Physics of a Rocket's Trajectory

Physics of a Rocket's Trajectory

Length: 1018 words (2.9 double-spaced pages)

Rating: Excellent

Open Document

Essay Preview

More ↓
Missing equations / figures

We as humans have always been fascinated with the unknown.� We seek to conquer every frontier.� Today, the final frontier is space.� So, many people are very interested in rockets, the vehicle for conquering the final frontier.� 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.� For example, a car engine produces rotational energy to turn the wheels of the car.� And, a airplane engine produces rotational energy to spin a turbine.� But, rocket propulsion is based on Newton�s Third Law, which says that for every action, there is an equal and opposite reaction.� So, rockets work by pushing fuel out the back, which in turn pushes the rocket forward.� 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.� 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.� Newton�s second law says that force is equal to mass times acceleration (F=ma).� However, for a rocket the calculations are not that simple because the rocket�s mass is always changing as it burns up fuel.� So, we have to replace a new term with F, leading to

�where is a term for the thrust of the rocket and it is defined by R, the fuel consumption rate, and is the fuel�s exhaust speed relative to the rocket.� 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.� The force of gravity is equal to mg.� The force of air resistance is

�where 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.� By themselves, these formulas seem somewhat easy, but a rocket�s flight incorporates many variable forces that make the calculations much more difficult.� We have already examined the rocket�s upward force and how the changing mass makes the force vary.

How to Cite this Page

MLA Citation:
"Physics of a Rocket's Trajectory." 19 May 2019

Need Writing Help?

Get feedback on grammar, clarity, concision and logic instantly.

Check your paper »

Physics of Firearms Essay

- Shooting is a popular activity and it is enjoyed by many people, so much so that it is also done at a competitive level. Although many people may have shot a firearm of some sort, few of those people actually realize how much physics is involved with the shot. So what exactly is Ballistics. Ballistics is the science or study of the motion of projectiles and in the case of most firearms, these projectiles are the bullets. There are two things that affect the flight of a bullet once it has been shot out of the gun....   [tags: physics gun guns firearm ballistics]

Research Papers
615 words (1.8 pages)

Physics Behind Why Rockets Fly Essay

- In order for any rocket to fly, it must obey some basic rules of physics. No rocket can escape the cardinal rule that the center of gravity must be in front of the center of pressure. Center of Gravity The Center of Gravity or Cg is the point that behaves as if all the mass was concentrated in that one spot. Simply put it is the point at which you could balance the rocket on your finger. The Cg is also the point around which the rocket rotates. This becomes very important for the rocket's stability as you will soon see....   [tags: physics rocket rockets fly]

Free Essays
511 words (1.5 pages)

Fundamentals of Rocket Science Essay

- 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 self-contained. 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....   [tags: physics rocket science]

Free Essays
996 words (2.8 pages)

The Physics of the Arc Essay

- ABSTRACT Several researchers have devoted efforts on studying physics of arc and descriptive models are used to explain many arc welding related phenomena. However, due to the subject complexity, doubts still emerge about the mechanisms of some phenomena related to the arc. For instance, the description about electromagnetic interactions with the arc, which governs the arc trajectory and lead to plasma jet and arc blow formation, seems to be yet controversial. Thus, the present study aimed a better understanding of these phenomena....   [tags: Physics ]

Research Papers
1244 words (3.6 pages)

Essay about Measuring Electron Movement, Trajectory, and Charge-To-Mass Ratio

- The e/m (electron charge: mass) of electrons Aim The aim of this experiment was to study the movement and trajectory of an electron that moves perpendicular to a magnetic field and measure the charge-to-mass ratio of an electron. Abstract An electron beam was fired through a magnetic and electric field. These two fields are connected to two power supplies and these power supplies are altered. The alteration of these voltages will change the strength of the electric and magnetic fields. Varying the magnetic and electric fields will change the trajectory of the electron....   [tags: Physics]

Research Papers
2140 words (6.1 pages)

The Physics Of A Rocket 's Propulsion System Essay

- Nuclear Propulsion The true proposition of a possibility that we could use a nuclear device to allow us to easily travel to mars and back might seem absurd, but the fact of the matter it is an all posable realty. Due to the basic concept of a rocket 's propulsion system is a controlled series of bombs destined to be detonated at certain times creating an uplift of thrust that eventually launches the craft fast enough to break through the atmosphere. The bombs that we use today make up most of the weight of our spacecraft in the form of liquid hydrogen and liquid oxygen....   [tags: Nuclear weapon, Cold War, Nuclear fallout]

Research Papers
1231 words (3.5 pages)

