use strict;
use warnings;
my $G=6.67428*10**-11; # m^3/kg/s^2
my $c= 299792458;      # m/s
my $PI= 3.14159265358979323846264338327950288;
my $eV=  1.60217653*10**-19; # J

sub e2m { my $e= shift; return $e/$c**2; }

# gravitational force
sub Fg { my ($m1, $m2, $r)= @_; return $G*$m1*$m2/$r; }

# escape velocity: 
sub ve { my ($m, $r)= @_; return sqrt(2*$G*$m/$r); }

# volume of sphere = 4/3*PI*r**3
sub Vsphere { my $r= shift; return 4/3*$PI*$r**3; }

# density: 
sub density { my ($m, $r)= @_; return $m/Vsphere($r); }

my $mspoon= 0.005;  # kg

my $Melectron= 9.10938215*10**-31;
my $Mneutron= 1.67492729*10**-27;
my $Rneutron= 0.877*10**-15;
my $rho_neutronium= density($Mneutron, $Rneutron);
printf("neutron density: %g\n", $rho_neutronium);

my $vspoon= 0.05*10**-3; # m^3

my $Mneutronium_spoon= $rho_neutronium*$vspoon;
printf("weight of neutronium: %g\n", $Mneutronium_spoon);
my $l_spoon= 0.1;
my $m_spoon= 0.01;

my $Fspoon_neutronium= Fg($Mneutronium_spoon, $m_spoon, $l_spoon);
printf("force on spoon: %g\n", $Fspoon_neutronium);