Klrkwood.] J-"^ [Nov. 21, 



MM m m 



~x^ a^~ (a — xf ~ 'a^ (•^^• 



Applying this equation to the solar system, a- will be the equatorial radius, 

 of the solar nebula, and a — x that of a planet at the epoch of its sepa- 

 ration. Putting for simplicity a = 1, and reducing, 



2Jlf M 

 cc* — 2a;» + v^ x = ir. (2) . 



For Jupiter, m= \ and J!/= 1048, hence 



3^ — 2x^-Y 2.0019102a; = 1.0009551 (3), 



therefore x = 0.92501, 



1 — a; = 0.07499, 



(1 — a;) X 489,000,000 = 35,995,200. 

 Solving equation (2) in like manner for each of the principal planets we 

 obtain the distance from the centre of each to its limit as given in the fol- 

 lowing table : 



Planet. Dist. to Limit. 



Mercury 152,000 miles. 



Venus 700,208 



Earth 1,082,147 



Mars 764,650 



Jupiter 35,vl95,200 



Saturn 44,887,000 



Uranus 48,915,000 



Neptune 81,000,000 



In these estimates we neglect the eccentricity of the orbits as well as 

 the centrifugal force due to each planet's rotation. The masses and dis- 

 tances adopted are those given in Newcomb's Popular Astronomy, with, 

 the exception that for Mercury we have employed a mean between Von 



Asten's evaluation of the mass! „ qoo. 440 ] and the final value given by 



/ 1 \ 1 ^ 



Leverrier W o^» n.^^. J. The mean is ^ .^...j ^...r. • For the earth we have 



taken the sum of the masses of the earth and the moon. 



Applying equation (2) to some of the secondary systems we find the 

 following limits of stability : 



For the Moon 39,850 miles. 



Phobos 6.5 " 



First satellite of Jupiter 5,250 " 



Mimas 1.500(?) '« 



Practical Applications. 



The results obtained may now be employed in the approximate solution 

 of several interesting problems. The limits of stability will be regarded 

 as the primitive radii 01 the planets and satellites, as any exterior matter 

 would have been detached by the influence of the central body. To the 



