Part 33

Mrs. B. Let us suppose that when the earth is at A, (fig. 3.) its projectile force should not have given it a velocity sufficient to counterbalance that of gravity, so as to enable these powers conjointly to carry it round the sun in a circle; the earth, instead of describing the line A C, as in the former figure, will approach nearer the sun in the line A B.

Caroline. Under these circumstances, I see not what is to prevent our approaching nearer and nearer the sun, till we fall into it: for its attraction increases as we advance towards it, and produces an accelerated velocity in the earth, which increases the danger.

Mrs. B. There is another seeming danger, of which you are not aware. Observe, that as the earth approaches the sun, the direction of its projectile force is no longer perpendicular to that of its attraction, but inclines more nearly to it. When the earth reaches that part of its orbit at B, the force of projection would carry it to D, which brings it nearer the sun instead of bearing it away from it.

Emily. If, then, we are driven by one power, and drawn by the other to this centre of destruction, how is it possible for us to escape?

Mrs. B. A little patience, and you will find that we are not without resource. The earth continues approaching the sun with a uniformly increasing accelerated motion, till it reaches the point E; in what direction will the projectile force now impel it?

Emily. In the direction E F. Here then the two forces act perpendicularly to each other, the lines representing them forming a right angle, and the earth is situated just as it was in the preceding figure; therefore, from this point, it should revolve round the sun in a circle.

Mrs. B. No, all the circumstances do not agree. In motion round a centre, you recollect that the centrifugal force increases with the velocity of the body, or in other words, the quicker it moves the stronger is its tendency to fly off in a right line. When the earth, therefore, arrives at E, its accelerated motion will have so far increased its velocity, and consequently its centrifugal force, that the latter will prevail over the force of attraction, and force the earth away from the sun till it reaches G.

Caroline. It is thus then that we escape from the dangerous vicinity of the sun; and in proportion as we recede from it, the force of its attraction, and, consequently, the velocity of the earth's motion, are diminished.

Mrs. B. Yes. From G the direction of projection is towards H, that of attraction towards S, and the earth proceeds between them with a uniformly retarded motion, till it has completed its revolution. Thus you see that the earth travels round the sun, not in a circle, but an ellipsis, of which the sun occupies one of the foci; and that in its course, the earth alternately approaches and recedes from it, without any danger of being either swallowed up, or being entirely carried away from it.

Caroline. And I observe, that what I apprehended to be a dangerous irregularity, is the means by which the most perfect order and harmony are produced.

Emily. The earth travels then at a very unequal rate, its velocity being accelerated as it approaches the sun, and retarded as it recedes from it.

Mrs. B. It is mathematically demonstrable, that, in moving round a point towards which it is attracted, a body passes over equal areas, in equal times. The whole of the space contained within the earth's orbit, is in fig. 4, divided into a number of areas or surfaces; 1, 2, 3, 4, &c. all of which are of equal dimensions, though of very different forms; some of them, you see, are long and narrow, others broad and short: but they each of them contain an equal quantity of space. An imaginary line drawn from the centre of the earth to that of the sun, and keeping pace with the earth in its revolution, passes over equal areas in equal times; that is to say, if it is a month going from A to B, it will be a month going from B to C, and another from C to E, and so on; and the areas A B S, B C S, C E S, will be equal to each other, although the lines A B, B C, C E, are unequal.

Caroline. What long journeys the earth has to perform in the course of a month, in one part of her orbit, and how short they are in the other part!

Mrs. B. The inequality is not so considerable as appears in this figure; for the earth's orbit is not so eccentric as it is there described; and in reality, differs but little from a circle: that part of the earth's orbit nearest the sun is called its perihelion, that part most distant from the sun, its aphelion; and the earth is above three millions of miles nearer the sun at its perihelion than at its aphelion.

Emily. I think I can trace a consequence from these different situations of the earth; are not they the cause of summer and winter?

Mrs. B. On the contrary, during the height of summer, the earth is in that part of its orbit which is most distant from the sun, and it is during the severity of winter, that it approaches nearest to it.

Emily. That is very extraordinary; and how then do you account for the heat being greatest, when we are most distant from the sun?

Mrs. B. The difference of the earth's distance from the sun in summer and winter, when compared with its total distance from the sun, is but inconsiderable. The earth, it is true, is above three millions of miles nearer the sun in winter than in summer; but that distance, however great it at first appears, sinks into insignificance in comparison with 95 millions of miles, which is our mean distance from the sun. The change of temperature, arising from this difference, would scarcely be sensible, even were it not completely overpowered by other causes which produce the variations of the seasons; but these I shall defer explaining, till we have made some further observations on the heavenly bodies.

Caroline. And should not the sun appear smaller in summer, when it is so much further from us?

Mrs. B. It actually does, when accurately measured; but the apparent difference in size, is, I believe, not perceptible to the naked eye.

Emily. Then, since the earth moves with the greatest velocity in that part of its orbit in which it is nearest the sun, it must have completed its journey through that half of its orbit, in a shorter time than through the other?

Mrs. B. Yes, it is about seven days longer performing the summer-half of its orbit, than the winter-half; and the summers are consequently seven days longer in the northern, than they are in the southern hemisphere.

The revolution of all the planets round the sun, is the result of the same causes, and is performed in the same manner, as that of the earth.

Caroline. Pray what are the planets?

Mrs. B. They are those celestial bodies, which revolve like our earth, about the sun; they are supposed to resemble the earth also in many other respects; and we are led by analogy, to suppose them to be inhabited worlds.

Caroline. I have heard so, but do you not think such an opinion too great a stretch of the imagination?

Mrs. B. Some of the planets are proved to be larger than the earth; it is only their immense distance from us, which renders their apparent dimensions so small. Now, if we consider them as enormous globes, instead of small twinkling spots, we shall be led to suppose that the Almighty would not have created them merely for the purpose of giving us a little light in the night, as it was formerly imagined; and we should find it more consistent with our ideas of the Divine wisdom and beneficence, to suppose that these celestial bodies should be created for the habitation of beings, who are, like us, blessed by his providence. Both in a moral, as well as a physical point of view, it appears to me more rational to consider the planets as worlds revolving round the sun; and the fixed stars as other suns, each of them attended by their respective system of planets, to which they impart their influence. We have brought our telescopes to such a degree of perfection, that from the appearances which the moon exhibits when seen through them, we have very good reason to conclude that it is a habitable globe: for though it is true that we cannot discern its towns and people, we can plainly perceive its mountains and valleys: and some astronomers have gone so far as to imagine that they discovered volcanos.

Emily. If the fixed stars are suns, with planets revolving round them, why should we not see those planets as well as their suns?