Final answer:
The force of attraction that the planet has on the astronaut can be calculated using Newton's law of gravitation. The formula for calculating the force of attraction between two objects is F = G * (m1 * m2) / r^2, where F is the force of attraction, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects. In this case, the force of attraction can be calculated by plugging in the given values.
Step-by-step explanation:
The force of attraction that the planet has on the astronaut can be calculated using Newton's law of gravitation. The formula for calculating the force of attraction between two objects is:
F = G * (m1 * m2) / r^2
Where F is the force of attraction, G is the gravitational constant (approximately 6.674 x 10^-11 N*m^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects.
In this case, the astronaut's mass is 80 kg, the radius of the planet is half that of Earth (so the radius is 6.38 × 10^6 m / 2 = 3.19 × 10^6 m), and the mass of the planet is three times that of Earth (so the mass is 5.97 × 10^24 kg * 3 = 1.79 × 10^25 kg). Plugging these values into the formula, we get:
F = 6.674 x 10^-11 * (80 kg * 1.79 × 10^25 kg) / (3.19 × 10^6 m)^2
Solving this equation gives us the force of attraction that the planet has on the astronaut.