3 ms·
[edit, Made a mistake, added sanity checks] sin theta = r_earth / (r_earth + altitude) theta = arcsin( r_earth/(r_earth + altitude)) p_visible = (2pi - 2*the
by davidhollander 15y ago
[edit, Made a mistake, added sanity checks]
sin theta = r_earth / (r_earth + altitude)
theta = arcsin( r_earth/(r_earth + altitude))
p_visible = (2pi - 2*theta)/(2pi)
p_visible = 1 - arcsin ( r_earth / (r_earth + altitude))/pi
.
.
Sanity checks:
r_earth = 6378.1 X 1000 m
altitude = 1m
p_visible = .50006
.
altitude = 10^7 m
p_visible = .66766
This fits intuitively: the further away you are from the Earth's surface, the more of the sky you can see without the horizon interfering.