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Angular and orbital speed at perihelion
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[QUOTE="kuruman, post: 6204608, member: 192687"] The starting point for considerations of this kind is that angular momentum is conserved because the orbiting mass is moving under the influence of a central force which can exert no torque. This means that at all points on the orbit ##\vec L =\vec r \times \vec p=const.## The magnitude of the cross product is maximum when the linear momentum vector ##\vec p## is perpendicular to the position vector ##\vec r##. This occurs at perihelion and aphelion. The magnitude of the constant angular momentum is commonly calculated at either one of these points, ##|\vec L|=r_a~p_a=r_p~p_p## where subscripts "a" and "p" stand respectively for aphelion and perihelion. If you want to bring in ##\omega## through ##|\vec L|=\mu \omega r^2##, you would have to write ##\omega_a r_a^2=\omega_p r_p^2##. The expression ##\omega=v/r## is better written as ##\omega_a=v_a/r_a## at aphelion or ##\omega_p=v_p/r_p## at perihelion. At other points on the orbit a sine will be required. I cannot speak for your professor, but I think his/her objection is that writing ##\omega=v/r## is meaningless and misleading because ##\omega## varies along the orbit and it is equal to the ratio of the speed to the distance only at aphelion and perihelion with the understanding that ##\omega_a \neq \omega_p##. So how useful is this expression? [/QUOTE]
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Angular and orbital speed at perihelion
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