Escape VelocityIf a projectile is blasted from the earth, it may do one of several things.Most projectiles have a speed such that they soon begin to curve back downtowards the earth-this is the parabolic flight described by projectilemotion. However it is possible to give aprojectile sufficient speed (which is directly proportional to its energy) suchthat its downward curvature is exactly matched by the curvature of the earth.In this case, the projectile will never reach the ground, and will in fact be ina circular orbit around the earth. If the projectile is launched with evengreater energy, it will describe an elliptical path. This is consistent withwhat we have just seen in, where elliptical orbits were seento have higher energies than circular ones. In fact, because ε =, the greater the eccentricity of the orbit, thegreater the energy.
Jan 23, 2020 The escape velocity of a body which is at rest on the earth’s surface Is defined as that minimum velocity with which It should be projected from the surface of the earth so that it escapes from the earth’s gravitational influence.
Shows the differing paths ofprojectiles with increasing energy.Figure%: Trajectories of orbits with different energies.However, when the projectile is launched with even greater velocity, it willhave a sufficient energy to escape the gravitational field of the earth (or anyplanet or star). In these cases, a parabolic or hyperbolic orbit results. Wealso saw there that for a parabolic orbit the projectile has barely enoughenergy to reach infinity-that is, it arrives at infinity with no kineticenergy. Thus, the energy for a parabolic orbit is the minimum amount of energywe can give to a projectile such that it will escape from the gravitationalfield in which it is caught.Let us now calculate the velocity corresponding to this parabolic energy. Thisis the surface velocity required to completely escape the gravitational field ofa planet. We saw in Solving the Orbitsthat this corresponds to zero total energy.
That fact makes sense, becauseenergy is conserved and the projectile must have zero energy at infinity. Thuswe can write an expression for the total energy equal to kinetic plus potential. V =Where M and R are the mass and radius of the gravitating body. Note thatthis value is independent of the mass of the projectile.Viscous DragAnother interesting orbital phenomenon results when low-earth satellitesexperience viscous drag (friction) due to the atmosphere. We would expect thatthe drag due to the atmosphere would slow the satellite down. It is observedthat eventually the satellites spiral back towards the earth and burn up in theatmosphere (the atmosphere gets denser as the satellites approach the earth, andthus heat due to friction increases). The force on a satellite in orbit can begiven by both the Universal Law of Gravitation and the expression forcentripetal force.
Hence we can write.
Did you ever watch a group of children playing 'Red Rover?' Arms linked up for strength, they chant, 'Red Rover, Red Rover, let Sally come over,' and Sally's challenge is to break through that chain of linked arms. If she does it, Sally wins.Image to left: A Delta IV rocket launches at night. Credit: NASAIf Sally breaks through the chain of arms, she's also demonstrated several key aspects to the space concept of escape velocity.
Escape velocity (or a rousing game of Red Rover) requires an object to propel itself with enough speed and thrust to break through a barrier. Sally's reward is the cheers of her teammates. A spacecraft's reward is a journey into space or orbit.Escape velocity is the speed at which an object must travel to break free of a planet or moon's gravitational force and enter orbit. A spacecraft leaving the surface of Earth, for example, needs to be going about 11 kilometers (7 miles) per second, or over 40,000 kilometers per hour (25,000 miles per hour), to enter orbit.An Endless CycleAchieving escape velocity is one of the biggest challenges facing space travel. The vehicle requires an enormous amount of fuel to break through Earth's gravitational pull.
All that fuel adds significant weight to the spacecraft, and when an object is heavier, it takes more thrust to lift it. To create more thrust, you need more fuel. It's a cycle that scientists are hoping to resolve by creating lighter vehicles, more efficient fuels and new methods of propulsion that don't require the same ingredients to attain great speeds.Image to right: A Saturn V rocket is prepared for launch. Credit: NASAThat cycle of speed, fuel and weight was a primary reason the Saturn V rocket that took the first astronauts to the Moon was so large.
It required such enormous quantities of fuel to break free of the Earth's gravitational pull that a vehicle of this size was the only workable solution. The Space Shuttle in use now is much smaller, but it doesn't have nearly as far to travel or nearly as much gravitational force to overcome. Future space propulsion projects, such as magnetic levitation, could reduce size requirements because speed and propulsion will be created in a manner that doesn't require large fuel tanks.Image to right: This illustration shows possible orbital paths. Credit: NASAIn astronomy, the term orbit refers to the path of an object whose motion through space is controlled by the gravitational pull of another object. The Moon orbits the Earth, and the Earth, in turn, orbits the Sun. Spacecraft can also orbit the Earth. If an object gains enough speed to attain escape velocity, its orbit becomes an open curve called a parabola.
If it continues moving faster than escape velocity, its orbit is a flattened curve called a hyperbola. A spacecraft that leaves its orbit around the Earth on a journey toward another planet travels in a hyperbolic orbit.Image to right: This illustration shows a parabola and a hyperbola. Credit: NASAUsing Sally's 'Red Rover' game as an example, think how much more easily she could break through the chain if she approached the line on turbo-charged roller skates or if she had a spear-shaped battering ram in front of her.
Alternate methods of propulsion and maximized aerodynamics are two factors scientists are researching as they explore the possibilities for achieving escape velocity with less difficulty.