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This is a homework question and I don't want an answer but just want to understand what its asking for.

We are given that a star with a mass of x solar masses in our galaxy turns to a supernova and releases y amount of energy. Using this we are asked to calculate the average speed of the ejected mass.

v = sqrt(2*E_k/M) (Kinetic energy equation) gives the average speed.

Finally, the questions asks the following:

Compare your result with our Sun’s orbital speed around the centre of the Milky Way galaxy. Where would you expect this material to end up?

Is it asking to solve and check that the average speed > escape velocity if the star was at the same distance from the sun? Or how far from the center of the Galaxy would it end up?

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It's asking exactly what it says- where would you expect this material to end up? Giving a distance from the center of the galaxy may be relevant, or it may not, depending on exactly what speed you end up with, and how it compares to galactic orbital / escape velocity. If the velocity is well above galactic escape velocity, giving a specific distance from the galactic core doesn't make much sense- there will be no fixed distance, the stuff will just keep going, achieving greater and greater distances.

So, the first step is indeed to solve and check if average speed > orbital velocity or not (because the question says to do so), and a good second step would indeed be to check if it's less or greater than escape velocity. And from that information, you can guess generally where the stuff will go- stay reasonably close to the original orbit of the star? or stay in galactic orbit, but spread out in some wildly different range of orbits than what the original star had? or completely ejected from the galaxy?

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  • $\begingroup$ Thank you! The actual answer is well above the galactic escape velocity so I don't think we need to do the calculations for distance $\endgroup$
    – stackErr
    Jul 10 '15 at 2:35
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    $\begingroup$ @stackerr The supernovae ejecta is unlikely to follow a trajectory determined only by gravitational forces. Of course we owe our existence to the fact that supernova ejecta does not, under most circumstances, escape from the Galaxy. It plows into the ISM and slows down. I guess you were not meant to consider this (but that just makes it a poor question). $\endgroup$
    – ProfRob
    Jul 10 '15 at 9:21
  • $\begingroup$ @RobJeffries But those are always the assumptions when talking about escape velocities, or stars being totally disrupted, etc.: that there are no other interactions involved. Would you expect a first course in Newtonian mechanics, when covering Earth's escape velocity, to account for the potential collisions with space junk, micro-meteorites, gravitational interactions with nearby comets/asteroids, etc.? They might offhandedly mention that some or all of these things are important to a real space mission, but it's not going to appear on a homework problem. You keep it simple. $\endgroup$
    – zibadawa timmy
    Jul 10 '15 at 12:38
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    $\begingroup$ @zibadawatimmy All the above things you mention are negligible, unimportant or incredibly unlikely. It is a fact (and a very important one at that) that supernovae ejecta does not in general escape from the Galaxy. Think up a better question (e.g. start with a 3-body system, leave behind a more compact binary, work out the KE of the ejected object/star and see whether it would escape the Galaxy). $\endgroup$
    – ProfRob
    Jul 10 '15 at 13:10
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    $\begingroup$ @RobJeffries That's a better question for a graduate student but not for an undergrad in an introductory course. And I assume we are in the latter situation, not the former. One might hope the course at some point makes the fairly obvious observation that supernovae ejecta seem to routinely stay within the galaxy, using that to motivate discussion and material beyond the bare minimum introductory stuff. But for an introduction it seems entirely reasonable to not get bogged down with the complications of a more realistic scenario. $\endgroup$
    – zibadawa timmy
    Jul 10 '15 at 13:15

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