Liftoff
Rocket engines are different from car or jet engines in two fudamental ways.
1. Unlike cars, rockets don't need to "push off" of anything to propel themselves forward. 2. Rockets are selfcontained. In other words they don't need oxygen from the atmosphere to provide fuel for energy.
Rockets operate using the law of conservation of linear momentum. This law states that whenever two or more particles interact, the total momentum of the system remains constant. In this case the shuttle and it's fuel can be considered separate particles.
A rocket moves by ejecting its fuel out the nose at extremely high velocities (approx. 6000 mph). The fuel is given momentum as it is being ejected. To insure conservation of linear momentum, the shuttle must be given a compensating momentum in the opposite direction.
Rockets move exactly like Dr. Newman would if he were on a sheet of ice with 3 million pounds of baseballs throwing them at a rate of 22,000 lbs/sec. Actually Dr. Newman would move quite a bit faster, because he has MUCH less mass than the space shuttle.
To quickly summarize, thrust is equal to the exhaust velocity multiplied by the amount fuel leaving with respect to time. This is illustrated by the equation:
Thrust = ve(dM/dt)
This tells us the only way to increase the amount of thrust acting on the rocket, is by increasing the velocity of the exhaust, or the amount of fuel, M, leaving per second.
 This is why space shuttles don't hurl baseballs out the back of the rockets. It's takes a lot of energy to accelerate a baseball to 6000 mph!
Rocket Scientist (they don't call them that for nothing) prefer to use the ideal gas law: An ideal gas is one for which PV/nT is constant at all pressures.
 Fuel and an Oxidizing agent, usually liquid oxygen and hydrogen respectively, are forced into the combustion chamber where they are ignited. The temperature increases which forces the pressure in the chamber to increase to insure PV/T remains constant.
Volume inside the chamber is constant so:
Pi/Ti = Pf/Tf, => Pf = PiTf/Ti
Using Bernoulli's equation we can determine the velocity of the gas exiting the Nozzle:
Ve = Ac[2(Pc  Pn)/(p(Ac^2An^2))]^(1/2)
where V = velocity, A = cross sectional area, P = pressure, p = density of the fluid, and n,c = defines Nozzle and Combustion Chamber respectively.
The final step is to find the rate the mass is being ejected (dM/dt). The law of Conservation of Mass tells us mass is neither created nor destroyed. This means for every pound of fuel being being consumed, one pound of gas will be created. This is regardless of the pressure, density or volume of the gas.
Combining these facts it is easy to find the thrust a rocket will produce.
The 4 main forces acting on a rocket are the, Force of Gravity, Drag, Lift, and Thrust. The force of gravity, and the thrust act through the center of mass. Lift and drag acts at the center of pressure of the rocket.
The center of pressure varies depending on the distribution of drag and lift across the rocket. Some factors that affect this distribution are, nose design, fin size/shape, and a material's "smoothness".
External force such as a gust of wind will cause a torque about the center of mass. The torques cause rotation around the rockets axes. This rotation is referred to as Roll, Pitch, and Yaw. Roll isn't a problem, because it doesn't affect the rockets path. Even small amounts of pitch or yaw could create serious problems.
Conventional rockets stabilize themselves using fins in the rear. They work exactly like a weather vane. Here the center of mass is at the point where the arrow rotates about support. When the wind blows it causes a torque at the center of mass which forces the tip to point upwind.
The beauty with this system is that it is "passive". This means if a rocket rotates, drag will act at the center of pressure in the opposite direction of the velocity, and it will "right" itself. This is known as a restoring force. (see the diagram above)
Unfortunately in space there is little atmosphere and thus no drag to act as a restoring force. This is why you don't see fins on shuttles. To maintain stability, shuttles use an adjustable nozzle to deflect thrust one way or another. When in orbit, they use thrusters known as vernier rockets. These are actually small rockets placed on various parts of the ships exterior.
Orbit Insertion: Orbit Insertion is a tricky and dangerous part of space missions. As a shuttle reaches it's target orbit it has to turn reducing its radial velocity, and increase it's tangential velocity. If the shuttle is going too fast it will shoot out into space. If it's going to slow it will fall back to earth.
For a shuttle to remain in orbit, it's radial acceleration must be equal to and opposite of gravitational acceleration. This doesn't scare engineers (They are Rocket Scientists). Tangential Velocity is calculated below.
Gravitational acceleration is a function of height
ge = GMe/(r +h)^2
ge = ar
ar = vt^2/(r +h)^2
GMe/(r +h)^2 = vt^2/(r +h)^2
vt = (GMe)^(1/2)
G = Universal Gravitational Constant G = 6.673*10e11 N*m^2/kg^2
Me = Mass Earth = 5.96*10e24 kg
ar = radial acceleration
ge = acceleration due to gravity
r = radius earth, h = altitude
Radial acceleration should equal gravitational acceleration.
Which gives us
Combining the equations and solving for vt
 Typically a space shuttle will orbit the earth at about 300km, in order to stay in orbit the shuttle must travel 7.73 km/sec or 27,773 km/hr.
 Most scientific Satilites orbit the earth at an altitude ranging from 4800 km to 9700 km, with velocities ranging from 21,492 km/hr to 17,928 km/hr
 Military GPS satilites orbit the earth at altitudes ranging from 9600 km to 19200 km, with velocities ranging from 17,964 km/hr to 14,9220 km/hr
 The higher the orbit the slower velocity required.
Systematic approach adhered Timotheus Homas, Peter Lutsky and Tylor Ranson
1. Fundamentals of Physics, 5th or 6th edition, Halliday, Resnick, Walker How to Cite this Page MLA Citation: "Fundamentals of Rocket Science." 123HelpMe.com. 21 Dec 2012
<http://www.123HelpMe.com/view.asp?id=153359>.
This article uses material from the Wikipedia article Nathanaels Sogn, that was deleted or is being discussed for deletion, which is released under the Creative Commons AttributionShareAlike 3.0 Unported License.
