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See taylor's classical mechanics page 302.

where $E=T+V=\frac{1}{2}m\dot{r}^2+\frac{l^2}{2mr^2}+U(r)$ thus for a two body problem with angular momentum $\neq 0$ the objects could never come close to $0$.

However, as we know stars do merges, and I suppose because the stars themselves is rotating and therefore conserved the angular momentum.(or in another reference frame) However, I still lack a picture of how exactly is the angular momentum conserved(in the process of merging).

My questions were:

  1. i.e. would the conservation of angular "slow down" the merge of the stars or planetary objects?(compare to the direct hit) and how much would that factor be?

  2. Was is also necessary to consider the relativistic effect (since the angular momentum had a danger of blowing up) due to the angular momentum?

  3. (just for fun) Would the conservation of angular momentum cause some "special effects" in astronomy, affect planetary/star structure, or cause some energy surge like heat?

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    $\begingroup$ Have you considered the effects of the fact that the stars are not point objects but extended bodies, and that (both before and after the merger) they can have angular momentum in their spin? $\endgroup$ – Emilio Pisanty Aug 9 '18 at 16:27
  • $\begingroup$ @EmilioPisanty right, "stars themselves is rotating", I didn't like to use spin these days, it kind of remind me of QM. $\endgroup$ – J C Aug 9 '18 at 16:32
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    $\begingroup$ (1) In some mergers involving black holes or neutron stars, a significant amount of mass-energy and angular momentum is radiated away as gravitational radiation. (2) Often when stars merge, it's because one star evolves off the main sequence and becomes a giant that eats the other, not necessarily because the difference between their centers of mass decreases. $\endgroup$ – Ben Crowell Aug 9 '18 at 19:28

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