 B.C. the Greek philosopher Plilolaus advanced the theory that the Earth revolved on its axis, and followed an orbit about the Sun; others followed and agreed with him, though the general belief was in the apparent immobility of the Earth, with moving Sun, Moon, and stars.

In 100 A.D. the two theories were in existence, and Ptolmey worked on the theory of the stationary Earth. He combined his mathematical observations with observations of the planets and the Sun and Moon and finally, by immense labor, he developed the theory of cycles and epicycles; a rotating dome of heaven, across which the planets, the Sun, and the Moon moved, following a series of curved tracks.

Without the data represented by knowledge of gravitation, inertia and action and reaction, both theories seemed equally tenable -- the rotating Earth going about the Sun and the rotating bowl of heaven. Then the two must stand or fall by test of observation.

Ptolmey's won, because Ptolmey's was more accurate, not because people like it better. Sailors don't worry about how they like a theory, they want it to predict where they can look for star or planet to guide them. Ptolmey's did, more accurately than the theory of the orbits.

Accuracy had defeated the circular orbit by 125 A.D. At that time, the human eye being a very old observational instrument, and already at about its peak, there was little change in accuracy. Not till nearly 1600 was sufficient advance made in observational accuracy to detect errors in Ptolmey's theory.

About 1600 A.D. Tycho Brahe was doing his work. Tycho was a crusty old man, then, and not at all a theorist. He was not above practicing astrology, in which he did not greatly believe, to gain ends in which he thoroughly believed: bigger and better observational instruments, in a quite literal sense. To get second marks one sixteenth of an inch apart on a quadrant of 90 degrees, each degree having sixty minutes, in each of which are sixty seconds, would require a structure almost half again as high as the Empire State Building. Tycho couldn't get that.

But Tycho did build instruments of unexampled size. He used whole walls to lay out his quadrants; he used slits in the walls of a round tower for peep-holes while he stood on the other side of the tower to get accuracy.

He got accuracy, more than any man before him had, but he didn't stop to theorize. He recorded his data, and sought more. It was Kepler who did the theorizing on Tycho's data, some years later. Copernicus had revived the orbital planet hypothesis about 1525 with such convincing arguments it was never again abandoned, but he again had circular orbits.

At first Kepler, too, assumed circular orbits, but so accurate were Tycho's observations, they ruled out both the circular orbit and very definitely the Ptolmaic theory as well. For the first time, Kepler abandoned the perfect curve, the circle, and tried and found the elipse[ed. sic]. At last they had a theory that greater accuracy merely strengthened.

Perhaps it is not fair to call Ptolmey's system a theory to explain so much as a highly ingenious and successful system of mathematical analysis to locate planets. From that viewpoint it is, was and always will be a triumph, because it was absolutely successful for over a millennium and a half. Greater accuracy made it, as a system of mathematics, useless.

Modern work depends on the telescope's power of magnification -- not of objects but of lack of objects, the magnification of separation. The eye cannot separate two stars less than four and a half minutes of arc apart, while the telescope measures accurately a star's displacement of three fourths of a second caused by Earth's movement around the Sun -- a quantity about one three-hundredth as great.

The work of time and accuracy of vision combine to make possible the detection of binary stars. It takes as much as five centuries for some binary stars to complete one circuit of their orbits, and the telescope is required to separate them visually. Without the telescope, we would see one star. With the telescope, over a period of time, we would see two independent stars that happened to be close together. Only time makes their slow orbital creep observable.

But the telescope has its limitations, of course, for, accurate as it is in the measurement of angles, once beyond the solar system the angles it is called upon to measure are too minute for even the greatest instrument's capabilities. The lower limit of error is approximately .005" of arc, and that limit of error means that stars more than 650 light years away cannot be located by direct measure of triangulation with an accuracy greater than one part in two. The error is equal to the quantity to be measured.

Then evidently, if we want to retain accuracy, we must keep away from slight angles; if all measurements contain at least that error, the bigger the angle measured, the smaller the percentage of error.

