A spacecraft of mass 2000kg is located at a distance r=8.0×106m from the centre of a planet X whose mass is 4.0×1022kg. Gravitational constant G=6.67×10−11N m2kg−2. After some time the planet gains extra matter, increasing its mass by 5%, and simultaneously the spacecraft shifts to a new orbit at a distance 1.5r from the planet’s centre.
(i) Calculate the initial magnitude of the gravitational force exerted on the spacecraft.
(ii) Using suitable scaling factors, determine the new gravitational force acting on the spacecraft after both the mass increase and the change in orbital radius.
(iii) Find the percentage change in the force compared with its initial value.