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Rocket Science and orbital mechanics of Satellites.
There are about 3000 operational satellites, owned by over 100 different countries orbiting the earth right now. About 550 of these are in geo stationary orbits - the satellite appears stationary compared to the rotation of the earth. Communications satellites are typically in such orbits. These allow you to leave your satellite dish in one position, and never have to change it.

Orbital mechanics is rooted in Keppler’s laws of planetary motion & Newton’s laws of universal gravitation.

These laws allow us to calculate the period and speed of such a satellite.
Speed = S = sq root(mu/r) mu= standard gravitational parameter
Period = T = 2pi*sq root(r^3/mu)
r = radius of orbit = altitude + radius of earth
mu = Newton’s universal gravitational constant x mass of planet

A geostationary orbit is 35,786 km from the equator. The orbital period is 23.93 hours, or 23 hours 56 minutes which is the time it actually takes for the earth to complete one rotation. The reason we normally count 24 hours as being one day, is because 24 hours is the precise time the sun is at the same spot in the sky every day.

To got into its orbit, the satellite is launched on a rocket. In the United States, one workhorse rocket has been the Atlas V. It weighs 700,000 lbs at launch and can lift 28,000 lbs to geostationary orbit. The main engine is powered by liquid oxygen, the oxidizer and RP-1 – which is form of kerosene, similar to jet fuel.

Rocket engines are an application of Newton’s third law, for every action, there is an equal and opposite reaction. The combustion of fuel causes high pressure exhaust gases to be expelled at supersonic speed. The rearward acceleration of the mass of the fuel leaving the rocket nozzle causes the equal and opposite reaction of forward thrust powering the rocket upward.

Maintaining a stable straight flight comes from swiveling the thrust nozzle to keep it stable. This is called gimbaled thrust.

A geosynchronous orbit is achieved in stages. Typically, the rocket takes the satellite on its orbital altitude, but the initial orbit is elliptical. This elliptical orbit has to be changed to a circular orbit to become geostationary. The satellite continues on an elliptical orbit until accelerating the rocket at precisely the right time during its trajectory forms a circular orbit at the geostationary distance, which is at 35,786 km above the earth’s equator. There is no other geostationary orbit.

Since there are 500 satellites at that altitude, the real estate is limited. This real estate at the geo stationary orbit is tightly controlled by an organization called, the international telecommunications union (ITU) which assigns each satellite a slot at this perimeter.

In addition, unless the rocket is launched from somewhere in the equator, it will have an orbit that is not quite geo stationary because it will not be in line or in the same plane relative to the equator. So for example, when satellites are launched from Cape Canaveral, which is located at about 28.5 degrees north latitude, the orbit will be inclined 28.5 degrees from the equator. This has to be adjusted, in a directional change requiring fuel. Thus, it is beneficial for countries to launch their rockets as close to the equator as possible so that less rocket fuel is needed to make this adjustment.

The first thing that happens after a satellite reaches its permanent orbit is that solar panels are deployed so that the satellite can have power to function. It orients itself relative to the sun and the earth, and establishes communication links. The main function of the satellite is to receive signals from earth mainly in the form of radio transmissions, amplify them, and relay them back at a different frequency back to the surface of the earth. The shift in frequency is used to prevent interference of incoming signals with outgoing signals.
#geostationary
#rocketscience
#satellites
Since radio waves are a form of electromagnetic radiation, same as visible light, they do not bend around the curvature of earth – photons are too fast after all, the job of the satellite is to transmit radio waves over long distances. Otherwise, this would require a string of thousands of relay stations on earth to do the same task.

Interestingly, a geostationary orbit is sometimes called the Clarke orbit, named for science fiction writer Arthur C. Clarke, who wrote 2001-a space odyssey. Believe it or not, he was the first person to detail the usefulness of such an orbit in a story he wrote back in 1945.