Final answer:
To find the acceleration due to gravity on Europa, we calculate its radius from its given mass and assumed density using the mass-density-volume relationship, then apply Newton's universal law of gravitation to find g using the gravitational constant and Europa's estimated radius.
Step-by-step explanation:
To estimate the acceleration due to gravity at the surface of Europa, assuming it has the same average density as Earth, we first need to estimate Europa's radius based on its mass and density. The density (ρ) of both Earth and Europa is the same, so we can directly use Earth's density which is approximately 5500 kg/m³. By using the formula for the volume of a sphere (V = 4/3 πr³) and the relationship between mass (m), density (ρ), and volume (V), which is m = ρV, we can estimate Europa's radius.
Then, we apply Newton's universal law of gravitation, which states the gravitational force (F) between two masses is F = Gm₁m₂/r², where G is the gravitational constant, m₁ and m₂ are the two masses, and r is the distance between their centers. For a moon's surface gravity, we set one of the masses (m₂) as the mass of an object on the surface, and r as the moon's radius calculated earlier. We then solve for the acceleration due to gravity (g), which is the force per unit mass (F/m₂), resulting in: g = Gm₁/r².
With G = 6.67 × 10^-11 N·m²/kg², and the given mass for Europa (m₁ = 4.9×10²² kg), after calculating the radius (r) from the density equation, we can determine the value of g.