Download or view holeearthfullgradient.frink in plain text format
// Program to find the time spent falling through a hole in the earth assuming
// a non-uniform earth. The density of the earth is modeled using several
// layers which model closely the known density of the earth.
// This program is written in Frink:
// https://frinklang.org/
//
// Alan Eliasen, eliasen@mindspring.com
use Grid.frink
// The mass of a whole shell with inner radius d0 and outer radius d1
// and inner density r0 and outer density r1
wholeShellMass[d0 is length, d1 is length, r0 is mass_density, r1 is mass_density] :=
{
((d1 - d0) pi (2 d0 d1 (r0 + r1) + d0^2 (3 r0 + r1) + d1^2 (r0 + 3 r1))) / 3
}
// The mass of the partial shell with inner radius d0 and outer radius d1
// and inner density r0 and outer density r1 which is below an object
// at radius d.
partShellMass[d is length, d0 is length, d1 is length, r0 is mass_density, r1 is mass_density] :=
{
(pi (3 d^4 (r0 - r1) + d^3 (-4 d1 r0 + 4 d0 r1) -
d0^3 (-4 d1 r0 + d0 (3 r0 + r1)))) / (3 (d0 - d1))
}
// The mass of a whole or partial shell with inner radius d0 and outer radius
// d1 and inner density r0 and outer density r1 which is below an object at
// radius d.
shellMass[d is length, d0 is length, d1 is length, r0 is mass_density, r1 is mass_density] :=
{
if (d < d0)
0 kg // inside inner surface of shell
else
if d > d1
wholeShellMass[d0, d1, r0, r1] // completely outside shell
else
partShellMass[d, d0, d1, r0, r1] // partway through shell
}
// The different layers of density in the Earth
shells = [[ 0 km, 1221 km, 13.1 g/cm^3, 12.8 g/cm^3],
[1221 km, 3480 km, 12.2 g/cm^3, 9.9 g/cm^3],
[3480 km, 5651 km, 5.6 g/cm^3, 4.4 g/cm^3],
[5651 km, 6341 km, 4.4 g/cm^3, 3.4 g/cm^3],
[6341 km, earthradius, 2.9 g/cm^3, 2.2 g/cm^3]]
// This finds the mass that's still below you at a given distance from the
// earth's center.
mass[d is length, shells] :=
{
var m is mass = 0 kg
for [d0, d1, r0, r1] shells
m = m + shellMass[d, d0, d1, r0, r1]
// Fudge factor to make integral come out
// with the known mass of the earth.
return 0.995775976555 m
}
// Find the acceleration at a given distance from the core.
a[dist is length, shells] := G mass[dist, shells]/dist^2
var v is velocity = 0 m/s // Velocity at end of timestep
var stepsize is time = 1/100 s
var d is length = earthradius
var t is time = 0 s
var a is acceleration = 0 gravity
ga = new graphics // Graphics for distance-vs-acceleration graph
pa = new polyline
while (d > 0 m)
{
t = t + stepsize
a = a[d, shells]
v = v + a stepsize
d = d - v stepsize
pa.addPoint[d/km, -a]
// Print results every second
if (t mod sec == 0 s)
println[(t -> sec) + "\t" + (d->km) + "\t" + (v->mph) + "\t" + (a->m/s^2)]
}
// Print final times
println["Time to core : " + (1. t -> ["min", "sec"]) + "\t, " + (v->"mph")]
println["Time through earth: " + (2. t -> ["min", "sec"])]
ga.add[pa]
grid = new Grid
grid.setUnits[1, -m/s^2]
grid.auto[ga, false, 10, 25]
ga.add[grid.getGrid[]]
ga.show[]
Download or view holeearthfullgradient.frink in plain text format
This is a program written in the programming language Frink.
For more information, view the Frink
Documentation or see More Sample Frink Programs.
Alan Eliasen was born 20217 days, 23 hours, 31 minutes ago.