An astronaut of mass 80 kg is transferred from a space station P to...

The gravitational force exerted by a planet of mass $M$ and radius $R$ on an object of mass $m$ at a distance $r$ from its center is given by $F = \dfrac{GMm}{r^2}$.

The acceleration due to gravity on the surface of the planet is $g = \dfrac{GM}{R^2}$, which gives $GM = gR^2$.

The distance of space station $P$ from the center of the planet is $r_P = R + R = 2R$.

The gravitational force on the astronaut at $P$ is:
$F_P = \dfrac{GMm}{(2R)^2} = \dfrac{gR^2m}{4R^2} = \dfrac{mg}{4}$

The distance of space station $Q$ from the center of the planet is $r_Q = R + 3R = 4R$.

The gravitational force on the astronaut at $Q$ is:
$F_Q = \dfrac{GMm}{(4R)^2} = \dfrac{gR^2m}{16R^2} = \dfrac{mg}{16}$

The decrease in gravitational force when moving from $P$ to $Q$ is:
$\Delta F = F_P - F_Q = \dfrac{mg}{4} - \dfrac{mg}{16} = \dfrac{3mg}{16}$

Substituting the given values $m = 80\text{ kg}$ and $g = 10\text{ m s}^{-2}$:
$\Delta F = \dfrac{3 \times 80 \times 10}{16} = 150\text{ N}$

Answer: $150\text{ N}$