# Escape Velocity(OCR A Level Physics)

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Ashika

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## Escape Velocity

• To escape a gravitational field, a mass must travel at the escape velocity
• This is dependent on the mass and radius of the object creating the gravitational field, such as a planet, a moon or a black hole
• Escape velocity is defined as:

The minimum speed that will allow an object to escape a gravitational field with no further energy input

• It is the same for all masses in the same gravitational field i.e., the escape velocity of a rocket from Earth is the same as a tennis ball

• An object reaches escape velocity when all its kinetic energy has been transferred to gravitational potential energy
• Mathematically, equating the kinetic energy to gravitational potential energy gives:

• Where:
• m = mass of the object in the gravitational field of mass M (kg)
• v = escape velocity of the object (m s-1)
• G = Newton's Gravitational Constant
• M = mass of the object to be escaped from, causing the gravitational field (i.e., a planet) (kg)
• r = distance from the centre of mass of M (m)

• Since mass m is the same on both sides of the equation, it can be cancelled
• This is the reason why the escape velocity is the same for any object in the gravitational field of M
• Therefore, the equation simplifies to give:

• Rearranging this equation gives the escape velocity, v:

• This equation is not given: be sure to memorise how to derive it

In order to escape Earth's gravitational field, objects have to travel greater than Earth's escape velocity. However, rockets burn fuel continuously, so they are given sufficient energy to escape while travelling significantly less than escape velocity

• Rockets launched from the Earth's surface do not need to achieve escape velocity to reach their orbit around the Earth
• This is because:
• They are given energy through fuel continuously to provide thrust
• Less energy is needed to achieve orbit than to escape from Earth's gravitational field

• The escape velocity is not the velocity needed to escape the planet but to escape the planet's gravitational field altogether
• This could be quite a large distance away from the planet

#### Worked example

Calculate the escape velocity at the surface of the Moon given that its density is 3340 kg m-3 and has a mass of 7.35 × 1022 kg.

Newton's Gravitational Constant = 6.67 × 10-11 N m2 kg-2

#### Exam Tip

When writing the definition of escape velocity, avoid terms such as 'gravity' or the 'gravitational pull / attraction' of the planet. It is best to refer to its gravitational field.

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