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Torque about centre of sun is zero. $$T=Ia$$ So angular acceleration is zero too, so angular velocity should remain constant. However it is not the case. Please tell where I went wrong.

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Torque is change in angular momentum , and hence angular momentum of this system must be conserved as in deep space we have assumed that there is no external force , so the change in angular momentum is $0$ (as it is conserved) hence torque is $0$

If we recall that the orbits are elliptical the radius is constantly changing with each point in the orbit , so we also know $L=mvr$ and $v=rw$ , hence $$L=mr^{2}w$$

here L is a constant and m is assumed to be a constant , in ideal situations to make L the constant it is , $w$ changes to counteract the change in radius to make the value of L same every time

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