Circular Orbits in Gravitational Fields (CIE A Level Physics)

• For objects in a circular orbit in a gravitational field the gravitational force is related to the centripetal acceleration it causes
• Planets travel around the Sun in orbits that are (approximately) circular and within the Sun's gravitational field
  • Objects in a circular orbit travel at a constant speed
• The orbit is a circular path, therefore the direction in which the object is travelling will be constantly changing
  • A change in direction causes a change in velocity
• Acceleration is the rate of change of velocity, therefore if an object is constantly changing direction then its velocity is constantly changing, so an object in orbit is accelerating
• A resultant force is needed to cause an acceleration
• This resultant centripetal force is due to the gravitational force F_G created by the object being orbitted 
• The resultant force must act at right angles to the instantaneous velocity of the object to create a circular orbit
  • This is always towards the centre of the orbit
  • The instantaneous velocity of the object is the velocity at a given time

Gravitational force and instantaneous velocity

The direction of the instantaneous velocity and the gravitational force at different points of the Earth’s orbit around the sun