Question

The mean diameter of the planet Mercury is 4.88 × 10^6 m, and the acceleration due to gravity at its surface is 3.78 m/s^2. Estimate the mass of this planet.

a) 2.12 × 10^23 kg
b) 3.60 × 10^23 kg
c) 1.08 × 10^23 kg
d) 4.80 × 10^23 kg

Answer 1

Using Newton's law of universal gravitation and given the mean diameter and acceleration due to gravity on Mercury, we calculate that the mass of Mercury is approximately 3.60 × 10^23 kg, which is option (b).

Step-by-step explanation:

The mean diameter of the planet Mercury is 4.88 × 106 m, which gives us a radius of half that value, or 2.44 × 106 m. To estimate the mass of the planet, we can use Newton's law of universal gravitation which relates the force of gravity to mass and distance. The formula to find the mass (M) of Mercury given the acceleration due to gravity (g) and the radius (r) is:

M = (g × r2) / G

where G is the gravitational constant, G = 6.674 × 10-11 N(m/kg)2.

Plugging in the values:

M = (3.78 m/s2 × (2.44 × 106 m)2) / (6.674 × 10-11 N(m/kg)2)

M = (3.78 × 2.442 × 1012) / 6.674 × 10-11

M = 3.60 × 1023 kg

Therefore, the estimated mass of the planet Mercury is 3.60 × 1023 kg, which corresponds to option (b).