この文章の和訳を教えてください。
In the preceding papar (Nakazawa et al., 1989a,referred to as Papar I), we have proposed that a framework of Hill’s equations (Hill, 1878) is of great advantages to find precisely the collisional rate between Keplerian particles over wide ranges of initial conditions. First, in Hill’s equations, the relative motion separates from the barycenter motion, and the equation of the barycenter motion can be integrated analytically (see also Henon and petit, 1986). Second, the equation of motion can be scaled by h and Ω; h is the reduced Hill radius and Ω is the Keplerian angular velocity.
They are given by
h=(m_p/3M_?)^(1/3) (4)
and
Ω={G(M_?+m_p)/a_0*^3}^(1/2), (5)
Where a_0* is the reference heliocentric distance (which is usually taken to be equal to the semimajor axis of the protoplanet) and M_? is the solar mass. The first characteristic of Hill’s equations permits us to reduce the degree of freedom of particle motion and, hence, to reduce greatly the number of orbits to be pursued numerically. The second permits us to apply the result of an orbital calculation with particular m_p and a_0* to orbital motion with other arbitrary mass and heliocentric distance.
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