Final answer:a) The ratio of the mean density of Mars to that of Earth is 0.11 times the ratio of the volume of Earth to the volume of Mars. b) The value of the gravitational acceleration on Mars is 3.7 m/s². c) The escape speed on Mars is 5.03 km/s.Explanation:a) To find the ratio of the mean density of Mars to that of Earth, we need to divide the mass of Mars by the volume of Mars and divide the mass of Earth by the volume of Earth. The mean density is given by:Mean density (Mars) = mass (Mars) / volume (Mars)Mean density (Earth) = mass (Earth) / volume (Earth)Substituting the given values, we have:Mean density (Mars) = (0.11 x mass (Earth)) / volume (Mars)Mean density (Earth) = mass (Earth) / volume (Earth)Dividing these two equations, we get the ratio of the mean densities as:Ratio of mean density (Mars to Earth) = (0.11 x mass (Earth)) / volume (Mars) / (mass (Earth) / volume (Earth))Simplifying, the ratio of mean densities is 0.11 times the ratio of the volume of Earth to the volume of Mars.b) The value of the gravitational acceleration on Mars can be found using Newton's law of gravitation. The formula for gravitational acceleration is:Gravitational acceleration = (Gravitational constant * mass of Mars) / radius of Mars^2Substituting the given values, we have:Gravitational acceleration on Mars = (6.67 x 10^-11 N m^2/kg^2 * 6.418 x 10^23 kg) / (3.38 x 10^6 m)^2 = 3.7 m/s^2c) The escape speed on Mars can be found using the formula:Escape speed = sqrt(2 x Gravitational constant x mass of Mars / radius of Mars)Substituting the given values, we have:Escape speed on Mars = sqrt(2 x 6.67 x 10^-11 N m^2/kg^2 x 6.418 x 10^23 kg / 3.38 x 106 m) = 5.03 km/s...

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