> The gravity of the Earth absolutely changes the speed of the probe.
Wait! Wouldn't Earth's gravity take away when departing just as much as given when arriving? However, the probe's direction could change based on how close it passes Earth.
As the probe passes Earth, a mass proportionate amount of Earth's velocity would be shared to the probe. I have a distant grade-school memory of an analogy of two people on a roller-skate rink. The passing and passed persons link hands and some of the passed person's velocity is emparted to the passing person's velocity.
The magnitude of the probe's "average" velocity relative to the Earth-object barycenter remains the same. If the universe was just the Earth and it, then you'd see the object making nice ellipical orbits around the Earth, and the Earth wobbling a bit.
However, the barycenter is moving relative to Venus. Imagine just the three things--the Earth, Venus, and this little object. Now imagine the object is coming almost directly from Venus, loops in a tight ellipse around the Earth, and goes shooting back almost directly towards Venus. The velocity relative to Venus changes enormously. Even if you're just concerned with the magnitude, some of the Earth - Venus relative motion gets added to the probe. Think bouncing a rubber ball against a wall that's moving towards you. The wall slows down a tiny amount, and almost all of the wall's velocity is added to the ball when it shoots back towards you.
That is a nice explanation. However, it fails to answer the question posed to the assertion regarding gravity:
>> The gravity of the Earth absolutely changes the speed of the probe.
> Wait! Wouldn't Earth's gravity take away when departing just as much as given when arriving?
As I understand your contribution, it is congruent with Earth's velocity altering the speed of the probe, not Earth's gravity.
The flyby of Earth reduced Juice’s speed by 4.8 km/s relative to the Sun, guiding Juice onto a new trajectory towards Venus. Overall, the lunar-Earth flyby deflected Juice by an angle of 100° compared to its pre-flyby path.
I can see how your characterization of "goes shooting back" doesn't mean 180° change, but a change relative to where Venus will be as the probe interacts with Earth and arrives back to Venus.
I have a hard time understanding how the flyby fits in the overall plan however. This is the first Earth flyby, right? "Flybys en route: August 2024 Lunar-Earth, August 2025 Venus, September 2026 Earth, January 2029 Earth" [0] If so, the probe is not going "back" to Venus, because it hasn't been there yet. It has been on an orbit of a different ellipse than Earth and so this flyby is where it takes a left turn to head towards Venus for the first time.
As JUICE starts its first elliptical solar orbit, its distance to the Sun decreases. This results in an increase in speed—according to Kepler's second law of planetary motion—and the spacecraft overtakes Earth. [1]
Well, it's the gravity that alters the spacecraft's trajectory. If the Earth was massless then the craft would just sail by.
Here's a nice short-ish web page from NASA with nice details [1].
Yeah, "back" seems a little wonky. Maybe somebody got confused by earlier plans? Your second link, to the ESA video, is from 2017 and evidently isn't what they wound up with. According to that video the Vensus flyby was supposed to have been last October, and next encounter would be Mars. Or maybe they're thinking "back down to Venus's orbit."
Wait! Wouldn't Earth's gravity take away when departing just as much as given when arriving? However, the probe's direction could change based on how close it passes Earth.
As the probe passes Earth, a mass proportionate amount of Earth's velocity would be shared to the probe. I have a distant grade-school memory of an analogy of two people on a roller-skate rink. The passing and passed persons link hands and some of the passed person's velocity is emparted to the passing person's velocity.