<?php
/*
Quick Density Calcs
© Charles Chandler
http://qdl.scs-inc.us/?top=6744
*/
/*
Given the known mass and volume of the Sun, and given that the convective zone is the outer
30% of the Sun's radius, and assuming that the density of the convective zone averages that
of liquid hydrogen, we can determine the mass of the convective zone, subtract that from the
mass of the Sun, yielding the mass of the interior. Then we calculate the density of the interior.
*/
function VolumeOfSphere($radius) {
return (4 * PI * pow($radius, 3)) / 3;
}
$v['denOuter'] = 0.0763 * pow(10, 12); // density of liquid hydrogen, gm/cm^3 * 10^12 = kg/km^3
$v['masTotal'] = 1.9891 * pow(10, 30); // mass of Sun (in kg)
$v['radTotal'] = 6.9600 * pow(10, 5); // radius of Sun (in km)
$v['radInner'] = $v['radTotal'] * .7; // radius of radiative zone is 70% of Sun's radius
$v['volInner'] = VolumeOfSphere($v['radInner']); // volume of radiative zone & core combined
$v['volTotal'] = VolumeOfSphere($v['radTotal']); // volume of Sun
$v['volOuter'] = $v['volTotal'] - $v['volInner']; // volume of convective zone
$v['masOuter'] = $v['volOuter'] * $v['denOuter']; // mass of convective zone
$v['masInner'] = $v['masTotal'] - $v['masOuter']; // mass of radiative zone & core combined
$v['denInner'] = $v['masInner'] / $v['volInner']; // density of radiative zone & core combined
$v['denRatio'] = $v['denInner'] / $v['denOuter']; // density of radiative zone & core / convective zone
// results
$v = array (
'denOuter' => 7.63E+10,
'masTotal' => 1.9891E+30,
'radTotal' => 696000,
'radInner' => 487200,
'volInner' => 484407041629810000,
'volTotal' => 1.4122654274921E+18,
'volOuter' => 927858385862340000,
'masOuter' => 7.0795594841297E+28,
'masInner' => 1.9183044051587E+30,
'denInner' => 3960108421843.9,
'denRatio' => 51.90181417882,
);
?>
|