Escape velocity is the speed that an object needs to be traveling to break free of a planet or moon's gravitational force and leave it without further propulsion to enter orbit.
So if we throw an object straight up, it will ...
Escape velocity is the speed that an object needs to be traveling to break free of a planet or moon's gravitational force and leave it without further propulsion to enter orbit.
So if we throw an object straight up, it will rise until the negative acceleration of gravity stops it, then returns it to Earth. Gravity's force diminishes as distance from the center of the Earth increases, however if we can throw the object with enough initial upward velocity so that gravity's decreasing force can never quite slow it to a complete stop, its decreasing velocity can always be just high enough to overcome gravity's pull. The initial velocity needed to achieve that condition is the escape velocity.
From the surface of the Earth, escape velocity (ignoring air friction) is about 7 miles per second, or 25,000 miles per hour. Given that initial speed, an object needs no additional force applied to completely escapes Earth's gravity; for example,
a spacecraft leaving the surface of Earth needs to be going 7 miles per second, or nearly 25,000 miles per hour to leave without falling back to the surface or falling into orbit.
The object must have greater energy than its gravitational binding energy to escape the earth's gravitational field. So:
1/2 mv
2
= GMm/R
Where m is the mass of the object, M mass of the earth, G is the gravitational constant, R is the radius of the earth, and v is the escape velocity. It simplifies to:
v = sqrt(2GM/R)
or
v = sqrt(2gR)
Where g is acceleration of gravity on the earth's surface.
The value evaluates to be approximately:
11100 m/s
40200 km/h
25000 mi/h
So, an object which has this velocity at the surface of the earth, will totally escape the earth's gravitational field (ignoring the losses due to the atmosphere)
.
Since escape velocity depends on the mass of the planet or moon that a spacecraft is blasting off of, a spacecraft leaving the moon's surface could go slower than one blasting off of the Earth, because the moon has less gravity than the Earth.
On the other hand, the escape velocity for Jupiter would be many times that of Earth's because Jupiter is so huge and has so much gravity.
One reason that manned missions to other planets are difficult to plan is that a ship would have to take enough fuel into space to blast off of the other planet when the astronauts wanted to go home. The weight of the fuel would make the spaceship so heavy it would be hard to blast it off of Earth!
An Endless Cycle
Achieving 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. To create more thrust, we need more fuel. It’s a cycle that scientists are hoping to resolve by creating lighter vehicles, more efficient fuel and new methods of propulsion that don’t require the same ingredients to attain great speeds.
That 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 fre e 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 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.
In 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, 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 journey toward another planet travels in a hyperbolic orbit.
https://informal.jpl.nasa.gov/museum/content/escape-velocity-2018
https://escapevelocity.events/
