Answer:
the radius of Earth's orbit will become 4 times the original radius
Explanation:
The gravitational force between the Sun and the Earth is given by:
![F=G\frac{Mm}{r^2}](https://tex.z-dn.net/?f=F%3DG%5Cfrac%7BMm%7D%7Br%5E2%7D)
where
G is the gravitational constant
M is the mass of the Sun
m is the mass of the Earth
r is the radius of the Earth's orbit
This force provides the centripetal force that keeps the Earth in (approximately) circular motion around the Sun, therefore we can write
![G\frac{Mm}{r^2}=m\frac{v^2}{r}](https://tex.z-dn.net/?f=G%5Cfrac%7BMm%7D%7Br%5E2%7D%3Dm%5Cfrac%7Bv%5E2%7D%7Br%7D)
where the term on the right is the centripetal force, with v being the Earth's velocity. Re-arranging the equation, we can write r (the radius of the orbit) as a function of the velocity v:
![r=\frac{GM}{v^2}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7BGM%7D%7Bv%5E2%7D)
we see that the orbital radius is inversely proportional to the square of the velocity: therefore, if the velocity is halved, the radius will acquire a factor
![\frac{1}{(1/2)^2}=\frac{1}{1/4}=4](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%281%2F2%29%5E2%7D%3D%5Cfrac%7B1%7D%7B1%2F4%7D%3D4)
So, the radius will increase by a factor 4, and the Earth will have a larger orbit.