##### Suppose two worlds, each having mass M and radius R, coalesce into a single worl

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Suppose two worlds, each having mass M and radius R, coalesce into a single world. Due to gravitational contraction, the combined world has a radius of only

 3 4
R.
What is the average density of the combined world as a multiple of ρ0, the average density of the original two worlds?
ρ0

Jun 11th, 2015

Density = mass/volume

Volume =V =  4/3Pi R^3

initially density of each world = ρ0, = M/V

after coalesce mass  = 2M  and radius = 3/4R

volume of combined world (sphere ) = 4/3 x Pi x  (3/4 R)^3 = 27/64 V

hence Density = 2M/(27/64V) = 128/27 ρ0   = 4.74 ρ0

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Jun 11th, 2015

ok thanks

Jun 11th, 2015

you atleast best me with some comment ... its lengthy problem

Jun 11th, 2015

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Jun 11th, 2015
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Jun 11th, 2015
Oct 21st, 2017
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