If I could snap my fingers and move Earth to an orbital distance at 9 AU, what would happen to the strength of the Sun's gravitational force on Earth?

    = 1.2 10⁻²

force of attraction of the sun decreases by a factor of 1.2 10⁻² times

Explanation:

The force of gravity is given by the universal law of attraction

          F = G m Ms / r²

where m is the mass of the Earth, Ms the mass of the Sun and r the distance from the Earth to the Sun

for the initial orbit

          F₀ = G m Ms / R₀²

for one orbit

          R = 9R₀

         F =

         F =

we substitute

         F = F₀ / 81

          = 1.2 10⁻²

therefore the force of attraction of the sun decreases by a factor of 1.2 10⁻² times