#!/usr/bin/perl
## xiuguluan_mabolasi -- Are the distances enough to make the further higher one look lower?
## Copyright       : https://www.gnu.org/licenses/gpl.html
## Author          : https://www.jidanni.org/
## Created On      : Tue Jun 11 00:27:33 2019
## Last Modified By: Dan Jacobson
## Last Modified On: Tue Jun 11 03:00:50 2019
## Update Count    : 84
# https://tp69.blog/2017/08/13/curvature-of-the-earth/
# Conclusion: indeed even though higher by 20m, Xiuguluan looks 11m lower.
use strict;
use warnings FATAL => q(all);
use Math::Trig;
my $w      = 10;
my $radius = 6378137;
my %v      = (
    altitude => { Mabolasi => 3785, Xiuguluan => 3805 },
    distance => { Mabolasi => 76.1, Xiuguluan => 78.7 }    #km
);
printf "%${w}s %4s %4s\n", qw/Mountain Alti Visu/;
for (qw/Xiuguluan Mabolasi/) {
    $v{h}{$_} = sqrt( $radius**2 + ( $v{distance}{$_} * 1000 )**2 ) - $radius;
    printf "%${w}s %d %d\n", $_, $v{altitude}{$_}, $v{altitude}{$_} - $v{h}{$_};
}
printf "%${w}s\n",         "-" x 11;
printf "%${w}s %4d %4d\n", "Difference",
  $v{altitude}{Xiuguluan} - $v{altitude}{Mabolasi},
  ( $v{altitude}{Xiuguluan} - $v{h}{Xiuguluan} ) -
  ( $v{altitude}{Mabolasi} - $v{h}{Mabolasi} );

# https://en.wikipedia.org/wiki/Naked_eye says we can detect one arcminute
printf "%${w}s %4d+ needed\n", "Naked eye", 2 * pi *
  ( $v{distance}{Xiuguluan} + $v{distance}{Mabolasi} ) / 2 * 1000 / 360 / 60;
print "so must use binoculars to see difference.\n"