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

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

1
Mar 9, 2018

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( $T \propto \frac{R}{v}$).
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 : ${v}^{2} / R \propto \frac{1}{R} ^ 2 \implies v \propto {R}^{- \frac{1}{2}}$

Combining the two gives us Kepler's third law

$T \propto \frac{R}{R} ^ \left(- \frac{1}{2}\right) = {R}^{\frac{3}{2}} q \quad \setminus m b \otimes \left\{\mathmr{and}\right\} q \quad {T}^{2} \propto {R}^{3}$

• An hour ago
• An hour ago
• An hour ago
• An hour ago
• A minute ago
• 6 minutes ago
• 7 minutes ago
• 20 minutes ago
• 28 minutes ago
• 47 minutes ago
• An hour ago
• An hour ago
• An hour ago
• An hour ago