Type definition for Schwartzschild equations

Hello

Just a short code to illustrate the type functionality. Reading input from a data file, writing the formatted results to a file and also to the console as a check. There are even more basic routes to do the same, but interesting to explore the Fortran 95 syntax further.

module schwarzschild_mod
  implicit none

  !integer, parameter :: dp = selected_real_kind(12,100)
  integer, parameter :: dp = kind(1.0d0)

  !==============================
  ! Derived type definition
  !==============================
  type :: Schwartzschild_properties
     real(dp) :: S_radius
     real(dp) :: S_density
  end type Schwartzschild_properties

contains

  !==============================
  ! Schwarzschild function
  !==============================
  function GR_Schwartzschild(mass) result(properties)
    implicit none

    real(dp) :: mass
    type(Schwartzschild_properties) :: properties

    real(dp), parameter :: G = 6.67430e-11_dp
    real(dp), parameter :: c_light = 2.99792458e8_dp
    real(dp), parameter :: pi = 4.0_dp * atan(1.0_dp)

    properties%S_radius = 2.0_dp * G * mass / c_light**2

    properties%S_density = (3.0_dp * c_light**2) / &
         (8.0_dp * pi * G * properties%S_radius**2)

  end function GR_Schwartzschild

end module schwarzschild_mod

program RS1
  use schwarzschild_mod
  implicit none

  integer :: i, n, ios, ierror
  character(len=25) :: Mass_object
  real(dp) :: mass
  type(Schwartzschild_properties) :: results

  open(22, file='objects1.dat', status='old', action='read', iostat=ierror)
  if (ierror /= 0) stop 'Cannot open input file'

  n = 0
  do
     read(22, *, iostat=ios)
     if (ios /= 0) exit
     n = n + 1
  end do
  rewind(22)

  open(25, file='objects1-calc.dat', status='replace')

! write header for file
  write(25,'(A)') '==========================================================================='
  write(25,'(A)') '      Object                Mass(kg)     Radius (m)      Density (kg m-3)'
  write(25,'(A)') '==========================================================================='


! Check results at the console
  print *, '      Object                Mass(kg)     Radius (m)      Density (kg m-3)'
  print *, '==========================================================================='

  do i = 1, n
     read(22, *) Mass_object, mass

     results = GR_Schwartzschild(mass)
     write(*,'(1x,A,1x,es12.5,3x,es12.5,5x,es12.5)') &
          Mass_object,mass,results%S_radius,results%S_density ! check results at console
     write(25,'(1x,A,1x,es12.5,3x,es12.5,5x,es12.5)') &
          Mass_object, mass, results%S_radius, results%S_density ! write results to file
  end do

  close(22)
  close(25)

end program RS1

For anyone interested, the test data (kg), a random selection, are:

Observable_universe,8.80e+52
Milky_Way,1.60e+42
SMBH_NGC4889,4.20e+40
SMBH_Messier_87,1.30e+40
SMBH_Andromeda_Galaxy,3.40e+38
RMC_R136A1,6.2685e32
SMBH_Sagittarius_A,8.20e+36
Sun,1.99e+30
Earth,5.972e+24
Moon,7.346e+22
Jupiter,1.90e+27
Plaskett's_Star_B,1.1144e32
Donald_Trump,110
Big_Mac,0.215
Planck_mass,2.18e-8

Lester

The mass of the observable universe leads to a radius of 14 billion lightyears -- which is conveniently the approximate age of the universe.

If I understand the physics correctly, if you crushed an object down smaller and smaller, this program tells you the size at which it would turn into a black hole, and how dense it would have to be.