Why escape velocity is independent of angle of projection

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SUMMARY

Escape velocity is independent of the angle of projection due to the nature of gravitational fields being conservative, meaning that the work done does not depend on the path taken. The kinetic energy required to reach escape velocity is converted to potential energy, which remains constant regardless of direction. This principle holds true in ideal conditions, specifically in the absence of atmospheric resistance. Geometrically, any trajectory will ultimately align closely with a path directed away from the celestial body as it approaches infinity.

PREREQUISITES
  • Understanding of gravitational fields and their properties
  • Basic knowledge of kinetic and potential energy
  • Familiarity with the concept of escape velocity
  • Geometric interpretation of trajectories in physics
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  • Research the principles of conservative forces in physics
  • Study the derivation of escape velocity equations
  • Explore the effects of atmospheric drag on projectile motion
  • Investigate geometric optics and its relation to trajectories
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Students of physics, educators explaining gravitational concepts, and anyone interested in the mechanics of motion in celestial contexts.

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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