2 reasons why it takes long for the outer planets to orbit around the sun?

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Mar 9, 2018

Answer:

Longer orbits and slower speeds

Explanation:

  1. 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#).
  2. 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

#T propto R/R^(-1/2) = R^(3/2) qquad \mbox{or}qquad T^2 propto R^3#

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