THE MEAN DISTANCES OF THE PLANETS. 



By R. T. A. Innes. 



The mean distance of a planet is equal to the semi-axis major 

 of its orbit considered as an ellipse. This mean distance only 

 coincides with its average distance if the eccentric anomaly is 

 taken as the independent variable. If time is taken as the inde- 

 pendent variable the average distance is 



a (I + f), 

 in which a is the semi-axis major and c the eccentricity. 



This equation by itself shows that as e diminishes, the 

 total amount of radiation received from the Sun increases, 

 because the average distance is getting less, and this is the case 

 of the Earth in the present age. as the eccentricity of its orbit 

 is decreasing slowly. If, with the present rate of decrease of 

 the eccentricity, the Earth is neither getting hotter nor colder, 

 or, in other words, that its radiation is exactly balanced by its 

 absorption, as meteorologists confidently assert, then the moment 

 the eccentricity ceases to decrease, and more so when it begins 

 to increase, the Earth's temperature will fall until a balance is 

 again struck. If this reasoning is correct, it follows that an Ice 

 Age would not be due so much to the large eccentricity of the 

 Earth's orbit as to the fact that the eccentricity is increasing.*. 



If the true anomaly is taken as the independent variable, 

 the average distance is 



a(i— r-^). 

 The researches of Laplace. Lagrange, Poisson and other 

 astronomer-mathematicians have proved that the mean distances 

 of the planets from the Sun are invariable, so far as concerns 

 their mutual attractions, but it is possible that secondary causes 

 such as increases of mass due to the fall of meteorites, tidal 

 effects, retardation due to matter in space, etc., may cause the 

 mean distances to change. The astronomer can only assert that 

 such changes, if they do exist, are too minute to have yet been 

 revealed in the cases of the planets ; the decrease of the distance 

 of Encke's Comet which is very irregular in its amount shows 



* Perhaps the argument needs enlarging. During the period of 

 perihelion the Earth receives more heat from the Sun than it does at 

 aphelion in any given number of days, but as a whole its rise in tempera- 

 ture is very slight, because as the temperature of a body rises its 

 radiating power increases (as the 4th power of the absolute tempera- 

 ture in the case of a black body). If we accept that over a series of 

 years during which the Earth's average distance is decreasing from 



a (1+2") to a {l+f — ''A e) 

 it just maintains a balance between its rates of absorption and radiation, 

 it would follow that when A e (change of the eccentricity) alters its 

 sign, the equilibrium will be upset and the Earth as a whole will change 

 its temperature, and as long as c is mcreasing the Earth will grow 

 colder. " In other words, the combined effect of the 4th power law 

 and the diminution of the eccentricity of the Earth's orbit is to maintain 

 the Earth at its present mean temperature. 



