Why do objects follow different trajectories in freefall and orbit?

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Discussion Overview

The discussion explores the nature of trajectories followed by objects in freefall versus those in orbit, particularly focusing on the shapes of these paths, such as parabolas, ellipses, and hyperbolas. It touches on theoretical and conceptual aspects of motion under gravity.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that objects in freefall do not follow parabolic paths but rather elliptical orbits that intersect the Earth's surface.
  • One participant suggests that the elliptical nature of these orbits can appear parabolic when the minor axis is significantly smaller than the major axis, making the focus seem distant.
  • Another participant challenges the claim that saying objects fall in parabolas is misleading, arguing that current instrumentation cannot distinguish between a thrown object's path and a parabolic trajectory.
  • There is a mention of the educational context where the term 'things fall in parabolas' is commonly taught, leading to some confusion among learners.
  • One participant notes that while the paths can be approximated as parabolas for practical purposes, the accuracy of this approximation can vary based on distance and other factors affecting trajectories.

Areas of Agreement / Disagreement

Participants express differing views on the validity of describing freefall paths as parabolas, with some supporting the idea and others contesting it. The discussion remains unresolved regarding the appropriateness of the parabolic description in various contexts.

Contextual Notes

Limitations include the dependence on assumptions about proximity to the Earth's surface and the accuracy of models used to describe motion under gravity. The discussion highlights the complexity of distinguishing between different trajectory shapes in practical scenarios.

Vorde
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Why do objects fall in parabolas, but things orbit in either ellipses or hyperbolas?
 
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Vorde said:
Why do objects fall in parabolas
They don't.

They move in an elliptical orbit about the centre of mass of the Earth; it just happens that the orbit intersects the surface of the Earth.

When the minor axis of an ellipse is on the order of few dozen yards, but the major axis is on the order of 4000 miles, an ellipse looks very much like a parabola i.e. the focus (of the ellipse) is so far away it might as well be at infinity (i.e. a parabola) for all the difference it makes.

If you tossed a ball in the air, and and that moment, the Earth suddenly collapsed to the size of a marble while keeping its mass, your ball would fall all the way to the centre, round it (with a perigee of just a few dozen yards) and come back out, following that elliptical orbit.
 
Last edited:
So really whenever anyone tells us that things fall in parabolas, they are lying. Makes sense, but still...

Thank you for the answer.
 
Vorde said:
So really whenever anyone tells us that things fall in parabolas, they are lying. Makes sense, but still...

Thank you for the answer.

I don't think that is a fair statement. We do not have instrumentation that can separate the path of a thrown rock from a parabola. In fact, under the assumption that you are close to the Earth's surface, our basic models say that it IS a parabola.
 
I don't disagree, but I went through a whole Analytic Geometry class with the term 'things fall in parabolas' etched into my brain. I'm surprised this wasn't at least mentioned.
 
Vorde said:
I don't disagree, but I went through a whole Analytic Geometry class with the term 'things fall in parabolas' etched into my brain. I'm surprised this wasn't at least mentioned.

They are parabolas to an acceptable degree of accuracy. Two plumb bobs 10 yards apart, both pointing at the centre of the Earth, will be parallel to within one part in 700,000.

There are many factors affecting ballastic trajectories that are much greater than that.
 

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