Calculating Orbital Speeds

• When planets move around the Sun, or a moon moves around a planet, they orbit in circular motion

  • This means that in one orbit, a planet travels a distance equal to the circumference of a circle (the shape of the orbit)
  • This is equal to 2πr where r is the radius a circle
• The relationship between speed, distance and time is: speed = distance/time
• The average orbital speed of an object can be defined by the equation: v = 2πr/T

  • v = orbital speed in metres per second (m/s)
  • r = average radius of the orbit in metres (m)
  • T = orbital period in seconds (s)
• This orbital period (or time period) is defined as the time taken for an object to complete one orbit
• The orbital radius r is always taken from the centre of the object being orbited to the object orbiting
• Orbital radius and orbital speed of a planet moving around a Sun

  A) sun

  B) orbital radius, r

  C) orbital speed, v

  D) planet

  
• Remember to check that the orbital radius r given is the distance from the centre of the Sun (if a planet is orbiting a Sun) or the planet (if a moon is orbiting a planet) and not just from the surface

  • If the distance is a height above the surface you must add the radius of the body, to get the height above the centre of mass of the body
  • This is because orbits are caused by the mass, which can be assumed to act at the centre, rather than the surface
  • Don't forget to check your units and convert any if required!
• The time taken for one orbit is a period
• • Speed of the earth’s orbit is 2πr
  • T = period
• What is the formula to calculate average orbital speed?

  Average orbital speed = 2πr / T, where r is the distance from the center of the orbit and T is the orbital period.