The US Military WGS (Wideband Global SATCOM) system of communication satellites have been launched into GEO. Each satellite offers 4,875 GHz of instantaneous switchable bandwidth, covering simultaneously 19 geographical areas around the globe. These satellites can also change orbits slightly using a mix of 10 and 22-Newton thrusters.
The satellites are controlled and monitored by the 3rd Space Operations Squadron stationed at Shriver Air Force Base
What does "GEO" stand for?
Given: (not ALL of these facts below may be useful, so need to judge and choose)
• G = 6.67 x 10-11 Nm2/kg2
• gE at sea level = 9.81 N/kg
• Earth mass = M = 5.972 x 1024
• WGS Satellite mass = m = 5,987 kg
• Earth Radius = RE = 6,371 km
• GEO from Earth Equator = rS = 35,786 km
• GEO from Earth Center = rC = 42,164 km
Also using the answers to the questions below, find the answer to g:
(a) Calculate the period and angular velocity of a WGS satellite in GEO (in appropriate units, SF, notation)
Answer: 7.27 x 10^-5
(b) Orbital velocity of WGS satellite in GEO
Answer: 3070
(c) Gravitational Potential Energy of Satellite in GEO
Answer: 5.66x10^-15
(d) Earth's Gravitational Field at GEO
Answer: 224000
(e) Kinetic Energy of satellite in GEO
Answer: 2.81x10^12
(f) Total Mechanical Energy of Satellite at GEO
Answer: 5.94x10^13
(g) Escape velocity of any satellite, IF one wanted to boost it into deep space, beyond the gravitational boundaries of the solar system.
GEO stands for Geostationary Earth Orbit.
(g) The escape velocity of any satellite is given by the equation:
Ve = sqrt(2GM / r)
where:
Ve = escape velocity
G = gravitational constant = 6.67 x 10^-11 Nm^2/kg^2
M = mass of the Earth = 5.972 x 10^24 kg
r = distance from the center of the Earth to the satellite (in this case, the radius of the Earth + distance of GEO orbit)
Plugging in the values:
r = 6,371 km + 35,786 km = 42,157 km = 4.2157 x 10^7 m
Ve = sqrt(2*6.67x10^-11*5.972x10^24 / 4.2157x10^7)
Ve = sqrt(7.98x10^14 / 4.2157x10^7)
Ve = sqrt(18,931,313)
Ve = 4,352 m/s
Therefore, the escape velocity of any satellite would be 4,352 m/s.