How can I understand?
"Speed increment at infinity"
"Infinity" seems to be a speed measurement point,  by space probe trajectories,  but where is "infinity"
http://en.wikipedia.org/wiki/Flyby_anomaly

How can I understand?
"Speed increment at infinity"
"Infinity" seems to be a speed measurement point,  by space probe trajectories,  but where is "infinity"
http://en.wikipedia.org/wiki/Flyby_anomaly
It's the term used for the speed when the probe is "no longer under the gravitational influence of the Sun".
(Although that description too is somewhat nebulous...)
It's the speed achieved once "escape velocity" has ensured that the probe is no longer orbiting the Sun  essentially the speed that it will continue to hold until it "reaches infinity".
(If it were orbiting then its speed would vary, unless it were in a perfectly circular orbit).
There's no necessity for swing by to achieve a speed at infinity. Granted we use it because it's practical.
Not quite sure what you're getting at here.Due to the acceleration (towards perigee) escape velocity will be reached before the space probe isreaching perigee,  right?
How about: the speed at infinity is the speed of the probe on its way "to" infinity  because the apogee is "at" infinity.
I think I begin to understand  for example the Spaceprobe NEAR (andmany other spaceprobes) was orbiting the Sun not the Earth, so these spaceprobes will reach aphelion (not apogee)  I understand that,  but still I am confused to where (approximately) at the orbit is then "infinity speed" ?
Well, strictly speaking, they don't "reach" aphelion, since every time you check they're further away from the Sun, and will continue to increase that distance. They're never coming back. (Would that mean that it's not, by definition, an "orbit"?)
As to "where" the speed is reached that would be, at its most basic, when the final burn (or slingshot) is complete.
Hmm, okay, try this one:
As any probe gets further away its speed reduces  that's basic, since, although it's moving away gravity is also "attempting" to drag it back.
The "speed at infinity" is the final velocity achieved, the one which will never reduce (with respect to the Sun), or, to put it another way, its limiting speed.
There's a mathematical treatment of it here.
For a given "definition" of aphelion yes.
« Supernova?  Gravitational lensing or hot gas? » 