how maximum range could occupy elliptical path in projectile motion i cant imagine how this happens if earth is sphere and the path is parabolic so still it wont make any of the elliptical path. then how could one say that its max range is ellipse?
closed as unclear what you're asking by peterh, Jon Custer, Yashas, ZeroTheHero, AccidentalFourierTransform May 13 '17 at 12:26
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We say the trajectory of an object is parabolic only because of the approximation of a flat earth, with gravity uniformly pointing in one direction ("down").
However, like you suggest, if we instead treat the earth as a sphere, with gravity pointing toward the center, the path will follow an ellipse.
Note that if the velocity of the object is exactly equal to the escape velocity of Earth, the path actually will be parabolic. If the velocity exceeds the escape velocity, the path will be hyperbolic. Hyperbolas, parabolas, and ellipses (and circles) are all "conic sections", meaning they take the form of cross-sections of cones. In the end, they are all very related to each other.