Answer the following questions for the two body Sun-Earth system. Assume that the forces due to all other heavenly bodies can be neglected. Use \(\vec{r}_1, \vec{r}_2\) to denote positions, and \(\vec{p}_1, \vec{p}_2\) to denote the momenta of the Sun and the Earth, respectively. Check if the quantities listed below are conserved.
- The sum of angular momenta of the Sun and the Earth
- The sum of momenta of the Sun and the Earth
- The angular momentum \(\vec{r}\times\vec{p}\) where \(\vec{r}=\vec{r}_2- \vec{r}_1\) is the position of the earth relative to the Sun. and \(\vec{p}=\mu \vec{v}\) where \(\mu\) is the reduced mass and \(\vec{v}\) is the velocity of the Earth relative to the Sun.
- Write approximation, if any, under which the angular momentum of the earth will be a constant of motion.
Using Newtonian mechanics only, give brief arguments in support of your answer
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4727:Diamond Point
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