<em>The earth's density divided by that of the sun = 3.85.10⁻³</em>
Density is the ratio of mass per unit volume
<h3><em>Further explanation
</em></h3>
Density is a quantity derived from the mass and volume
density is the ratio of mass per unit volume
With the same mass, the volume of objects that have a high density will be smaller than the low density
The unit of density can be expressed in ![\frac{g}{cm^3}\:or\:\frac{kg}{m^3}](https://tex.z-dn.net/?f=%5Cfrac%7Bg%7D%7Bcm%5E3%7D%5C%3Aor%5C%3A%5Cfrac%7Bkg%7D%7Bm%5E3%7D)
Density formula:
![\large{\boxed{\bold{\rho\:=\:\frac{m}{V} }}}](https://tex.z-dn.net/?f=%5Clarge%7B%5Cboxed%7B%5Cbold%7B%5Crho%5C%3A%3D%5C%3A%5Cfrac%7Bm%7D%7BV%7D%20%7D%7D%7D)
ρ = density
m = mass
v = volume
We consider the Earth and the Sun to be spheres
We can know from the task that :
m earth = 6.10²⁴ kg
r earth = 4.10³ miles = 6,436.10⁶ m
earth volume =
![\frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3)
![=\:\frac{4}{3} \pi(6.436.10^6)^3](https://tex.z-dn.net/?f=%3D%5C%3A%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%286.436.10%5E6%29%5E3)
V earth = 1.12.10²¹ m³
m sun = 2.10³³ kg
r sun = 7.10⁵ miles = 7.10⁸ m
sun volume =
![\frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3)
![=\:\frac{4}{3} \pi( 7.10^8)^3](https://tex.z-dn.net/?f=%3D%5C%3A%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%28%207.10%5E8%29%5E3)
V sun = 1.436 .10²⁷m³
So
![\rho_{earth}\:=\:\frac{6.10^{24}}{1.12.10^{21}}](https://tex.z-dn.net/?f=%5Crho_%7Bearth%7D%5C%3A%3D%5C%3A%5Cfrac%7B6.10%5E%7B24%7D%7D%7B1.12.10%5E%7B21%7D%7D)
![\rho_{earth}\:=\:5.36.10^3\:\frac{kg}{m^3}](https://tex.z-dn.net/?f=%5Crho_%7Bearth%7D%5C%3A%3D%5C%3A5.36.10%5E3%5C%3A%5Cfrac%7Bkg%7D%7Bm%5E3%7D)
![\rho_{sun}\:=\:\frac{2.10^{33}}{1.436^{27}}](https://tex.z-dn.net/?f=%5Crho_%7Bsun%7D%5C%3A%3D%5C%3A%5Cfrac%7B2.10%5E%7B33%7D%7D%7B1.436%5E%7B27%7D%7D)
![\rho_{sun}\:=\:1.393.10^6\:\frac{kg}{m^3}](https://tex.z-dn.net/?f=%5Crho_%7Bsun%7D%5C%3A%3D%5C%3A1.393.10%5E6%5C%3A%5Cfrac%7Bkg%7D%7Bm%5E3%7D)
Then :
![\frac{\rho_{earth}}{\rho_{sun}}\:=\:\frac{5.36.10^3}{1.393.10^6}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Crho_%7Bearth%7D%7D%7B%5Crho_%7Bsun%7D%7D%5C%3A%3D%5C%3A%5Cfrac%7B5.36.10%5E3%7D%7B1.393.10%5E6%7D)
ρ earth : ρ sun ratio = 3.85.10⁻³
<h3><em>
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</em></h3>
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Keywords: density's sun, density's earth, mass, volume, spheres,miles, km