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The first and most important, is gravity. Sir Isaac Newton laid the basis of gravity's effects in his Law of Universal Gravitation. It stated that every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and is inversely proportional to the square of the distances between the particles. In other words if the distance between two particles doubles, then the attractive forces is reduced to a quarter of its original strength. Gravity thus has an effect on how satellites are put into, and stay in, orbit. The velocity an object has to achieve thus depends upon its distance from the Earth, the closer it is, the faster it has to go. A satellite in the lowest Earth orbit has to maintain a velocity of 8 kilometres per second, while at a distance of sixty Earth radii, it would only have to maintain 1 km/sec. Alternatively, a satellite could be put into an elliptical orbit, with the points at which the satellite is clossest and farthest away from the Earth, being known as the perigee and apogee respectively.
Secondly, they have to take into account Kepler's Laws. The first law states that the orbit of a satellite is an ellipse, and that one focus of the ellipse must be located at the centre of the Earth. In other words, the plane of the orbit must pass through the Earth's centre. This law has implications for the citing of launch sites and the orbits achievable from those sites. If for example, a satellite was launched due cast from Cape Canaveral, it would have an orbit of with an angle of inclination to the equator of 28.5 degrees, which is the northerly latitude of the Cape. By varying the direction of launch, the angle of inclination can be varied. If an equatorial orbit is required, the satellite would be launched into a parking orbit, and at the correct time, a rocket motor would be fired to adjust it. The second law states that as the satellite orbits the Earth, an imaginary line joins it to the centre of the Earth, which sweeps out equal areas in equal time. Thus the satellite will be moving at maximum speed at perigee and minimum at apogee. Finally, the third law deals with orbital time and states that the orbital period is proportional to the cube of the semi-major axis. In practical terms the orbital period is dependent on the length of the major axis, and the degree of ellipticity doesn't come into it.
Thirdly, there are real world considerations. The Earth is not a perfect sphere, but a flattened (oblate) spheroid. This results in two disturbances to orbits, the first being the rotation of the orbital plane. This is a rotation of the orbital plane around the Earth's polar axis. The direction of rotation is always in the opposite direction to satellite travel and depends upon orbital height and the angle of inclination.
So a low orbit will be affected more than a higher one, and a polar orbit will suffer no rotation, but an equatorial one will suffer the most. Mile it can be a nuisance, it can be used to good effect, in 'sun-synchronous' orbits. This is where a satellite's orbit is calculated to bring it over the same spot, at roughly the same time every day by using a very gradual rotation in the orbital plane to compensate for the Earth's travel around the Sun. The second major disturbance is the rotation around the major axis (apsidal rotation) in other words, a movement of the apogee and perigee around the orbit- Again, this effect has most influence on low orbits, but the direction of rotation is only affected by the angle of inclination. So it is at maximum for one direction in polar orbit and the other direction for equatorial orbit. Finally other factors can play a part, such as the gravity pull from other objects, the Earth's magnetic field, micrometeroid impact, the orbital decay caused by the Earth's atmosphere and the Earth's rotation.
The methods of getting a satellite into orbit are all fairly similar and only vary according to whether they are liquid or solid fuelled, and manned or unmanned. Liquid fuels tend to have a higher specific impulse and have greater controllability, while solid fuels have greater stability and are easier to store, but once ignited cannot be controlled. The launch vehicle initially propels its way through the Earth's atmosphere going straight up, and then after the initial stages have been lost, gradually curves over to adopt the launch azimuth. -Satellites are usually 'parked' in low earth orbit, and if required to be in a higher orbit, transferred by means of the Hohmann minimum energy transfer. The final stage booster is used to give the satellite an elliptical orbit, in which its injection point becomes the perigee, and its apogee, the injection point into the new orbit. Great care is taken to ensure the satellite is injected as accurately as possible at each stage, as the greater the accuracy, the less fuel will be needed to modify its path, thus prolonging its useful life. Unmanned launch vehicles are rockets, and are often based on Intercontinental Ballistic Missiles (ICBMs), which, having been kept at a high state of readiness, tend to be solid fuelled. The Soviet Union had by far the greater choice of launch vehicles, with a reusable space plane, a shuttle (called Buran) and heavy lifter under development. The US has had a far smaller number of launchers, but its Space Shuttle fleet has been in service since 1981.