IN STARRY SKIES

Evening Post, Volume CXIX, Issue 104, 4 May 1935, Page 13

IN STARRY SKIES

THE DISTANCES OF THE STARS

By "Omega Centauri."

11l studying the marvellous stellar system to which our sun belongs one of the earliest questions we are likely to ask is: "What is its size?" This turns out to be an extremely difficult one^to answer. As soon as it was realised that the earth travels annually in an immense orbit round the sun a solution of the problem seemed to be in sight. If we walk through a grove of trees the nearer : trunks seem to move across in front of the more distant ones. If the earth travels in an orbit 186,000,000 miles across, surely the nearer stars will appear to move on the background spangled with the multitudes that are much farther off. They do. But the apparent movement is so surprisingly small that! it can be accurately measured in only a few: cases. All are familiar with the ordinary method of triangulation. An object is observed from the ends of a measured base line,'and'the angle that its direction makes with the base as seen from each end observed. Then a triangle can be drawn to scale, or its dimensions can be calculated. This method is applicable even in measuring the distance of the moon, and with less accuracy that of the sun, using some terrestrial distance as the bases." "If.viewed simultaneously from two widely-separated observatories, such, for instance, as those at Greenwich and the Cape of Good Hope, the. position, of the moon

on the stellar background is: noticeably different. Similarly, when Venus i passes between' the earth and the sun its apparent path, across the solar disc is different as seen from the two observatories. The apparent change of position of any , object .when viewed from different points is called its parallax. This change clearly mus> depend on the -length of the base, jand if a number or observatories made, simultaneous observations each'pair-would arrive at a different, result, To' make all observations directly- : comparable some special convention must beadppted. The usual one is to reduce observations to the value they would have if made from the centre of the earth. The difference of direction as seen from the observer's station arid irbm the earth's centre is called the geocentric parallax. To get a value that is independent of the position of the observer we imagine the observations taken when the object is exactly on the horizon. So the horizontal' parallax is equal to the angular semidiameter of the earth as seen from toe body. But the earth is .not a sphere, so we, must decide which radius to take. The one chosen is that to a point on the equator, and when.we talk of the" moon's parallax we mean its equatorial horizontal parallax. Since the moon's distance ranges from.' 221,463 to 252,710 miles, this parallax varies from.about 54 to 61 minutes of, arc, its mean value being just over 57 minutes. That is, the earth, as seen' from the moon, would have an apparent diameter of 114 minutes. Now the sun is about 389 time's as far from us as the moon is, so the problem of determining its parallax is a difficult one. It is not tackled directly, but the value sought has been found from observations ■of particular asteroids, by the study of perturbations of Eros, by the velocity. of light, and by other independent methods, and all agree in making the value of the horizontal parallax very slightly greater than 8.8 seconds of arc. Now, even the nearest star fs considerably more than a quarter of a million' and all but four more than'a million, times "as far off as the sun. So'it would ije" hopeless Jo attempt to find the geocentric parallax of any one of them. ( 3ut fortunately the earth's motion round'the sun'provides us with a much longer base. The distance of the earth from the sun is nearly 23,500. times the .radius of the earth. If the earth could be seen from one of the nearer-stars- it would appear to move round the sun.once a year. The path is nearly circular, but, unless

the star was near one of the poles of the ecliptic, it would appear elliptical. The angle which the radius of the earth's orbit subtends at the star is called the helio-centric parallax. - If that can be determined we can easily deduce the distance of the star. Tycho Brahe made more accurate observations than had ever been made before, with the surprising result that he could find no parallax for the stars. They appeared to him, as to the ancient astronomers, fixed relatively to one another. For this reason he rejected the Copernican theory and assumed that the earth was at rest. By considering the sun to revolve round the earth and all the other planets to revolve round the sun, the apparent motions were made to agree with those postulated by Copernicus. By showing that the Nova of 1572 had no apparent parallax Tycho proved that it could not be within the earth's atmosphere but must, at the very least, ;be many times as far off- as the moon. Tycho had no optical aid, and made his wonderful observations with the naked eye, using, instruments of his own construction. Little did'he know of the difficulty of the problems he was,attempting to solve. In spite of the great improvement in astronomical instruments, that followed the invention of the telescope, these difficulties baffled the astronomers of the World for another 260 years. It was not only that the angles to be measured. were extremely small. The apparent mpvemehts due to the earth's change ■ of position in its orbit were masked by others whose courses were unknown. Matters were brought to a head by the requirements of the British Navy. Lunar tables were not accurate enough for the precise determination of lopgitude. More accurate ones could not be prepared without revising, with

telescopic aid, Tycho's catalogue of the positions, of the stars. Flamsteed had drawn attention to these defects, so Charles II established the Royal Observatory at Greenwich in 1675 and appointed Flamsteed Astronomer Royal. Unfortunately - the necessary instruments were not provided and Flamsteed had to do the best he could with those he could procure mostly at his own expense," but the catalogue he produced was: a. great advance onfall that had been, made before. When Halley succeeded Flams'teed in 1720 he was already, 64 years of age, but he undertook a series of lunar observations which required a period of more than eighteen years, that is the time in .which one complete revolution of the nodes takes place. This he .carried cut. successfully. When he died in 1742 his brilliant successor, James Bradley, was already fifty years old. He had already made one of the important discoveries that cleared the way for the determination of parallax, and, six; years after becoming Astronomer Royal, he. announced another. The first, published in 1728, is known as the aberration of light. The earth, moving in.a continually changing direction with an average speed of about 18£ miles a second, and light, having a finite velocity of 186,300 miles per second, cause an apparent annual displacement of a star along a tiny ellipse • surrounding its true position. The second discovery was that the varying position t>f the moon's orbit enables its T attraction" on the equatorial bulge of the earth to cause a slow movement in the position of the earth's axis. The pole thus traces, out a small ellipse 18 second? by 16 seconds iri' a: period of ratiier more than 18 years. . Except when a differential method is used both these displacements due to aberration and nutation, have to be allowed for before it is possible, to determine the,parallax of a star. Repeated, attempts were made to solve this fundamental. problem but for nearly-another century- all ended in failure. In 1832-33 Henderson made observations of Alpha Centauri from which he deduced a parallax of 1.16 seconds^ whicih is "about 50 per' cent, too large, but he'did not publish the result until . January, 1839, two months after Bessel had announced a parallax for the double star 61 Cygni. Meanwhile in 1835 Struve found a parallax for Vega which, however, was 100 per cent, too great. Since then over 200 parallaxes have been found trigonometrically and nearly 2000 by other methods.