Question

What happens to the orbit of earth when its velocity is halved

Answer 1

The real answer is, The orbit becomes more elliptical. On Edg.

Answer 2

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.