Not necessarily. The point is, the encounter changes the direction of your travel. Let’s say you were travelling 10km/s, pointed 90 degrees away from the sun (parallel to the circular orbit). After the encounter with jupiter, you are still travelling 10km/s, but you are pointed maybe 120 degrees away from Jupiter. This orbit will get you farther towards your goal. (Assuming your goal is somewhere farther from the sun than Jupiter)
If you are wondering why this happens, draw a circle for Jupiter, and draw a horizontal straight line just below the circle. The line is the original spacecraft trajectory. Now, gravitational pull on the spacecraft is always towards Jupiter. If the spacecraft comes in from the right, initially Jupiter pulls it towards the upper left. At closest encounter, it pulls straight up. As the spacecraft flies away, it is pulled to the upper right. The leftward pull on the incoming path is cancelled by the rightward pull on the outbound path, so there is no net gain in speed. But the spacecraft is pulled upwards throughout the encounter. So the trajectory is bent upwards.
Achernar, momentum is NOT mass times velocity, that’s my point. It is mass times velocity divided by that reltivity radical that pops up all the time: p=mv/(1-(v/c)^2)^0.5 . This is not a definition of mass, but of momentum. What I was saying was that situations where people speak of relativistic mass are, when examined, situations where they are really seeing MOMENTUM changes, which they are “misinterpreting” (according to the popular framework where the only mass is rest mass) as “realtivistic mass”. Again, this is not my own assertion, I’m repeating what a couple of physicists have told me. One of them is from CalTech, and I got the impression that this view may be a partiality of the people there. The other went to Princeton, and he seemed less emphatic about it, although he agreed with it.
I think Punoqllads explained it perfectly. (And how the hell do you do superscripts?)
As to “relativistic mass” versus “rest mass” versus just “mass”, it’s just a question of terminology, and either system can be used, so long as you use it consistently. While it’s true that physicists typically mean “rest mass” when we say “mass”, there’s still plenty of folks who use the other system of terminology, and in a situation where it isn’t clear which is being used (such as a public message board geared to laymen), it’s a good idea to explicitly specify what you mean.
And you do superscripts by using the sup tag-- If I type
Chronos: “…it’s just a question of terminology, and either system can be used, so long as you use it consistently.”
But! But! Sigh… Point conceded. I guess, after all, it’s a matter of personal preference. I tend to like my way, because it seems a heck of a lot more consistent with Classical Physics, and thereby less confusing. If you measure something’s mass in every known Classical way, you’ll get its relativistic mass. But, I see your side of the quark, too. Since nothing intrinsic about an object seems to change as its speed changes, and mass is an intrinsic property, ya ya ya.