The Amazing Rocket Essay

- Rockets In Ancient times The first rocket like device was invented around 100BC by a Greek named Hero of Alexandria. This device was called an aeolipile. It consisted of a sphere mounted on a water kettle. A fire beneath the kettle turned the water to steam, which then traveled through pipes to the sphere and was expelled through two L-shaped pipes that caused the sphere to rotate. Hero Engine When rockets as we know them were first invented is not known. The first date we know true rockets were used was the year 1232, however it is believed possible that the Chinese had primitive rocket like devices before this....   [tags: It Is Rocket Science]

Research Papers
3301 words (9.4 pages)

The Physics of Basketball Essays

- The Physics of Basketball Introduction Any child can pick up a basketball, bounce it a few times, and throw it at the hoop without realizing the complex physics he is involving himself in. However, a greater understanding of the sport can be gained by applying the principles of physics to these actions. Through this paper I will be examining the physics of dribbling and shooting. For the equations, I will use a standard men’s basketball with a mass of 25 oz. (0.7 kg) and a diameter of 9.39”. Dribbling If the basketball was simply dropped from a height of 1 meter with no initial push from the dribbler and rebounded from the floor in a perfectly elastic collision, Mechanical Energy for the...   [tags: Physics Essays]

Research Papers
1826 words (5.2 pages)

Essay on Physics of Tsunamis

- Tsunamis are waves, or series of waves, created by a disturbance in the ocean. Most of the time this disturbance is by an earthquake but can be from meteorites, landslides, or even explosions. They are sometimes known as tidal waves but this is a misnomer because tsunamis have nothing to do with tides. While tsunamis are feared particularly in light of the December 26th tsunami, the physics behind them is fascinating. One the largest tsunamis in recent history was the Cascadia tsunami in 1700. This occured when two continental plates (stretching from Vancouver to California) slipped causing a 9.0 magnitude earthquake....   [tags: physics tsunami]

Research Papers
974 words (2.8 pages)

Essay on Physics of Golf

- Golf is one of the toughest sports there is. The entire goal of the game is to get a very small ball into a cup that is several hundred yards away. What most people may not realize is that physics plays a role in just about every aspect of trying to get the ball into that cup. Every part of the game, from the tee-off until the ball drops into the cup, is affected by physics in one way or another. The purpose of this web page is to introduce you to the role that physics plays in the game of golf....   [tags: physics sport sports golf]

Research Papers
1959 words (5.6 pages)

Related Searches

� But, the other forces on the rocket also vary.� The force of gravity is equal to Mg, but the mass of the rocket is always changing, and as the rocket travels higher and higher, gravity also changes.� And, the force of air resistance is

�but the coefficient of drag is not always constant, air density decreases with height above the earth, and velocity is always changing because the rocket is accelerating.� So, the calculations soon involve many integrals and become very difficult.

We can write the general equation for a rocket�s upward flight during liftoff as

We can apply this formula to any instant in the rocket�s path and find the net force fairly easily as long as we have all the information about the rocket at that instant.

By taking the integral of the formula we have for the flight of the rocket, we can analyze the rocket�s flight at any time t.� Although finding the value for a certain t would be fairly simple, the calculations become very time consuming when you have to perform them over and over again to analyze the whole flight of the rocket.� So, we can use a simple computer programming, such as Excel, so that the computer will do all the integrals for us.� By writing out the equations for conservation of energy, gravity, and air density and using the definition of the derivative, we come up with a final equation of:

We then start off with values of 0 for dt, v(t) and h(t) and plug our formula into Excel.� We then expand these formulas to include hundreds of calculations and graph the end result.

This graph demonstrates that as time increases, so do both velocity and height, which is to be expected.� Also, both increase slowly at first.� The velocity is increasing, so the rocket has some acceleration, which also causes the height to rise more quickly.

In order to completely break out of the earth�s gravitational field and continue on indefinitely, a particle has to exceed a certain initial velocity, called the escape velocity.� The escape velocity for a particle on earth�s surface is 40,320 km/h, or 11,200 m/s, which is very fast.� However, a rocket does not need to exceed that kind of a speed because the escape velocity is calculated for a particle with some initial velocity starting off from the ground and having no successive propulsion, such as a bullet shot from a gun.� A rocket, on the other hand can increase in velocity, keep a steady velocity, or at least keep from decreasing in velocity as much as a particle with only an initial velocity would.

Satellites placed into orbit never need to reach escape velocity either.� Instead, they are still acted on by gravity, which is why they are in orbit around the Earth.� The speed that they have to reach to achieve orbit is called orbital velocity, and it is a balance between the force of the gravitation pull of the earth and the rotational inertia of the satellite.� And, it varies according to the distance the satellite orbits from the Earth.� An approximate value for an orbit of 242 km (150 miles) is 27,359 km/h (17,000mph).

So, escape velocity is not all that important for rockets or their design for several reasons.� One is that most rockets never leave the Earth�s gravitation field, but instead fall into an orbit some distance from the earth.� Also, rockets have engines for propulsion and can increase in velocity if needed.� So, they do not simply have an initial velocity and can be propelled to whatever height is needed.

Return to