Is Additional Speed Beyond Orbital Velocity Needed for Escape?

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Discussion Overview

The discussion revolves around the concept of escape velocity in relation to orbital velocity, specifically whether additional speed beyond orbital velocity is necessary for an object to escape a gravitational field. The scope includes theoretical considerations and mathematical reasoning related to energy conservation in gravitational fields.

Discussion Character

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

Main Points Raised

  • One participant questions if the minimum speed required for an object to escape is simply the difference between escape velocity and orbital velocity.
  • Another participant suggests using energy conservation principles to derive the relationship between orbital velocity and escape velocity, referencing the equation u² = 2GM/R.
  • A participant raises a scenario involving an object with horizontal velocity on Earth and questions whether exceeding escape velocity would guarantee escape.
  • A later reply asserts that if the horizontal velocity exceeds escape velocity, the mass will escape.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between orbital velocity and escape velocity, with some proposing calculations based on energy conservation while others present hypothetical scenarios. The discussion remains unresolved regarding the implications of horizontal velocity on escape.

Contextual Notes

Limitations include assumptions about the nature of the gravitational field and the conditions under which escape velocity is defined. The discussion does not resolve the mathematical steps involved in applying energy conservation.

menager31
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of course i know how to count thaht but i ve got one question. If something is moving on the orbit with velocity v, and escape velocity is u, then when we want our object to escape , the minimum speed which we must add is u-v ?
 
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You have an object of mass m which has first an orbital velocity Vo (or "v") and an additional velocity V' at a radius R from a mass M, and, afterwards, zero velocity at infinity (R = infinite) escaping from mass M. If you apply energy conservation between (1) and (2) and check against u² = 2GM/R you will find out the answer to your question.
 
i know how to count it but you are thinking about sth else let's say that our mass has got horizontal velocity on the Earth If this velocity is more than escape velocity, will the mass escape?
 
menager31 said:
i know how to count it but you are thinking about sth else let's say that our mass has got horizontal velocity on the Earth If this velocity is more than escape velocity, will the mass escape?

Yes, it will.
 

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