From Infinity to Here: Explaining Objects, Escape Velocity & More

[Goodies]

A phrase that I heard several times in the 2 years of high school AP physics I've completed (being a computer science major, I haven't taken any physics classes in college) was moving an object from "infinity to a point" and I'm a little confused as to what that means and how it works.

Also, how does it fit with escape velocity? The escape velocity of the Earth is about 11km/s. This is also the velocity that an object would have when moved from infinity to Earth (assuming no other planetary object). I'd love an explanation. Thanks, guys! I appreciate any help!

 

[DrClaude]

A phrase that I heard several times in the 2 years of high school AP physics I've completed (being a computer science major, I haven't taken any physics classes in college) was moving an object from "infinity to a point" and I'm a little confused as to what that means and how it works.

When you have two systems that interact, for instance through gravitational or electrostatic interactions, you often want to compare to a situation where the two systems are present but not interacting. As the interactions do not turn off at a certain distance, but continue for ever, the only way to achieve this is to have them an infinite distance apart. If the potential energy due to the interaction is $V(r)$, where $r$ is the distance between the systems, then $\lim_{r \rightarrow \infty} V(r) = 0$. So you start by considering the systems an inifinite distance apart, and then bring them closer to investigate the effect of the interaction.

Also, how does it fit with escape velocity? The escape velocity of the Earth is about 11km/s. This is also the velocity that an object would have when moved from infinity to Earth (assuming no other planetary object).

I've never heard used in that context, so I can't comment. Maybe someone else can chime in here.

 

[HallsofIvy]

What do you mean by "escape"? Any object, at any distance from the Earth will feels some small gravitational attraction and so eventually return to earth. To truly "escape" it must be able to go to infinity.

The "escape velocity" of an object is the velocity at a given instant such that, with its velocity decreasing as it moves away from Earth (due to gravitational pull back toward the earth), with no additional forces (in particular no rocket engines), it would, none the less, "escape" to infinity.