Why is angular momentum conserved when a planet revolves about sun in an elliptical orbit? Why is linear momentum not conserved in this case?
Please use the minimum amount of equations and try to explain using pure physics logic if possible.
Answer
Why is angular momentum conserved when a planet revolves about sun in an elliptical orbit? Why is linear momentum not conserved in this case?
$$\rm \text{no external }\color{red}{torque}\to\color{red}{angular}\text{ momentum conserved}\\ \text{no external }\color{red}{force}\to\color{red}{linear} \text{ momentum conserved}\\$$
There is no external torque about the sun since the force of the sun and position vector are always at an angle $180^\circ$ since $\bar \tau =\bar r\times\bar F$, so angular momentum is conserved.
But since the path in not circular but elliptical, the position vector is not perpendicular to direction of motion hence some work is done, which changes the momentum indirectly by changing magnitude of velocity directly.
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