Final answer:
The gravitational force between Phobos and Deimos is approximately \(1.74 \times 10^{10}\) N. Calculated using Newton's law of gravitation, it takes into account the masses of Phobos and Deimos (1.07 x 10^16 kg and 1.48 x 10^15 kg, respectively) and the distance between their centers (3.2 x 10^7 m).
Step-by-step explanation:
The gravitational force between two objects can be calculated using the equation: F = G * (m1 * m2) / r^2. Where F is the gravitational force, G is the gravitational constant (6.67430 × 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, we can use the given masses of Phobos (1.07 x 10^16 kg) and Deimos (1.48 x 10^15 kg) and the given distance of 3.2 x 10^7 m to calculate the gravitational force between them. Plugging in the values into the equation, we get F = (6.67430 × 10^-11 N*m^2/kg^2) * ((1.07 x 10^16 kg) * (1.48 x 10^15 kg)) / (3.2 x 10^7 m)^2. Simplifying the equation, we find that the gravitational force between Phobos and Deimos is approximately 1.74 x 10^10 N.