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\Dauthor{ ��R ���� } % �����̖��O
\Ddate{ 2004/04/09 } % �쐬��
\Dfile{ sec0408.tex } % �t�@�C���̖��O

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\subsection{���b�V���͈�} % �߂̃^�C�g��
% ��������{���������ĉ�����.
����$m_p$�C���a$R_p$�̘f���̎���𓯊����]����C
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�q���̉~�O���̔�������$a$�Ƃ��C���ω^����$n$�Ƃ���D
3.6�߂Ō���ꂽ�悤�ɁC�s����ȃ��O�����W�����t�_$L_1$�C$L_2$�́C
�f���Ɖq���̒��S�����Ԑ���ŉq���̒��S���狗��$d_L$�̂Ƃ���ɂ���C
������$d_L$��
\begin{equation}	%%%128%%%
	d_L = \biggl( \frac{m_s}{3m_p}  \biggr)^{1/3}a
	\label{128}
\end{equation}
�Ə�����D���R�r�萔��
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�q��������(3.13�߂�����)���狁�߂��C
$C_H = 9 (m_s / 3 m_p)^{2/3}$�ŗ^������D
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{\bfseries ���b�V������[�u(Roche lobe)}�ƌĂ΂�C
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�q���̐ԓ��ƁC�q���Ƙf���̒��S�����Ԑ���
�����ɂ̂��Ă��闱�q�̈��萫�ɂ��čl���Ă݂悤�D
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���̗��q�����͂�q���ɏd�͓I�ɕ⑫����Ȃ��Ȃ�
������$a_L$���v�Z���邱�Ƃł���D
�q���̒��S�ɂ��闱�q�ł́C�d�͂Ɖ��S�͕͂��t��
$\mathcal{G} m_p / a^2 = n^2 a $�ł���D
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(i) �����V�A�[�ɂ��C�ߏ�Ȃ����d�͂܂��͉��S�́D
(ii) �q���̎��]�ɂ�鉓�S�́D
(iii) �q���̏d�͂ɂ��́D
���󂯂�D
�������̗��q�����t���Ƃ����̗͂͒ނ荇���C
\begin{equation}  %%%129%%%
	-\frac{\partial }{\partial a} \biggl( \frac{\mathcal{G}m_p}{a^2} \biggr) R_s+ n^2 R_s = \frac{\mathcal{G}m_s}{R_s^2}
	\label{129}
\end{equation}
�Ə����C���̂��Ƃɂ��ȉ��̂悤�ɏ�����D
\begin{equation}  %%%130%%%
	\frac{3 m_p}{m_s} = \biggl( \frac{a}{R_s} \biggr)^3
	\label{130}
\end{equation}
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����������̉q���ł�
{\bfseries ���b�V�����E (Roche limit)} $a_L$(spherical)��
�ȉ��̂悤�ɗ^������D
\begin{equation}  %%%131%%%
	a_L (spherical) = \biggl( \frac{3 m_p}{m_s} \biggr) ^{1/3} R_s = \biggl( \frac{3 \rho _p}{\rho _s} \biggr)^{1/3} R_p
	\label{131}
\end{equation}
������$\rho _p$��$\rho _s$�͂��ꂼ��f���Ɖq���̕��ϖ��x�ł���D
��(\ref{128})�Ǝ�(\ref{131})���ׂ��
���b�V�����E�ɂ�����$L_1$��$L_2$�͉q���̕\�ʂɐڂ��Ă��邱�Ƃ��킩��D
�ӂ��̖��x���ߎ��I�ɓ������ƁC�f���̔��a�ŏ�����
$a_L (spherical) \approx 1.44 R_p$�ƂȂ�D

�������Ȃ���C
�q����(�������͍P����)�Ð������t�ɂ���ƁC
���b�V�����E�ŉq���͂��̃��b�V������[�u�𖞂����D
���̏ꍇ�C��(\ref{129})�͂������̏C����v����D
�����͂Ɖ��S�͂��傫���Ȃ�C
����ŉq���ɂ��d�͂͏������Ȃ�C
��(\ref{129})�̒��̏d�͂̍���
�悭�Ȃ��ߎ��ɂȂ��Ă��܂��D
��芮�S�ȉ�͂ɂ��
$a_L (hydrostatic) = 2.46 R_p$
��������Ă���(Chandrasekahar 1987)

�f���̃����O�̌n�͑S��
$a_L (spherical)$��$a_L (hydrostatic)$�̊Ԃ�
{\bfseries ���b�V���͈� (Roche zone)}
�̒��ɂ���(�}10.1���Q��)�D
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���z�n�̔N������Z���^�C���X�P�[���ɂ����āC
�f���Ɍ������ė�������ł���
(4.9�ߎQ��)�D
�����̉q�������b�V���͈͂ɓ���C
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���̂��Ƃ͘f���̃����O�̋N���ƋO�����a�ɂ��Ă�
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��(\ref{129})�ň��͂͏d�͂ɂ����̂����ł��邪�C
�ȉ��̈������苭�x(tensile strength)
\begin{equation}  %%%132%%%
	\mathcal{T} \ge (8/57)\pi \mathcal{G} \rho_p \rho_s R_s ^2
	\label{132}
\end{equation}
������q���͘f���̕\�ʂ̋O�������邱�Ƃ��ł���(Aggarwal �� Oberbeck 1974)�D
���̂��Ƃ���C
$\mathcal{T} \ge 10^6$ Nm$^{-2}$ �̈������苭�x������
�傫����$R_s \sim 200$km �̕X�q���͓y���̕\�ʂ̋O�������邱�Ƃ��ł���D
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�����ȉq�������b�V���͈͂̊O���ɂ���ꍇ�́C
�S�ĕ��ӂ��C��ɍďW�ς���C
�����ȉq�������b�V���͈͂̓����ɂ���ꍇ�́C
�S�ĕ��ӂ��C�U�����C�����O���`�������
(Smith et al 1981)�D


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