Gravitation Reasonings

Generally, the path of a projectile from the surface of earth is parabolic but it is elliptical for projectiles going to a very great height. Why?

Upto ordinary heights, the change in the distance of a projectile from the centre of the earth is negligibly small as compared to the radius of the earth. As a result, the projectile moves under a uniform gravitational force and the path will be parabolic.

But if the height is great, the gravitational force decreases which is directly proportional to the square of the distance of the projectile from the centre of the earth. Under such a variable force, the path of projectile cannot remain parabolic. Instead, it becomes elliptical.