A satellite of mass M is in a circular orbit | vedclass

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(B) Let the satellite move with velocity $v$ in the tangential direction (say,along the $y$-axis) and the meteorite move with velocity $v$ towards the

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in an elliptical orbit

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(B) Let the satellite move with velocity $v$ in the tangential direction (say,along the $y$-axis) and the meteorite move with velocity $v$ towards the Earth (along the $x$-axis). After the perfectly inelastic collision,the combined mass $2M$ moves with a new velocity vector $\vec{V}$.By conservation of linear momentum:Along the $x$-axis: $Mv = (2M)v_x \Rightarrow v_x = v/2$.Along the $y$-axis: $Mv = (2M)v_y \Rightarrow v_y = v/2$.The magnitude of the new velocity is $V = \sqrt{v_x^2 + v_y^2} = \sqrt{(v/2)^2 + (v/2)^2} = v/\sqrt{2}$.Since the satellite was in a circular orbit,its initial velocity was $v = \sqrt{GM/R}$. The new velocity $V = v/\sqrt{2} < v$. Also,the direction of the velocity is no longer purely tangential. $A$ change in both speed and direction at the same orbital radius $R$ results in an elliptical orbit.

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