Using Newton's law of universal gravitation, the distance between Mars and its moon Phobos is calculated to be approximately 9.378 × 10²6 meters.
To determine the distance between Mars and its moon Phobos, we use Newton's law of universal gravitation, which states that the force between two masses is given by F = G * (m1 * m2) / r², where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two bodies, and r is the distance between their centers. Given that the mass of Mars (m1) is 6.24 × 10²23 kg, the mass of Phobos (m2) is 9.2 × 10²15 kg, the gravitational force (F) is 4.47 × 10²15 N, and the gravitational constant (G) is 6.673 × 10²11 N · m²/kg², we can rearrange the formula to solve for r:
r = √(G * (m1 * m2) / F)
Plugging in the values we get:
r = √((6.673 × 10²11 N · m²/kg²) * (6.24 × 10²23 kg * 9.2 × 10²15 kg) / (4.47 × 10²15 N))
After calculations:
r ≈ 9.378 × 10²6 meters