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:
\(F=G\frac{Mm}{r^2}\)
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
\(G\frac{Mm}{r^2}=m\frac{v^2}{r}\)
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:
\(r=\frac{GM}{v^2}\)
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
\(\frac{1}{(1/2)^2}=\frac{1}{1/4}=4\)
So, the radius will increase by a factor 4, and the Earth will have a larger orbit.
