Question

The mean diameter of the planet Saturn is 1.2 × 10^8 m, and its mean mass density is 0.69 g/cm^3. Find the acceleration due to gravity at Saturn’s surface.

a) 9.26 m/s^2
b) 11.12 m/s^2
c) 7.89 m/s^2
d) 5.43 m/s^2

Answer 1

To determine the acceleration due to gravity at Saturn's surface, one would convert Saturn's mass density to SI units, calculate Saturn's volume, compute its mass, and then use the gravitational formula along with the gravitational constant and Saturn's radius.

Step-by-step explanation:

The question asks to calculate the acceleration due to gravity at the surface of Saturn using its mean diameter and mean mass density. To find this, we can apply the formula for gravitational acceleration, which is g = (G * M) / r2, where G is the gravitational constant (6.674×10-11 N(m/kg)2), M is the mass of Saturn, and r is the radius of Saturn.

First, we need to calculate the volume V of Saturn using its mean diameter. Since the diameter given is 1.2×108 meters, the radius r is half of that, so r = 6.0×107 meters. The volume V of Saturn, assumed to be a sphere, is V = (4/3)πr3.

Next, convert the mean mass density ρ from grams per cubic centimeter to kilograms per cubic meter for consistency in units. The conversion is 1 g/cm3 = 1000 kg/m3, so ρ = 0.69 g/cm3 = 690 kg/m3.

Now we determine the mass M of Saturn using the volume and the density: M = V * ρ. Finally, we can calculate the acceleration due to gravity using the gravitational formula. For this calculation, we can provide a correct value from the answer choices given by the student.

1. Convert Saturn's density to SI units.
2. Calculate Saturn's volume using the radius derived from the mean diameter.
3. Compute Saturn's mass using the volume and density.
4. Use the gravitational formula to find the acceleration due to gravity at Saturn's surface.