Final answer:
To determine the astronaut's weight on Ganymede, use the gravitational force ratio formula. The closest answer to our calculation of the astronaut's weight is 5/8 of the Earth weight, which is not listed as an option. The closest provided answer is 4W/5; however, it's important to note the possibility of a mismatch in the provided choices.
Step-by-step explanation:
To calculate the weight of an astronaut on Ganymede in terms of his Earth weight, we use the ratio of the gravitational forces that would act on the astronaut on both Ganymede and Earth. Given that Ganymede has one-fortieth the mass of the Earth and two-fifths the radius, we can use the formula for gravitational force, F = G(m1*m2)/r^2, where G is the gravitational constant, m1 and m2 are the masses involved, and r is the distance between the centers of the two masses. Since weight is the force of gravity acting on a mass, the weight on Ganymede (Wg) in relation to the weight on Earth (We) would be:
Wg/We = (Mg/Me)*(Re/Rg)^2, where Mg and Me are the masses of Ganymede and Earth, respectively, and Re and Rg are the radii of Earth and Ganymede, respectively.
Substituting the given ratios for mass and radius:
Wg/We = (1/40) / (2/5)^2 = 1/40 * 25/4 = 5/8
Therefore, the correct answer is not explicitly listed, but the closest answer that matches our calculation is (C) 4W/5, assuming the fractional representation 4W/5 was intended to be 5W/8.