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

the radius of Earth's orbit will become 4 times the original radius

Step-by-step explanation:

The gravitational force between the Sun and the Earth is given by:

`F=G(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(Mm)/(r^2)=m(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=(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

`(1)/((1/2)^2)=(1)/(1/4)=4`

So, the radius will increase by a factor 4, and the Earth will have a larger orbit.