When an astronaut is on a spacewalk and begins to move away from the space shuttle, the gravitational force between the astronaut and the shuttle changes in accordance with the law of universal gravitation, which states that the gravitational force (\(F\)) between two objects is given by the equation:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where:
- \(F\) is the gravitational force,
- \(G\) is the gravitational constant (\(6.674 \times 10^{-11} , \text{N(m/kg)}^2\)),
- \(m_1\) and \(m_2\) are the masses of the two objects (the astronaut and the shuttle),
- \(r\) is the distance between the centers of the two objects.
As the astronaut moves away from the space shuttle, the distance \(r\) increases. According to the equation, since the gravitational force is inversely proportional to the square of the distance (\(r^2\)), this means that as \(r\) increases, the gravitational force \(F\) decreases.
Therefore, as the astronaut moves away from the space shuttle, the gravitational force between the two will decrease. However, it is important to note that even at a distance, there is still some gravitational attraction between them, although it may become quite small.