Parabolic paths vs Elliptical paths.

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Discussion Overview

The discussion centers on the nature of projectile motion, specifically whether the path of a projectile is parabolic or elliptical. Participants explore the implications of different assumptions about gravitational forces and the curvature of the Earth, considering both theoretical and practical aspects of projectile motion.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant asserts that projectiles follow an elliptical path rather than a parabolic one, questioning the traditional teaching that neglects air resistance.
  • Another participant argues that the path is indeed parabolic, suggesting that a parabola can be approximated by an ellipse by adjusting the distance between foci.
  • A third participant introduces the idea that the classic parabolic path assumes a flat Earth, while elliptical paths occur when projectiles travel below escape velocity.
  • It is noted that if a projectile travels at escape velocity, the path is parabolic, and if it exceeds escape velocity, the path becomes hyperbolic.
  • One participant emphasizes that the variation of gravitational force with height, rather than Earth's curvature, is responsible for an elliptical path when the velocity is less than escape velocity.
  • Another participant clarifies that the earlier mention of curvature was in reference to treating gravity as originating from a flat plane rather than a point source, which affects the path shape.

Areas of Agreement / Disagreement

Participants express differing views on whether projectile paths are parabolic or elliptical, with no consensus reached. Some agree that the curvature of the Earth and gravitational variations play roles in determining the path, while others maintain that the traditional parabolic model is sufficient under certain conditions.

Contextual Notes

Participants acknowledge that air resistance significantly influences projectile motion, complicating the analysis of paths. There is also a recognition that the variation of gravitational force with height is generally negligible for typical projectile motions.

mprm86
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We are always taught that a projectile describes a parabolic path (neglecting air resistance), but the path is actually elliptical. So, my question is this: A projectile is thrown in point A (on the ground), it reaches a maximum height H, and it finally falls in point B (same height as A, that is, the ground). Which will be the difference between the paths if (a) it is elliptical, and (b) it is parabolic? Any ideas, suggestions?
Thanks in advance.

P.S. The answer I´m looking for is one of the kind of 1 part in a million or somewhat.
 
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We are always taught that a projectile describes a parabolic path (neglecting air resistance), but the path is actually elliptical.

Where did you get this idea? The path is parabolic. You can approximate a parabola by an ellipse as close as you want by simply moving the foci farther apart. The parabola can be looked at as the limit as the separation becomes infinite.

Added note: You may have a point since the Earth is not flat. The distant focus will be the center of the earth.
 
The classic parabolic path assumes a flat earth.

If the projectile travels below escape velocity, the path is elliptical.

If the projectile travels exactly at escape velocity, the path is parabolic.

If the projectile travels faster than escape velocity, the path is hyperbolic.

A link for some formulas (go to orbital mechanics page)

http://www.braeunig.us/space
 
What's responsible for an elliptic path (if v< v_escape) is not the curvature of the earth, but the variation of the gravitational force with height.
You could solve Newton's law under a inverse square force field to find the actual path. The variation g with height is very small to take into consideration when throwing stuff in the air though. (Air resistance is WAY more dominant)
 
Galileo said:
What's responsible for an elliptic path (if v< v_escape) is not the curvature of the earth, but the variation of the gravitational force with height.

No one mentioned curvature of the Earth in this thread. My reference to a parabola being correct for flat Earth was a reference to treating gravity as being effectively generated from a flat plane instead of effectively from a point source (in which case you get an elliptical path).
 

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