An astronaut of mass 80 kg is transferred from a space station P to another space station Q . As shown in the figure, P and Q are at heights R and 3R respectively from the surface of a planet of radius R . If the acceleration due to gravity on the surface of the planet is 10 m s ⁻² , what is the decrease in the gravitational force exerted by the planet on the astronaut when moving from P to Q ?

Step-by-step solution

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 = GMm r^2 . The acceleration due to gravity on the surface of the planet is g = 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 = GMm (2R)^2 = gR^2m 4R^2 = mg 4 The distance of space station Q from the center of the planet is r_Q = R + 3R = 4R . The gravitation