Parabolic paths vs Elliptical paths.

  • Thread starter mprm86
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In summary, We are taught that projectiles follow a parabolic path, but in reality, their path is actually elliptical. The difference in paths between an elliptical and parabolic trajectory is dependent on the escape velocity. If the projectile travels below escape velocity, the path is elliptical, while at escape velocity it is parabolic, and above escape velocity it is hyperbolic. The variation of gravitational force with height is responsible for the elliptical path, rather than the curvature of the Earth.
  • #1
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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  • #2
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.
 
  • #3
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
 
  • #4
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)
 
  • #5
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).
 

1. What is the difference between a parabolic path and an elliptical path?

A parabolic path is a type of trajectory in which an object moves in a curved path with a constant acceleration due to gravity. An elliptical path, on the other hand, is a type of trajectory in which an object moves in a curved path around a central point, such as a planet or star. The main difference between these two paths is that a parabolic path has a single focus point, while an elliptical path has two focus points.

2. Which type of path is more commonly observed in nature?

Elliptical paths are more commonly observed in nature, as they are the result of the gravitational pull of large celestial bodies like planets and stars. For example, the Earth follows an elliptical path around the Sun, and the Moon follows an elliptical path around the Earth.

3. What determines whether an object follows a parabolic or elliptical path?

The shape of an object's path is determined by its initial velocity and the force acting on it. If the initial velocity and force are just right, the object will follow an elliptical path. If the initial velocity is greater than the force, the object will follow a parabolic path. If the initial velocity is less than the force, the object will follow a hyperbolic path.

4. Can an object's path change from parabolic to elliptical?

Yes, an object's path can change from a parabolic to an elliptical path if its initial velocity or the force acting on it changes. For example, a comet may initially follow a parabolic path when it enters the solar system, but as it gets closer to the Sun and experiences more gravitational force, its path may become more elliptical.

5. Are there any real-world applications for understanding parabolic and elliptical paths?

Yes, understanding these types of paths is essential in fields such as astronomy and rocket science. For example, spacecraft must follow a specific trajectory to reach other planets, and this trajectory is often elliptical. Additionally, understanding the paths of celestial bodies helps us predict their movements and make accurate astronomical observations.

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