Question

Titan, with a radius of (2.58 times 10^6 )m, is the largest moon of the planet Saturn. If the mass of Titan is (1.35 times 10^{23} )kg, what is the acceleration due to gravity on the surface of this moon?

a) (1.5 , {m/s}^2)

b) (3.7 , {m/s}^2)

c) (5.2 , {m/s}^2)

d) (7.4 , {m/s}^2)

Answer 1

Using Newton's Law of Universal Gravitation, the acceleration due to gravity on the surface of Titan is calculated to be approximately 1.352 m/s^2, which is closest to choice (a) 1.5 m/s^2.

Step-by-step explanation:

To determine the acceleration due to gravity on the surface of Titan, Saturn's largest moon, we use Newton's Law of Universal Gravitation. The formula to find the gravitational acceleration (g) is g = G * (M/R^2), where G is the universal gravitational constant (6.674 x 10^-11 N(m/kg)^2), M is the mass of the celestial body, and R is its radius.

Given Titan's radius (R) of 2.58 x 10^6 meters and its mass (M) of 1.35 x 10^23 kilograms, we can plug these values into the formula:

g = (6.674 x 10^-11 N(m/kg)^2) * (1.35 x 10^23 kg) / (2.58 x 10^6 m)^2

Calculating the above expression, we find that the acceleration due to gravity on Titan's surface is approximately 1.352 m/s^2. This value can be rounded to the given choice (a), which is 1.5 m/s^2 as the closest estimation.