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### What is escape velocity?

This is the minimum initial velocity required to move from a point to infinity in a gravitational field.

Infinity is defined to have a potential, V of zero; this is the point where the gravitational field has no influence on the object and no force is acting on it due to the gravitational field (in theory). In reality this point of infinity is simply described as a point incredibly far away as though the field is not acting on the object.

Note that the definition does not include the mass of the object and is only concerned with the grav. Field itself.

The formula used to calculate the escape velocity:           V_e = sqrt[2GM/r]

Where G is the Universal gravitational constant; M is the mass of the body producing the grav. Field; r is the radius of the body.

For example, on earth:

The Earth’s mass approximately: M = 6x10^24 kg;

Universal gravitational constant: G = 6.67×10^-11 m^3 kg^-1 s^-2;

Radius of Earth approximately: r = 6,400,000m.

Sub in the numbers:

V_e = sqrt[(2)(6x10^24)(6.67×10^-11)/(6,400,000)]

Results in:

The escape velocity of the earth: V_e = 11.2 km/s.

Any object, irrelevant of mass would require this initial velocity to escape the earth.

Space Rockets:

Of course rockets when sent to space, escaping earth’s field they are clearly not travelling anywhere near 11.2 km/s at launch. This is because the rocket is continuously accelerating as it pushes propellant out the exhaust and so travels upwards. Note the careful wording of the definition of escape velocity: “Initial velocity required” so this 11.2 km/s only applies to an object with no further acceleration.

3 years ago

Answered by Ashkan, an A Level Physics tutor with MyTutor

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