• 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 ie. the escape velocity of a rocket is the same as a tennis ball on Earth

• An object reaches escape velocity when all its kinetic energy has been transferred to gravitational potential energy
• This is calculated by equating the equations:

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

• Since mass?m is the same on both sides of the equations, it can cancel on both sides of the equation:

• Multiplying both sides by 2 and taking the square root gives the equation for escape velocity,?v:

• This equation is?not?given on the datasheet. Be sure to memorise how to derive it

For an object to leave the Earth's gravitational field, it will have to travel at a speed greater than the Earth's escape velocity, v

• 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 continuously given energy through fuel and thrust to help them move
  • 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

Exam Tip