What is the vector equation for escape velocity?

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Discussion Overview

The discussion centers around the vector equation for escape velocity, particularly in the context of a three-body gravitational problem. Participants explore the relationship between escape velocity as a scalar quantity and its representation in vector form.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant presents the scalar formula for escape velocity, v=sqrt(2GM/r), and seeks a vector form for their programming project.
  • Another participant suggests a vector representation as \bold{v}=\frac{\sqrt{2GM}}{r}\hat{r}.
  • A third participant comments on the terminology, stating that "escape velocity" is misleading and should be referred to as "escape speed," emphasizing its scalar nature.
  • One participant notes the challenge of determining the correct direction for escape velocity, indicating that any direction is valid as long as the trajectory does not intersect the surface of the body being escaped from.
  • This participant further explains that the range of possible directions is influenced by the distance from the center of the body and the body's radius.

Areas of Agreement / Disagreement

Participants express differing views on the terminology of escape velocity versus escape speed, and there is no consensus on a definitive vector equation. The discussion remains unresolved regarding the best approach to represent escape velocity in vector form.

Contextual Notes

Participants highlight the dependence on factors such as distance from the body and its radius when discussing the direction of escape velocity, indicating that these aspects are not fully resolved in the discussion.

rich86
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hi, i have been looking for a while but stillnot managed to find a vector equation for the Escape Velocity. i know the escape velocity is:

v=sqrt(2GM/r)

i would like a vector form to extend a program i am making for a three body gravitational problem

many thanks

richard
 
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Would it not just be \bold{v}=\frac{\sqrt{2GM}}{r}\hat{r}?
 
The term "escape velocity" is a bit of a misnomer: it really should be called "escape speed" because it truly is a scalar quantity.
 
thanks, that helps a lot...

..but makes my project harder in finding the right direction for the escape velocity!
 
rich86 said:
thanks, that helps a lot...

..but makes my project harder in finding the right direction for the escape velocity!

The right direction is any direction, as long as the resulting trajectory doesn't intersect the surface of the body you are trying to escape from. Whether any given trajectory intersects the surface depends a couple of factors, The distance you are from center of the body and the radius of the body. If you are sitting right above the surface of the body you have a smaller range of possible directions that do not result in collision with the surface than you would if you started some greater distance away from the body.
 

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