# Maximum range in projectile motion (elliptical path)

Elementary Newtonian mechanics tells us that if a projectile is shot at 45 degrees from the ground, and a downward gravitational field is acting on it, it will follow a parabolic path and achieve maximum range.

But the Earth's gravitational field rather points radially inward, meaning that the projectile instead follows an elliptical path. What angle from the ground would allow it to achieve maximum range?

• In true projectile, effect of air resistance is so much more than variation of gravitational field. – lucas Jun 24 '16 at 11:25
• Way too true for me. I'll change the title – giobrach Jun 24 '16 at 11:27
• If you want to consider to variation of $g$, then you should consider to curvature of the earth surface too. Because the earth's surface isn't flat (horizontal). – lucas Jun 24 '16 at 11:34
• Interesting question. What attempt(s) have you made to solve it yourself? – sammy gerbil Jun 24 '16 at 12:38
• You might want to edit the question to limit the initial velocity to values less than the orbital velocity ... if that's your intent. And that there is no atmosphere, and that the earth is spherical, and that you are at the equator. There are a lot of pendants on this site. :) – garyp Jun 24 '16 at 14:06