Move the Earth so it is one box from the Sun. (Note: one box side equals about 46,000,000 miles.) Do not change the length of the velocity vector. Predict what will happen to the Earth and Sun when you hit Play?

When we change the distance, the universal attraction force increases, so that the system is free to reach a new equilibrium, the linear speed of the earth must rise to the calculated value.

v = √ (G M / r)

Explanation:

For this exercise it is asked that if you maintain the linear speed of the Earth and bring it closer to the sun that would pass.

We pass the distance from Ro = 1.49 10¹¹ m to r = 0.736 10¹¹ m shortens, we write Newton's second law

             F = m a

where the force is the universal force of attraction

            F = G mM / r²

acceleration is central

            a = v² / r

           G m M / r² = m v² / r

            v = √ (G M / r)

When we change the distance, the universal attraction force increases, so that the system is free to reach a new equilibrium, the linear speed of the earth must rise to the calculated value.

We can compare this value with that of the normal orbit

           v₀ = √ (GM / R₀)

            v / v₀ =√ (Ro / r)

           v² r = v₀² R₀

 either of these two expressions gives the relations gives the change in velocity with the radius of the orbit

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