ORIGIN OF THE SOLAR SYSTEM JEANS 153 



very nearly in one plane, which, to this extent, is, of course, a plane 

 of symmetry. But the sun's axis of rotation is not perpendicular 

 to this plane; the sun has its own plane of symmetry in its equator, 

 and this is inclined at an angle of 7° to the plane of orbits. 



Tlie existence of these two distinct planes is enough in itself to 

 suggest that our system has not developed simply out of an undis- 

 turbed rotating mass. Thus, in tracing our system back to its origin, 

 we naturally look at the effects to be expected from rotation plus 

 some external influence. To a first rough approximation, it is 

 natural to suppose that the plane of the sun's equator records the 

 plane of rotation of the original system, while the plane of the plan- 

 etary orbits was in some way determined by the extraneous disturb- 

 ance. 



Of all the interactions between two separate astronomical bodies, 

 gravitational attraction is likely to be by far the most potent. The 

 moon has been accused of exerting all kinds of influences on our 

 earth, as, for example, on its weather, on the destinies, the emotions, 

 and even on the sanity of its inhabitants; but the only influence 

 which survives scientific examination is gravitational attraction as 

 evidenced by the semidiurnal tides. It is true that a head-on colli- 

 sion between two astronomical bodies would produce more imme- 

 diately dramatic results than a mere tidal pull; but we shall not 

 consider such an event here. Head-on collisions must of necessity 

 be exceedingly rare; systems that experience them would undoubt- 

 edly be deflected from the main line of evolutionary progress on to 

 a branch line; but it does not seem likely that this branch line con- 

 tains systems like our own. As time does not permit the explora- 

 tion of all conceivable branch lines, let us turn at once to that which 

 seems most likely to reveal the origin of our system — the branch 

 line that diverges from the main line at the occurrence of a violent 

 tidal encounter. 



On the earth, our moon raises tides the average height of which 

 at high tide is only a few feet. This height of high tide is only 

 about a ten-millionth part of the earth's radius, a fraction which we 

 may designate as the tidal fraction. If the moon were ten times as 

 massive, the tidal fraction would be increased tenfold; if it were 

 brought to half its present distance, the tidal fraction would be in- 

 creased eightfold. If we agree to measure masses in terms of the 

 body on which the tide is raised as unity and to measure lengths 

 in terms of the radius of the same body, then the tidal fraction is 

 equal to the mass of the tide-generating body divided by the cube 

 of its distance, say M/R^ Using this formula, we find that our 

 nearest neighbor, Proxima Centauri, raises on the sun a tide of 

 quite infinitesimal magnitude; the tidal fraction is about 10-2«, and 

 the actual height of tide is of the order of 10-" cm., or, say, one- 



