2 reasons why it takes long for the outer planets to orbit around the sun?
Longer orbits and slower speeds
- The orbits of the outer planets is longer. So, even if the orbital speeds of the outer planets had been the same as the inner planets (they are not - see point 2), they would have taken more time to complete an orbit(
#T propto R/v#).
- The gravitational force of the sun is weaker than on the inner planets due to the inverse square nature of the force- this means that the centripetal acceleration is smaller, leading to a smaller velocity :
#v^2/R propto 1/R^2 implies v propto R^(-1/2)#
Combining the two gives us Kepler's third law