The distance to the Moon can be found by having one observatory on one side of the Earth and one on the antipodal point of the Earth, both focused on some selected spot on the Moon. We know the diameter of the Earth, and thus with three angles and a side of the triangle, we can readily determine the distance to the Moon.

Extremely accurate work on the Earth itself has determined its diameter with precision about equal to the constancy of the planet -- it is distorted by tides, planetary cross pulls, earthquakes, by the seasonal shifting of incalculable tons of snow and ice, etc. -- to be 7,899.984 miles.

The distance to the Moon works out to be 238,854 miles. And because the angles are quite measurable, and the diameter of the Earth quite accurately determined we have a right to say the last figure is just about 4, and figure certainly isn't as much as 238,875 miles.

But the next step is the Sun, and there we simply can't get a big angle. It's just about the same angle you have between your left eye and your right eye looking at a man a mile away. It is vanishingly small, anyway, and furthermore that optimum figure of only a few thousands of a second error doesn't apply because the conditions are not optimum.

The sun is shining on the instruments -- they don't use the big telescopes because it would ruin them to have the full heat of the sun strike them -- and they are distorted. The air is heated unevenly, so that it acts to produce heat ripples, and the image of the Sun wavers badly, more so than the image of a star on a clear, cool night, and the distance we are trying to measure is some 11,000 times our base line.

We can't get a good determination, and we won't till we set up our observatory on the Moon, where there is no interfering atmosphere. We'll rough it in as about 92,897,000 miles, but know that our error is such that that last figure isn't any too good; it may be 887 or it may be 907, or 900, but it is about that. We can't get a good determination, and we won't till we set up our observatory on the Moon, where there is no interfering atmosphere. We'll rough it in as about 92,897,000 miles, but know that our error is such that that last figure isn't any too good; it may be 887 or it may be 907, or 900, but it is about that.

But we can do this: We will assume that the distance is one unit; we will define it as one astronomical unit, and let the exact distance go for a bit. But since we defined it, whatever it is in miles as being one unit, we can go on from there and assemble another few dozen of the scraps of the cosmic jigsaw puzzle of knowledge, isolated as yet, but ones we can connect in with other blocks later, when we know what that unit is in actual miles. For the time we can make progress along other lines.

We can use a new base line now: the diameter, not of the Earth, but of Earth's orbit, not 8,000 miles now, but 186,000,000 miles. Now to determine the distance to Mars. We can direct telescopes toward it in June, and again in December, when Earth has moved on hundreds f millions of miles. Mars has moved, too, but there are fairly easy ways to eliminate that in the equation.

The angle formed from the June position, the December position, and Mars gives us three angles of the triangle, and our orbit gives us a base line two units long. The base line is the same sort of size that the distance we are measuring is, so the angles are large and easy to measure accurately, much more accurately than we can measure the angle to the Sun.

The same sort of system applies for Jupiter, Saturn, Uranus, Neptune, and Pluto, all superior planets, planets beyond the Earth from the Sun.

For the inferior or inner planets, Venus and Mercury, a slightly different system is needed, but the general outline is the same.

Step One has been taken; we have laid out the solar system to scale, with a pretty fair idea of its accurate size. The table now reads:

Knowing now their distances from the Sun, and our own distance from the Sun, it is easy to calculate their distances from us at any given moment. With photographs which give the apparent diameter of the planet, knowing the magnification the telescope made, it is easy to calculate the actual diameter of the planet.

We get results fairly accurate for all save Pluto, so far and so small that it is very difficult to photograph, though the very fact that it is difficult gives us some data as to the planet's size. It certainly isn't large. The results on their diameters plus results from calculations on their gravitational influences on other planets, their own satellites if they have any, give us their masses, and finally their densities. They range:

It will be noticed that the diameter of Pluto, in fact all its properties, are questioned, for the photographs are so inaccurate. The masses, and hence the densities, of Mercury and Venus are questioned because, having no satellites, they cannot be "weighted" as accurately as the planets having satellites. Actually, the indicated data on Pluto is scientifically called an "estimate" and colloquially, "an educated guess."

The solar system is taking shape, but a surprising and intensely interesting shape! It is not one, but two systems!

This scientific discussion of the solar system will be continued next month.