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.

Answered by Ashkan P. Physics tutor

6040 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

How do I find the half-life of radioactive isotope?


Two trains are heading in opposite directions on the same track. Train X has a mass of 16000kg and a speed of 2.8m/s. Train Y has a mass of 12000kg and a speed of 3.1m/s. At what speed do the joined trains move off together immediately after the collison?


What is the most effective use of the equation sheet?


An ideal gas at a temperature of 22 C is trapped in a metal cylinder of volume 0.2 m^3 at a pressure of 1.6x10^6 Pa. The gas has a molar mass of 4.3 x 10^(-2) kg mol^(-1). Calculate the density of the gas in the cylinder.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2024

Terms & Conditions|Privacy Policy
Cookie Preferences