Heiwa - seriously you've been presented with evidence that Rosetta performed orbital corrections before and after its gravity assists. What else do you want?
Hm, according to the link provided above
Rosetta didn't burn any fuel immediately before the first
kick and immediately after the fourth
kick, i.e. no corrections were done to carry out four
kicks. Take the first
kick 4 March 2005. Our planet Earth is in its normal orbit around Sun at speed 29 800 m/s.
Rosetta is coming up from behind at ~40 800 m/s speed at an angle of ~5° (Rosetta is in elliptic orbit around the Sun) and at 1 200 000 m altitude or distance from Earth.
Rosetta is 11 000 m/s faster than Earth and when Rosetta is 1 200 km from Earth -
kick! - there is a magic transfer of kinetic energy from Earth to
Rosetta and
Rosetta is
kicked away into a new elliptic orbit around the Sun that crosses the orbit of Mars around the Sun ... exactly when Mars is there many months later.
ESA asked every amateur astronomer on Earth to look out for Rosetta on 4 March 2005 and to take photos of the
kick. Result? Zero!
How do you take a photo of a small object diameter 1 m with some solar panels sticking out that is 1 200 000 m away and having a speed 11 000 m/s faster than Earth? What telescope can do that? And why didn't ESA do it itself?
I would have expected Earth gravity to attract
Rosetta, when she arrived behind Earth to accelerate Rosetta more and more and to divert Rosetta towards the center of Earth and CRASH!
GG demonstrated it 500 years ago, the Pope got upset and the Inquisition (the Pope's DHS with the then Patriot Act and plenty FE believers) wanted to burn GG for his innocent ideas and suggestions.
You know - if you
kick something on/from Earth in the direction of travel, it always comes back ... even if it has to swing around the Sun.
Anyway, I am looking forward the what ESA has to say about the four
kicks.