Time delay for a signal from Earth to a Satelite in geostationary orbit and back

Description

A geostationary orbit, geostationary Earth orbit or geosynchronous equatorial orbit (GEO), is an orbit whose position in the sky remains the same for a stationary observer on earth. For ground stations on the same meridian as the satellite, the time taken for a signal to pass from Earth to the satellite and back again can be computed using the cosine rule, given the geostationary orbital radius , the Earth’s radius and the speed of light.
(Geostationary satellites are directly overhead at the Equator, and become lower in the sky the further north or south one travels. As the observer’s latitude increases, communication becomes more difficult due to factors such as atmospheric refraction,)

Related formulas

Variables

ΔtTime taken for a signal to pass from Earth to the satellite and back again (sec)
cSpeed of light
REarth' s radius ( 6.371.000 m) (m)
rThe orbital radius (the distance from the centre of the Earth) (m)
ϕLatitude (degree)