And you are expecting me to believe that you inadvertedly swapped 4500 m/s by 2363 m/s "using only head " because it sounded more realistic?? really ?
Yes! Most rocket engines I deal with (see my webpage) seem to have an exhaust velocity ~2400 m/s, so it appears that number entered my head when doing the calculation to make you happy. Anyway - rocket engines are mainly used to
increase the speed of the spacecraft, e.g. to shoot up satellites into orbit around Earth through the atmosphere. Then the exhaust exists backwards at the bottom end of the rocket and aided by gyros and wing flaps (if atmosphere is still there) the spacecraft may be stabilized. Any crew are facing forward.
Rocket engines are rarely used to
reduce the speed of a space craft, as then the space craft is flipped around 180° - the bottom becomes the forward end - and the exhaust is directed forwards in the direction of travel - hopefully. A small instability of the spacecraft will change its heading and the spacecraft will go off course - like a car running off the road. And the crew is facing backwards.
The first, full scale, serious reduction of speed in space of a spacecraft was, as far as I understand, the Apollo in the 1960's, when slowing down and turning to get into orbit of the Moon that in turn orbits the Earth at substantial speed. In that case the spacecraft (Apollo) was also subject to Moon gravity pulling the spacecraft down towards the center of the Moon, while the rocket engine pushed in some other direction.
IMHO opinion NASA lacked in the 1960's both the theoretical and practical knowledges and the actual equipment, means and people to carry out such reduction of speed of a spacecraft, so therefore I have my doubts about NASA & Co. And the technology to brake in space has hardly developed since, i.e. it remains impossible.
But as NASA got away with the Apollo swindle, they and ESA, Russians and Chineses just carry on to copy/paste the shit.
In the 1960's I (and many others) fell in love with Valentina Tereshkova, the first woman in space and a beautiful one too. When in the 1990's when I worked a lot in Russia and Ukraine, I happened to meet Valentina, still very pretty and funny, and asked her how she/her spacecraft had managed to slow down for landing. She told me:
"Anders, I never went into space as it was and is impossible. It was just a big propaganda trick to impress the Americans".