Physics of a Rockets Trajectory :: physics rocket rockets trajectory science

Missing equations / figures We as humans have always been fascinated with the unknown.ï ¿ ½ We seek to conquer every frontier.ï ¿ ½ Today, the final frontier is space.ï ¿ ½ So, many people are very interested in rockets, the vehicle for conquering the final frontier.ï ¿ ½ Most people have a general idea of how rockets work, but very few have an understanding of the physics behind their flight, which scientists spent many years perfecting. Rocket propulsion is not like many other kinds of propulsion that are based on the principle of a rotation based engine.ï ¿ ½ For example, a car engine produces rotational energy to turn the wheels of the car.ï ¿ ½ And, a airplane engine produces rotational energy to spin a turbine.ï ¿ ½ But, rocket propulsion is based on Newtonï ¿ ½s Third Law, which says that for every action, there is an equal and opposite reaction.ï ¿ ½ So, rockets work by pushing fuel out the back, which in turn pushes the rocket forward.ï ¿ ½ The mass of the fuel pushed out the back of the rocket multiplied by the velocity of the fuel is equal to the mass of the rocket multiplied by the velocity of the rocket in the opposite direction.ï ¿ ½ Although there is always some energy loss in any type of engine, the rocket is propelled forward. There are many forces that a rocket must overcome, especially during liftoff.ï ¿ ½ Newtonï ¿ ½s second law says that force is equal to mass times acceleration (F=ma).ï ¿ ½ However, for a rocket the calculations are not that simple because the rocketï ¿ ½s mass is always changing as it burns up fuel.ï ¿ ½ So, we have to replace a new term with F, leading to ï ¿ ½where is a term for the thrust of the rocket and it is defined by R, the fuel consumption rate, and is the fuelï ¿ ½s exhaust speed relative to the rocket.ï ¿ ½ Also, we replace m with M and define M as the instantaneous mass of the rocket, including the unexpended fuel. We also have to incorporate the other forces acting on the rocket, such as gravity and air resistance.ï ¿ ½ The force of gravity is equal to mg.ï ¿ ½ The force of air resistance is ï ¿ ½where C is the drag coefficient, is the air density, A is the cross-sectional area of the body perpendicular to the velocity, and v is the velocity.ï ¿ ½ By themselves, these formulas seem somewhat easy, but a rocketï ¿ ½s flight incorporates many variable forces that make the calculations much more difficult.ï ¿ ½ We have already examined the rocketï ¿ ½s upward force and how the changing mass makes the force vary.