#!/opt/perl/bin/perl
# Simple calculations for solar system 
$pi = 3.1415926532;
$d2r = $pi/180.0; 	# to convert degrees to radians
$c = 2.99792458E08;	# light velocity
$a = 0.5330555555;	# angular size of Sun
$sundia = 1392700;	# absolute size of Sun km
$x = sin(0.5*$a*$d2r)/cos(0.5*$a*$d2r); # tan(omega/2)
$L = 0.5*$sundia/$x;	# distance of Sun to Earth
$l2r = 2.0*$L/$sundia;
$t = 1000.0*$L/$c;	# travelling time of the light from Sun to Earth
$t2 = $t - 480.0;	# 8 minutes plus t2 sec
$w = 2.0*$pi*$L;	# total length of orbit
$w2 = $w/365.25;	# the way travelled a day
$w3 = $w2/24.0/3.6;	# the average orbital tangential speed
$ov = 360.0/365.25;	# the angular speed degrees a day
$v2 = 2.0*$w3*sin(0.5*$d2r*$ov); # the radial speed
$accel = $v2/24.0/3600.0;
$G = $accel*$l2r*$l2r;
$g = 9.811;
# The next page is necessary for CGI purpose to make it work:
print "Content-type: text/plain\n\n";
print "The size of Sun and distance from Earth:\n";
print "Diameter of Sun $sundia km \n";
printf ("Angular diameter of Sun as seen from Earth, omega = %3.6f degr\n",$a);
print "Distance of Sun from earth L = Sun radius". "/tan(omega/2)=";
printf ("%10.0f km \n",$L);
print "\nLight velocity = $c m/s\n";
printf("Light migrates in %5.1f sec = 8 minutes %2.1f sec from Sun to Earth\n",$t,$t2);
print "\nWe calculate now the acceleration of Earth toward Sun:\n";
print "We assume a circular orbit with constant speed of Earth to make it easier to calculate.\n";
printf("Earth travels 2pi*L = %10.3E km around the Sun during a year\n",$w);
printf("This is in average %10.3E km during a day\n",$w2);
printf("This corresponds to an average velocity %6.0f m/s\n",$w3);
printf("Earth travels a = %1.4f degrees a day around the Sun \n",$ov);
print "Earth is falling with a constant speed v2 towards Sun.\n";
printf ("v2 = 2v1*sin(a/2) = %4.1f m/s\n",$v2);
print "The speed v2 is caused by the acceleration a1 of Earth toward Sun \n";
printf ("a1 = v2/24 hours = %2.3E m/s^2\n",$accel);
print "\nNext we calculate gravitation G on the surface of Sun:\n";
print "G is increasing in proportion to the square of the decreasing distance to Sun.\n";  
printf ("Distance of Sun from Earth L = %4.2f x Sun radius \n",$l2r);
printf ("G = a1*(L / Sun radius)^2 = %2.3E*%4.2f^2 = %4.3f m/s^2\n",$accel,$l2r,$G);
printf ("G = %3.2f x g on Earth (%3.3f m/s^2)\n",$G/$g,$g);