Thrown Object & Earth's Escape Velocity

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Discussion Overview

The discussion revolves around the concept of escape velocity and its implications for objects thrown from the Earth's surface. Participants explore whether an object thrown upwards or downwards at escape velocity can achieve orbit, as well as the conditions under which objects with speeds less than escape velocity can maintain circular orbits.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants question whether an object thrown upwards or downwards at escape velocity can orbit the Earth, suggesting a need to clarify the definitions of "escape" and "orbit."
  • One participant defines escape velocity as the speed required to overcome gravitational pull, providing a formula: ve = √2gr.
  • Another participant asserts that a body projected with a speed less than escape velocity can orbit the Earth in an elliptical path, with circular orbits being a special case.
  • It is proposed that for a circular orbit from the Earth's surface, a horizontal launch must occur at a speed equal to escape velocity divided by the square root of two, with other launch angles leading to intersections with the Earth's surface or non-circular orbits.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between escape velocity and orbital mechanics, with no consensus reached on whether objects thrown at escape velocity can orbit the Earth.

Contextual Notes

Participants highlight the importance of definitions and conditions for orbits, indicating that assumptions about launch angles and speeds significantly affect the outcomes discussed.

Ajit Kumar
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If an object is thrown upwards with escape velocity, will it orbit the earth?
 
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Think about it - If an object is thrown downwards with escape velocity, will it orbit the earth?
 
What does the word "escape" mean? Does that definition match the definition of "orbit"?
 
So now you have two questions, approaching the problem from two different directions, These are hints. What do you think the answer is?
 
escape velocity is the velocity by which any object overcomes the gravitational pull and flies away from planet.
ve = √2gr
 
Will a body projected with a speed less than the escape velocity may orbit the Earth in circular path?
 
Of course. All elliptic paths are closed orbits, so all speeds less than escape can take any elliptic path (of which the circular is special case)
 
Ajit Kumar said:
Will a body projected with a speed less than the escape velocity may orbit the Earth in circular path?
For a body launched from the surface of the Earth the only possibility for a circular orbit is a horizontal launch with a speed equal to escape velocity divided by the square root of two. Any other direction and the orbit will intersect with the surface of the Earth. Any higher velocity and the orbit will fail to be circular. It will rise above the surface of the earth. Any lower velocity and the orbit will fail to be circular. It will fall below the surface of the earth.
 

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