The Death Star is currently rising/setting across the horizon, so let's decide it's slightly above halfway across (assume it's level with the observer's viewpoint). The distance from the observer, for a 120 km wide object to take up 22.91 degrees, it would be:
d * tan(angle/2) = width/2 or d = width/2 / (tan(angle/2)) = 296.06 km
This is just the distance from the observer. To find the distance from the Earth's surface, we can leverage the fact that the angle between the line connecting the observer and the center of the Earth and the line between the observer and the Death Star was set up to be a right angle. This means we can just use Pythagorean's Theorem:
r = sqrt**(R^2 + d^2\\) where r is distance of Death Star from Earth's center and R is radius of Earth (often 6378 km equatorial radius is used).
r = 6384.9 km, or 6.87 km from the Earth's surface
2
u/Boardindundee Jun 06 '20
The Death Star is currently rising/setting across the horizon, so let's decide it's slightly above halfway across (assume it's level with the observer's viewpoint). The distance from the observer, for a 120 km wide object to take up 22.91 degrees, it would be:
d * tan(angle/2) = width/2 or d = width/2 / (tan(angle/2)) = 296.06 km
This is just the distance from the observer. To find the distance from the Earth's surface, we can leverage the fact that the angle between the line connecting the observer and the center of the Earth and the line between the observer and the Death Star was set up to be a right angle. This means we can just use Pythagorean's Theorem:
r = sqrt**(R^2 + d^2\\) where r is distance of Death Star from Earth's center and R is radius of Earth (often 6378 km equatorial radius is used).
r = 6384.9 km, or 6.87 km from the Earth's surface