Why escape velocity is independent of angle of projection

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Discussion Overview

The discussion centers on the concept of escape velocity and its independence from the angle of projection. Participants explore the physical reasoning behind this phenomenon, considering both energy transfer and geometric interpretations. The scope includes theoretical explanations and conceptual clarifications.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant requests an explanation for why escape velocity is independent of the angle of projection.
  • Another participant suggests that escape velocity is based on the transfer of kinetic energy to potential energy, which does not depend on direction.
  • A third participant notes that the independence of escape velocity from the angle of projection is due to the conservative nature of the gravitational field, where work does not depend on the path taken.
  • One participant proposes a geometric perspective, indicating that since escape velocity leads to infinity, any path will eventually resemble a ray directed away from the object.

Areas of Agreement / Disagreement

Participants present various viewpoints and interpretations, but there is no consensus on a singular explanation. Multiple competing views remain regarding the reasoning behind the independence of escape velocity from the angle of projection.

Contextual Notes

The discussion assumes an ideal scenario without atmospheric effects, which may influence the application of the concepts discussed.

Himal kharel
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can someone explain physically why escape velocity is independent of angle of projection.
 
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Because it is based on transfer of kinetic energy to potential energy which is independent of direction.
 
A short answer can be: because the gravitational field is conservative (work does not depend on path). I suppose by "angle of projection" you mean some angle between the initial velocity and some direction related to the planet.

Of course, this is true in the ideal case, without atmosphere.

Edit. Someone answered already, sorry.
 
Could it be looked at geometrically? Since escape velocity takes you to infinity, any path will end up forming a ray arbitrarily close to directly away from the object.
 

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