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Some variation of this question gets asked a lot:

We have 2 point masses, $m$ and $M$ in a perfect world separated by radius $r$. Starting from rest, they both begin to accelerate towards each other. So we have the gravitational force between them as:

$$F_g = \frac{GMm}{r^2}$$

How do we find out at what time they will collide?

There are two instances that seem to be emerging as "canonical", or at least that both seem to be the target of frequent duplicate closures:

  1. The Time That 2 Masses Will Collide Due To Newtonian Gravity (where the above quote comes from)
  2. Don't heavier objects actually fall faster because they exert their own gravity? (has more upvotes)

I think we should pick one of these (or potentially another version of this same question) to be the canonical target of duplicate closures. I would probably go ahead and pick #2 except that I happen to have the accepted answer on that question, and I wouldn't want people to think I'm doing it to accumulate reputation. Besides, there are some advantages to #1, namely that the question is more cleanly asked (IMO) and the accepted answer is much more direct.

What should we go with? #1 or #2, or another existing version of this, or write an entirely new canonical question for it?

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A canonical question, that is a question specifically intended to act as a definitive reference, is distinct from a question that just happens to cover the same topic. If I were writing a canonical question I would tailor the question to make it absolutely clear that the question was intended as a reference and to explain what it did and didn't cover.

So in this case I would write a brand new question and answer that combined the best aspects of the two questions you mention, the question Qmechanic links and indeed any other related questions.

I don't feel desperately strongly about this (at least, not strongly enough to volunteer to do it :-) and it's a lot of work writing a canonical Q/A in this fashion. However if you are attempting to provide the best possible reference i think a new question and answer are the best course.

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  • $\begingroup$ What I had in mind was really a canonical target for duplicate closures - maybe not "canonical question" in the sense that you mean it. Given that we have several good questions and answers on the topic already, I'd want to establish that there is no suitable candidate currently before starting on a brand new question and answer. So my response to this answer (not that I necessarily expect you to address this) would be, what are the shortcomings of each of the existing questions that make them unsuitable for being the target of future duplicate closures? $\endgroup$ – David Z Apr 21 '16 at 12:06
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This question comes in different versions:

  • with or without reduced mass.

  • with or without non-radial motion.

  • with or without relativistic effects.

  • with or without initial velocity.

  • taking the finite radii of the two bodies into account.

  • only asking for total time, or asking for radial coordinate as a function of time.

  • etc.

Since this question is often asked by beginners of physics, it is important to provide duplicates which are at the level of OP. E.g. I have often used Radial fall in a Newtonian gravitational field as a duplicate since it is easy to read and understand, and provides links for the interested reader. In other words, there doesn't seem to be currently a FAQ that adequately covers all cases.

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  • $\begingroup$ I meant to ask about the case where the objects are initially at rest, no relativistic effects are involved, and the finite radii of the objects are considered (point masses are a special case where the radii are zero). Given those restrictions, I think it's specific enough to be covered by a single question. $\endgroup$ – David Z Apr 21 '16 at 10:21

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