Page:Transactions NZ Institute Volume 13.djvu/198

152 and molecular exchange act as resistances to planetary motion and are both maximum at perihelion, thereby decreasing aphelion distance and rendering the orbit more circular.

When a body is moving forward in a gas, the gas adheres and produces retardation. If the body be revolving this retardation is unequal and the body is deflected. The well-known fact that if a projectile revolves on any other axis than its own direction it is deflected, is an illustration of this action, and it is to make the ball move in its true path that a gun is rifled. It has been shown in the paper "On the general problem of stellar collision" that all the bodies developed by "partial impact" tend to revolve in the same direction; in order, therefore, to ascertain the effect of this gaseous adhesion on the path of a planet revolving in a nebula we have especially to consider the case of a body revolving in the same direction as its orbit, and on an axis perpendicular to its plane.

Problem 3. To ascertain the influence of gaseous adhesion on a rotating planet revolving in a nebula.—Let the arrows in fig. 6 represent the general direction of motion. Let a b represent the planet rotating in the direction of its arrow; it is evident that a particle at a is tending to move forward faster than a particle at b, for if the path of b were an epycycle, as it might be, it is evident that for an instant it would be at rest; hence gaseous resistance is stronger at a than at b, hence a is retarded more than b, and the direction the body will tend to take is towards c. In other words, gaseous adhesion acting on a planet revolving on an axis perpendicular to its ecliptic in the same direction as its orbit tends to straighten the curve.

From the above problem it is evident that on the first return when it meets the nebula it tends to increase perihelion distance and alter apsides, as shown by the dotted ellipse fig. 6. After the first return, were the nebula uniform, it would tend to make a larger ellipse, that is increase its average distance from the centre, thus the potential energy of the planet would be increased, and this increase is done at the expense of the planet's rotation. It might be supposed that this would be a very small matter, but it must be remembered that all the time the body is contracting from a more or less dense gaseous to a liquid state the whole of this potential energy will be converted into rotation, thus the total effect may be very considerable, but as this action will be chiefly at perihelion it will tend materially to alter the eccentricity. It must be clearly understood that it is the differential resistance on the sides of the planet towards and away from the sun that is discussed in this paragraph; its general retarding action was studied in the last problem.