404
The Solar System [ch. xyi
Discussing the equipotentials il = constant in the manner adopted in
§ 229 we find that, whatever the values of M and M' may be, the equipotentials
surrounding the point M are at first spheres, but give place to open equi
potentials at a certain distance from M. Fig. 61 shews the equipotentials
drawn for the special case of M ' = 2 ilf. The last closed equipotential is
drawn thick, and its whole volume is found by quadrature to be equal
to that of a sphere of radius 0 - 348 R.
Similarly fig. 62 shews the equipotentials drawn for the limiting case of
M'/M = oo. The mass M' is now of course at infinity. The outermost
curve constitutes the last closed equipotential, and its volume is found by
/ j|/
quadrature to be that of a sphere of radius 0*72 i^jp) R-
The critical equipotential occurs when S' is at a distance R which bears a
certain ratio to the undisturbed radius of S. From the figures just given it
is found that the critical values of R are
/M'\&
when M'/M = 2, R = 2-87 r 0 = 2-28 r 0 (377 3),
when M'/M = oo, R = 1 ‘ 75 (m) r ° (377-4).