Question

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?

Answer 1

`(F)/(F_o)` = 1.2 10⁻²

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

Step-by-step 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 =
`G (m M_s)/( ((9R_o)^2)`

F =
`G (m M_s)/(81 \ R_o^2)`

we substitute

F = F₀ / 81

`(F)/(F_o)` = 1.2 10⁻²

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