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."
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."
[1] https://science.nasa.gov/learn/basics-of-space-flight/primer...