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The number of space rocks is exponentially related to the size of the rocks. There are more small space rocks than big ones. Stars are most commonly the size of the sun, big and smaller stars are rare, and giant stars are the rarest. Stars that are 0.5 solar masses should also be very bright and visible, but they are less numerous, when they should be more frequent than the sun.

What about planets? There should be many unaccompanied planets wandering in the darkness of space, without a star, and they should be a lot more common than stars themselves, becaues of the size distribution of space rocks and stars should be roughly parallel.

What am I missing?

graph of star size distribtion.

graph of space rock size distribution.

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  • $\begingroup$ This question is bothering me since long as well: Do you (or anybody else) have a source for the rock soze distribution or the star size distribution? $\endgroup$
    – B--rian
    Jan 5, 2021 at 13:15
  • $\begingroup$ Cool! ok I added some graphs to the query. $\endgroup$
    – bandybabboon
    Jan 5, 2021 at 13:20
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    $\begingroup$ There's a problem with your first graph. It is noted in the lecture notes "What fraction of these stars are smaller than the Sun? What fraction of all stars in the galaxy are smaller than the Sun? There is clearly a bias towards large stars -- why?" The answer to the rhetorical question is that it is easier to measure the diameter of large stars, so the many small stars are not part of the CADARS sample.... In fact most stars are smaller than the sun, and a few are much much bigger $\endgroup$
    – James K
    Jan 5, 2021 at 14:04
  • $\begingroup$ Your first graph is wrong or biased - the most common star is 0.2 solar masses and accordingly smaller than the sun. Also you are comparing a differential and a integral distribution, that's a classical 'apples and oranges' problem. $\endgroup$
    – AtmosphericPrisonEscape
    Jan 6, 2021 at 16:50

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You are comparing distributions in a way that they are not easily comparable and the eye is misled: watch the scaling of your axes of the plots you compare! In order to compare, you want to make sure that you use similar, either log-log for both graphs or linear-linear or something else - but identical in both graphs.

Mind also that the size distribution of the small solar system objects is NOT an exponential, but a power law distribution. A power law distribution is a sloped straight line in a log-log plot and the exponent of the power law is found in the slope in such plot.

The stellar size distribution usually is found under the keyword "initial mass function". And when you look at that (see the plot therein), you will find, that the size distribution of stars also follows a similar power law as does the size distribution of smaller bodies as found in our solar system. This ignores the evolution of stars - but that is what you want to do in order to compare the sizes of objects as they are created.

The slopes of the size distributions course differ as different processes play a role in formation of stars and the objects forming around a star-being-born.

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