Collisional probability of planetesimals in solar gravitational field
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We have calculated the collisional rate of planetesimals upon the protoplanet, considering the effect of solar gravity.
Our numerical scheme is based on Hill's equations, which reduce the degrees of freedom of orbital motion.
We made simplifications to evaluate the collisional rate more efficiently and determine the phase volume occupied by collision orbits.
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Collisional probability of planetesimals revolving in the solar gravitational field.III
Summary. We have calculated the collisional rate of planetesimals upon the protoplanet, taking fully into account the effect of solar gravity. Our numerical scheme is based on Hill’s equations describing approximately the three –body problem. By the adoption of Hill’s equations , we can reduce the degrees of freedom of orbital motion. Furthermore, we made some simplifications: First, an orbital motion is determined by the formula of the two-body approximation when the distance between the protoplanet and a planetesimal is smaller than a certain critical length. Second, collision orbits in the chaotic zones are neglected in evaluating the collisional rate because of their very small measure. These simplifications enable us to save considerable computation time of orbital integration and, hence, to find numerically the phase volume occupied by collision orbits over wide ranges of orbital initial conditions.
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