# 100% proof of flat earth? Or is it? Dogcam high altitude balloon flight put to the test

The dogcam balloon flight is a famous “proof” of the flat earth! But do we really see a totally flat horizon? Let’s analyze the footage and find out whether the earth is really flat!

For this video, I’ve used a Gnuplot script that simulates the horizon under ideal conditions. In order to visualize the geometry, please check the video “Warum flat-earther die Erdkrümmung nicht finden können!” by Aaron Pathfinder: https://www.youtube.com/watch?v=2ly29DmAku0

Special thanks to Aaron Pathfinder and two anonymous physicists! Ads are due to the owner of the background music. The money goes to the artist, not to me!

Music: Al’Tarba – Grey Town: https://www.youtube.com/watch?v=0noHMoJR2x8

For everyone interested, here is the script:

# Assumptions: The unity vectors are x_3d=cos(phi)*sin(theta)
# y_3d=sin(phi)*sin(theta)
# z_3d=cos(theta)
# i.e. theta is measured from the “north pole”
# The z-direction points straight away from the line between
# Earth’s center and the Camera. The camera looks exactly in
# x_3d-direction.
# We assume a perfect spherical Earth. i.e. R(phi,theta)
# of the earth surface to be constant for all theta, phi.
# Furthermore we neglect the atmospherical distortion

R = 6371 # radius of the earth in km
h = 33.1 # size of the camera above the surface in km

theta = (pi/2.0)+atan(sqrt(2*R*h+h**2)/R)

print “”
print “Radius of planet in km: “, R
print “Height about the planets surfacein km: “,h
print “Height of horizion in degree: “, (pi/2.0-theta)*180./pi
print “Distance to horizon along line of sight in km: “, sqrt(2*R*h+h**2)
print “Distance between suborbital point and horizon along the Great circle in km: “, R*atan(sqrt(2*R*h+h**2)/R)
print “”

f =5.0 # focal length of the distortion-free lens

sensor_size_x=5.76 # extent of the photographic sensor in x-direction
sensor_size_y=3.29 # extent of the photographic sensor in y- direction

set xrange[-sensor_size_x/2.0:+sensor_size_x/2.0] # The center of the sensor shows
set yrange[-sensor_size_y/2.0:+sensor_size_y/2.0] # objects exactly in x-direction

set parametric

set trange [-pi/2:pi/2] # parameter t wll be used for phi
# we consider only the forward direction

# Note: The coordinate system we use the senosr does not equal the 3D coordinate system
# we have used for the macroscopic objects. Here origin of the new coordinate system is
# in the center of the sensor.
# Furthermore, here we have used x_sensor as the horizontal coordinate
# on the sensor and y_sensor vor the vertical axis of the sensor

#Thus x_sens = y_3d and y_sens z_3d-(R+h)

x_sens(t) = f* tan(t) # x-position on sensor
y_sens(t) = f* 1.0/(tan(theta)*cos(t)) # y-position on sensor

set xlabel “x on sensor in mm”
set ylabel “y on sensor in mm”

plot x_sens(t) , y_sens(t) title “horizon line on sensor”

pause mouse any “Click on plot to quit.”