IN STARRY SKIES

Evening Post, Volume CXVI, Issue 25, 29 July 1933, Page 21

IN STARRY SKIES

SOME PLANETARY PROBLEMS

(By "Omega Centauri.")

Interesting questions are often asked ia connection with these articles. Two received recently are especially so. The first is whether 12,900 years hence Christinai in New Zealand will be iv midwinter. It is well known that about 125 B.C. Hipparchus made a surprising, discovery. He found that the ye?x-oi-'.thg seasons, from solstice to, solstice was shorter than the year determined by the return of the sun to the same point amongst the constellations. This phenomenon is called the Precession of the Equinoxes, because it appears as if the equinox steps forward a little to meet.the sun. The amount is very small, not much more than 50 seconds of arc per year, which would amount to a complete revolution in about 25,800 years. . Sir Isaac Newton showed that this change is due to the attraction of the moon, and to a lesser extent of the sun, on the bulge round the terrestrial equator, and that it would not have occurred if the earth had been a perfect sphere. Another way of looking at the resulting phenomenon is to say that in 25,800 years the earth 'a axis makes one turn in a conical movement like that of a spinning top whose axis is not vertical. The pole of the earth thus traces out a circle in the heavens with a radius of nearly twenty-three and a half degrees. In 12,900 years the North Pole in the sky will not be anywhere near Polaris, but fairly close to lota Hereulis, having passed Alpha Cephei about seven thousand years earlier. Well, this will clearly make. a decided difference in the aspect of the sky. The Scorpion, which now passes overhead in the winter evenings here, will then be a summer constellation in New Zealand. But it will be less than half as high in the northern sky.

This, however, does not answer the question. There are four different kinds of years. Two only of these concern us now, the sidereal and the tropical. The sidereal year is the time occupied by the sun in completing a

circuit of the heavens with reference to the ftars. Thia might well be cpusidcred as the true year, since it is the time' occupied by the earth in making ono complex revolution round the sun from one direction in space to the same direction again. But man is more directly concerned with the seasons than with the stars. He therefore attaches greater importance to the tropical year, which is the time between two successive passages of the vernal equinox by the sun. Unfortunately, neither of these years consists of an exact number of days.

The length of the tropical year is not absolutely constant, but it is approximately 365.242196 mean solar days. Clearly, if the year is taken to be 365 days the dates of the seasons will change by nearly a day in four years. To prevent this, Julius Caesar, in 45 8.C., ordained that every fourth year should contain 366 days. At the time of tho Council of Nice in 325 A.D., the vernal equinox was on March 21. By A.D. 1552 it had changed to March 11. Pope Gregory ordered that ten days should bo dropped, and that what would normally havo been October. 5 should be called October 15. Tho change was not made in England until 1752, when September 3 was called September 14. Eiots occurred in which the cry was, "Give us back our eleven days." Pope Gregory was not content merely to correct only the error that had already occurred, but tried to prevent further trouble by enacting that in future such century years only should be leap years, in which the number is exactly divisible by 400. The Gregorian calendar thus reduces the error to one day in over 3300 years. A simpler rule still might havo been adopted, namely, to make each year divisible by four a leap year, except those divisible by 128. This would have kept _ the calendar accurate for nearly fifty times as long. But history shows that the efforts of calendar-makers have been, and probably always will be, directed to keeping the seasons to the same times in the year. We must expect, therefore,

that as long as there are people in New Zealand'to celebrate Christmas it will continue to come in the summer.

The second question ia a more difficult one. It rests on a series of interesting observations and the answer to it depends on the relative sizes of the orbits of the planets and the speeds with which they are traversed. We must refer to somo of • these, points before stating the problem. The planets that have the shortest distances to go always travel fastest.' Mercury flies along its orbit at from 23 to 36 miles j a second. The approximate average speeds of the others are:—Venus 22, the earth ISA, Mars 15, Jupiter 8, Saturn (>, Uranus i, Neptune 3, and Pluto 2., This makes the periods: Mercury :8S days, Venus 225 days, Mars OS7 days, Jupiter 11.9 years, Saturn 29.5 years, Uranus 84 years, Neptune 164.8 years, and Pluto 247.7 years. If we could watch these movements from the sun they would appear much simpler. The inner planets would be continually catching up and passing the outer ones. It is easy to calculate how long any planet will take to catch up one round on another. For instance, since Mercury does one eighty-eighth of a round in one day, and Venus only one two-hund-red and twenty-fifth, we see that Mercury and Venus catch up one round with regard to the earth in 116 and 584 days respectively. The earth catches up to all the others. Mars is the most difficult to overtake. It takes the earth 780 days to gain one round. Jupiter, Saturn," Uranus, Neptune, and Pluto require only 399, 378, 370, 367^, and 366$ days respectively. Now, last year, 1932, the almanacs told us that' Mars was in conjunction with the sun on February 1, and that Venus was in inferior conjunction on June 29. An observer watched for these two planets to separate from the dawn, that is to appear in the morning sky before sunrise, naturally expecting that Mars, having such a long start, would appear first. He reasoned that in a quarter of 780 days, that is by August 13, Mars should be at right angles to the sun, and therefore on the meridian at midnight. It was not, however, until September 8, when Venus reached its greatest elongation, that > Mars attained the same elevation as Venus.

The problem is to explain why this happened. To treat the matter completely would be extremely difficult, for

the planets are all moving in ellipses with the sun in one focus, the orbits differ in eccentricity, the planes of these orbits are differently inclined to the ecliptic, .and the speed of each planet varies from aphelion to perihelion. But fortunately wo can get an approximate answer that will be sufficiently accurate if we consider all the orbits circular and the speeds constant. Seen from the south of the ecliptic, the revolution of the planets would appear clockwise. But it will be more convenient to take the line from the earth to the sun as our line of reference. Then, since the earth is travelling faster than Mars, the latter will appear to be moving counter-clockwise, and so separating from the sun in the early morning. When later "Venus passes inferior conjunction it is gaining on tlje earth, ad so it also tends to rise before the sun. Let M denote the position of Mars when in conjunction with the sun S, and let E be the position of the earth at that time. Now, if we consider the line ES fixed, Mars takes 780 days to make one round counter-clock-wise, and Venus 584 to complete one clockwise. It is clear from the diagram that Hars will take very much longer to pass from conjunction at M to quadrature at Q, than from the latter to opposition at O. By measuring the angles MSP and VSG you will find that, if the speeds were uniform and! the orbits all in one plane, it would take Mars three months longer to go from M to P, than it takes Venus to go from V to G. When Mars starts from M the rate at which its elongation (angular distance from the *un) is increasing is a minimum, while when Venus passes V its elongation is increasing at a maximum rate. Actually Venus rose at the same time as Mars about July 24, and then kept ahead until Mars overtook it again about September 8. The fact that Mara was further north than Venus had also an effect in making Mars rise later, and keep lower in the sky. Another factor was the variation of speed of the different planets in their orbits.