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What is the difference between escape velocity and escape speed , is their any error if we use them interchangeably?

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I think it is escape speed because it is derived by summing the kinetic energy (which depends on speed, not velocity) with gravitational potential energy. If the sum is greater than zero then the object will be on a hyperbolic escape trajectory (as long as there are no other forces involved eg no air resistance and you are not firing the object into the ground).

The term escape velocity is misused, unless you can show me instances of where it used and expressed properly with both a magnitude and direction...

The Wikipedia page https://en.m.wikipedia.org/wiki/Escape_velocity on escape velocity (sic) is particularly guilty:

"In physics, escape velocity is the minimum speed needed for an object to "break free" from the gravitational attraction of a massive body."

and then further down the page:

"The term escape velocity is actually a misnomer, and it is more accurately referred to as escape speed since the necessary speed is a scalar quantity (not a vector quantity) which is independent of direction (assuming a non-rotating planet and ignoring atmospheric friction or relativistic effects)." !

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  • $\begingroup$ @Floris "as long as there are no other forces involved" is clear enough. $\endgroup$ – Rob Jeffries Dec 30 '15 at 16:48