Question

Imagine if the Earth suddenly sped up. What do you think would happen to its orbit?

Answer 1

In order to maintain equilibrium, value of `r`, the radius of its orbit must decrease.

Explanation:

Please go through this answer `->` http://socratic.org/questions/why-does-the-earth-rotate-around-the-sun#218385

We see that in sun-earth system which is in equilibrium

`F_G =G (M_1.M_2)/r^2=F_(centri fugal)=mromega^2`
Where the various symbols have the meaning as ascribed in the above answer.

We also know that `v=romega` Substituting in the above expression we obtain

`G (M_s.M_e)/r^2=M_ev^2/r`

`=> G M_s/r=v^2`

`=> rv^2=G M_s`
RHS of the expression is constant.

`:.` in order to maintain equilibrium, value of `r`, the radius of its orbit must decrease.