Heiwa is under the mistaken impression that the spacecraft continues to orbit the "Earth and that Earth gravity controls the shape of the orbit".
Hm, as far as I know physics an orbit is the gravitationally curved trajectory of an object such as the trajectory of a planet around a star or a natural satellite/spacecraft around Earth. For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law.
OK, so far.
Newton's Laws of Motion and Universal Gravitation are fine for everything you or I might try to do.
So let's ignore Albert and geodesics in spacetime.
So any spacecraft being kicked away from Earth by a rocket will orbit Earth as per Newton and Earth gravity will control the shape of the orbit.
No, the spacecraft "will orbit Earth as per Newton and Earth gravity will control the shape of the orbit" unless it leaves the
Sphere of Influence and enters the
Sphere of Influence of another object, the Moon or the Sun in the case of the Earth.
I guess you didn't read these:
Gravitational Spheres of the Major Planets, Moon and Sun by G. A. Chebotarevor
Sphere of influence and gravitational capture radius: a dynamical approach by R. A. N. Araujo et alOf course, a spacecraft doesn't suddenly leave the Earth's gravitational field and enter, say, the Sun's.
The
Sphere of Influence is a guide as to which body has the dominant influence and which can be regarded as a perturbing influence.
So how to get out of such an orbit to get e.g. to the Moon or a planet?
There's no magic - the spacecraft just gets far enough from the Earth to a place where the gravitational field of the other body dominates.
To be more precise that also depends on the speed of the spacecraft.
That earlier paper by
G. A. Chebotarev ignores that for simplicity but the latter one by
R. A. N. Araujo et al goes into all that but is far more complex.
<< I'll ignore this totally meaningless bit >>
You cannot simply change an orbit by starting a rocket engine, etc, bla, bla, and that's the reason why anybody cannot win my Challenge and that only complete nobodies believe otherwise.
As noted above saying that "you cannot simply change an orbit by starting a rocket engine" is totally incorrect.
Simply transferring from a LEO to a GEO is changing an orbit and that typically requires a deltaV of about 2455 m/s to enter the elliptical transfer orbit and a deltaV of about 1480 m/s to inject the satellite into a circular GEO.
If that initial deltaV was about 3133 m/s and the final deltaV was about 826 m/s the spacecraft could be in an orbit at the same distance as the moon.
But to go to other planets the spacecraft has to get past the Earth's
Sphere of Influence which is about 1.5 million km away.
That could be done with an injection deltaV to enter into elliptical transfer orbit of about 3200 m/s followed by a burn of 467 at the apogee.
I doubt that would be used because a direct entry into a transfer orbit to, say, Mars from LEO would be easy enough for an expert in orbital mechanics to calculate.