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where r0 is the (dimensionless) radius of a spherical star of identical volume, and the quantities wk and v2 are defined by wk = 4t?(r0) > "2 = ^2(1 + q)F2ro3, (3.1.49) and Pk(l) are the Legendre polynomials of degree k:

3l2 1 5l3 3l 35l4 30l2 3

P2(l) = —;— • P3(l) =---• P4(l) =-3-. (3.1.50)

Similarly, as shown by Chandrasekhar (1933b), the gravitational acceleration associated with the deformation of components can be expressed as g =

where g0 is the acceleration for a spherical star of the same volume. The coefficients of Pk(A) describe the tidal deformations and the contributions to the equatorial ellip-ticity caused by the first three partial tides. In elliptic orbits, they vary with the size d = 1 - e cos E of the radius vector.

The coefficient of P2(v) describes the oblateness caused by the rotation. is a function that depends weakly on the polytropic index n; A2(n) « 1. In the limit n ^ 5 (Roche model), ^ 1. Equations (3.1.48) and (3.1.51) contain the expansion factors

0(q, ro, n) := 1 +1(1 + q)r3n(n), 0'(q, ro, n) := 1 - 4(1 + qrV(n), (3.1.52)

for the radius and the acceleration. n(n) and n'(n) are functions that approach 1 in the limiting case of the Roche model and are given in Chandrasekhar (1933a, Eq. 44) and Chandrasekhar (1933b, Eq. 101):

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