All stars in Milky Way equal one square light year?

  1. Hello,

    Can anyone confirm or, refute and correct the following statements?

    The volume of our galaxy, is roughly 8 trillion cubic light years. The combined volume of all the stars in our galaxy only equals one cubic light year.

    Thanks for any help you can provide!
  2. jcsd
  3. jedishrfu

    Staff: Mentor

    Here's some general scale stats that may help:

    and the Milky Way volume is computed to be 39 × 10E12 cubic light years or 39 trillion cubit light years (US)

    and Milky Way stats:

    with ~400 billion stars in total

    You can use these to work out whether the 1 cubic light year is correct or not.

    There is a lot of guesstimation here in order to come up with an answer like whats the average size of a Milky Way star for example
    as computed from the number of stars and the population percentages of stars dwarfs vs red giants vs ...
  4. marcus

    marcus 23,943
    Science Advisor
    Gold Member
    2014 Award

    Rusty I think the combined volume of all the stars in Milkyway is much less than a cubic lightyear.

    You can use the google calculator to quickly discover this. For starters put "solar mass" in the box and press =

    then put "100 billion solar mass" and press =
    It will give you kilograms.

    There are estimated 400 billion stars and the average star mass is about HALF the solar mass. So the mass of the stars is roughly on the order of ….
    put in "200 billion solar mass" and press =

    If you crowded all those stars into a cubic LY box the density would still be very low compared with the average density of the sun, or any ordinary star. they would not be taking up anywhere near the whole cubic LY.

    You can check this by simply making google calculate what the density would be. Put this into the box:

    "200 billion solar mass/cubic light year" and press =

    It is much less than the density of water.

    Of course red giants are bloated up big and have low density, but they are not a large part of the population. Most stars have density more like the sun---roughly on order of density of water.

    If I put in "400 billion solar mass/cubic light year" I get something like a millionth of a kg per cubic meter. That is a billionth of the density of water. It is much less than normal density of a star.

    What I'm saying is that the combined volume of all the stars in our galaxy does not amount to even a millionth of a cubic lightyear. That is still way too big an estimate of their combined volume.

    But I could be wrong. I just made a quick estimate using google calculator. Perhaps someone else will find a mistake and correct what I said.
    Last edited: Dec 22, 2013
  5. Nugatory

    Staff: Mentor

    My even quicker estimate: 10^11 stars, solar volume from google is 10^18 cubic kilometers, what's the cube root of 10^29? Something between 4x10^9 and 5x10^9 km, call it 5x10^12 meters.

    There are 86400 seconds in a day, so a light-day is about 3x10^12 meters. With 3x10^2 days in a year, cube that back out, and Marcus's "does not amount to even a millionth of a cubic light year" is looking pretty good.

    (I used google for the solar volume, long ago memorized 3x10^8, 86400, 365)
  6. D H

    Staff: Mentor

    I think you and Nugatory are wrong. Not enough wrong to come close to a cubic light year, but definitely wrong. You focused on the >95% or so of stars that aren't giants. You're right in that the total volume of those non-giant stars is tiny. You're wrong in that although the giant stars are tiny in number, they represent almost all of the total volume.

    In five billion years or so our own Sun will swell up to about 215 times it's current size in terms of radius, or ten million times its current size in terms of volume. Becoming a red giant is the fate of all stars between about 0.5 solar masses and 8 solar masses. That's about 1/4 of all stars that will eventually become red giants. Since these stars will spend about 10 to 20% of their life spans as a red giant, that means between 1/40th to 1/20th of the stars are red giants. Because they are many orders of magnitude more voluminous than their yellow dwarf counterparts, that small fraction of stars represents a huge fraction of the total stellar volume.

    The red supergiants and hypergiants make the red giants look tiny. They can be over three billion times the size of the Sun in terms of volume. I couldn't find a nice breakdown of stellar population of these extremely large stars, but that factor of a billion means that only a few are needed to make this tiny population of stars dominate over all others in terms of volume. Just one of them is more voluminous than are all of the red dwarfs.
  7. Nugatory

    Staff: Mentor

    And I think you're right. I thought about the size distribution, then without further thought assumed that the six-plus orders of magnitude Marcus and I found just HAD to be enough to overwhelm the effects of a small number of large stars. You're right, that's not a good assumption.
  8. D H

    Staff: Mentor

    But you're not wrong in rejecting the notion that "the combined volume of all the stars in our galaxy only equals one cubic light year." A decent sized red hypergiant is about one cubic light hour in volume. It would take on the order of 1012 hypergiants to equal a cubic light year, or about 1015 red giants.

    The combined volume of all the stars in a galactic supercluster is *maybe* one cubic light year.
  9. Thank you for your replies! I find what you say incredible but I'm sure you're right. Still, let me explain the context...or, where this issue is coming from. I'm a science fiction writer and in one of my stories an object traveling close to the speed of light (.999999) enters the rim of our spiral galaxy and travels in a relative straight line to the galaxies center. One person is making the point that the odds of this object hitting a star is very low and he explains this by saying that of the 8 trillion cubic light years of our galaxy only ???? cubic light years of it is stars.

    I don't think the context changes anything but I like to be as accurate as I can so, what should replace the '????' above?

    Thanks so much for your help!!
    Last edited: Dec 22, 2013
  10. phinds

    phinds 8,103
    Gold Member

    Well, here's another way to look at it. May be too verbose for your novel but it is this: if two galaxies with BILLIONS of stars each (and each way bigger than a spaceship, remember) collide, the chance of any two stars hitting each other is essentially zero. I've seen it estimated (sorry I can't find a reference) to be maybe 4 pairs of stars out of the billions of stars in each galaxy. That's zero for all practical purposes and that like billions of gigantic spaceships instead of just one, so the odds of it happening with a single real-world-size spaceship amounts to a rounding error somewhere around the 15th decimal place.
  11. Actually I've already used this analogy. Just like the quantum universe, the cosmos is mostly empty space.

  12. I'm not quite sure of how much this effect would change the likely-hood of a collision, but, at a greater and greater speed (as we are considering a spacecraft at close to light speed) a straight line trajectory is going to pass through a nebula or close to something denser than a vacuum. Although the odds of a collision would increase dramatically, the likely event of a collision would be slim to none.

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