Final answer:
The gravitational force between an asteroid and Mars is calculated using Newton's law of universal gravitation. If the distance between them is reduced by half, the gravitational force will increase by a factor of four.
Step-by-step explanation:
To find the gravitational force between the asteroid and Mars, we can use Newton's law of universal gravitation, which is given by the equation F = G∙M1∙M2/d²,
where F is the gravitational force, G is the gravitational constant (6.674 × 10^-11 N·m²/kg²), M1 is the mass of the first object (asteroid), M2 is the mass of the second object (Mars), and d is the distance between the centers of the two objects.
Using the provided values, M1 = 5.5 × 10^15 kg, M2 = 6.39 × 10^23 kg, and d = 2.4 × 10^7 m, the gravitational force can be calculated as follows:
F = (6.674 × 10^-11 N·m²/kg²) ∙ (5.5 × 10^15 kg) ∙ (6.39 × 10^23 kg) / (2.4 × 10^7 m)²
The second part of the question asks how the force changes if the distance d is halved.
According to the formula, the force is inversely proportional to the square of the distance.
Therefore, if the distance is reduced by half, the gravitational force would increase by a factor of four,
since (1/2)^2 = 1/4 and 1/ (1/4) = 4.