The simplest explanation is that an astronaut and his spacecraft, being launched from the Earth, possess the same momentum as the Earth: the astronaut derives about 99 percent of his speed and his rotational motion - whilst in orbit - from the Earth, i.e. it is what he started out with: all objects on Earth share the Earth's rotational velocity and rotational direction.
This is modified only very slightly by the thrust of take-off, most of the energy of which is used up in merely transfering him from the surface to his orbital altitude.
The astronaut thus continues to share the momentum of the Earth, hence responds to external gravity in the same way as the Earth. They do not have separate responses. This is partly due to their common velocity and common rotation, but also in part due to the gravitational pull of the Earth on the astronaut. The very strong local gravity of the Earth on the astronaut, so close at hand, completely obliterates the incredibly weak gravity of distant objects: such as other planets of the solar system, but also any bodies even further away (stars, galaxies).
The much stronger local gravity of the Earth causes it and the astronaut to be so strongly bound together that they, in effect, respond to external gravity as if they were a single unit.
The Earth's gravitational effect on the astronaut is so powerful that it is impossible to treat him separately from the Earth, in calculating the incredibly tiny gravitational effects (on them both) of bodies external to the solar system, because those effects are so small that it is in practice impossible to observe any difference between the response to them of the Moon compared to the response of the Earth, never mind trying to observe any difference in the response of an object so much lower in mass than the Earth or Moon, i.e. an astronaut.
Gravitational effects decrease with distance from the mass/object generating the gravity, such that if the distance from that mass is doubled the strength of its gravitational attraction reduces to one-quarter. This means that if the gravity is measured at a distance of 1 million miles, at 2 million miles its strength is only a quarter of that value. At 8 million miles, the strength is only one percent of its strength at 1 million (distance x2 = 100%/4 = 25%) (x4 = 25%/4 = 6.25%) (x8 = 6.25%/4 = 1.56%). With each doubling in distance, the latest value for the field strength (expressed as a percentage of the value at the first measured point) is reduced to a quarter.
Applied to any object, the measured strength of its gravity reduces so quickly that its gravitational attraction at any distance reduces to only one percent of that strength when the distance is multiplied by 8. On that basis, even the closest star (4 light years away) has almost no gravitational influence within our solar system, because the strength of its gravity is only a tiny fraction of 1 percent of the gravity of our Sun, so the Earth and our theoretical astronaut are entirely governed, to better than 99.999 percent, by the gravity of the Sun -- not by that of external objects such as distant stars.