Ballistic trajectory: parabola, ellipse, or what?

Details Ballistic trajectory: parabola, ellipse, or what? Ballistic trajectory: parabola, ellipse, or what?

2003-10-11

arxiv.org/abs/physics/0310049v2

Am. J. Phys. 73, 516-520 (2005)

Physics

Classical Physics

7 pages, 3 figures

Scientific paper

Mechanics texts tell us that a particle in a bound orbit under gravitational central force moves on an ellipse, while introductory physics texts approximate the earth as flat, and tell us that the particle moves in a parabola. The uniform-gravity, flat-earth parabola is clearly meant to be an approximation to a small segment of the true central-force/ellipse orbit. To look more deeply into this connection we convert earth-centered polar coordinates to ``flat-earth coordinates'' by treating radial lines as vertical, and by treating lines of constant radial distance as horizontal. With the exact trajectory and dynamics in this system, we consider such questions as whether gravity is purely vertical in this picture, and whether the central force nature of gravity is important only when the height or range of a ballistic trajectory is comparable to the earth radius. Somewhat surprisingly, the answers to both questions is ``no,'' and therein lie some interesting lessons.

Affiliated with

Also associated with

No associations

Rating

Ballistic trajectory: parabola, ellipse, or what? does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Ballistic trajectory: parabola, ellipse, or what?, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ballistic trajectory: parabola, ellipse, or what? will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-543400