Question

2. Saturn has a radius of about 9.0 earth radii, and a mass 95 times the Earth’s mass. Estimate the gravitational field on the surface of Saturn compared to that on the Earth. Show your work.

Answer 1

The gravitational field on the surface of Saturn is approximately 1.17 m/s² compared to Earth's gravitational field.

Step-by-step explanation:

The gravitational field on the surface of Saturn can be estimated using the formula:

g = G * (M / r²)

Where:

• g is the gravitational field
• G is the gravitational constant, approximately 6.67 x 10^-11 N(m/kg)²
• M is the mass of Saturn, which is 95 times the mass of Earth
• r is the radius of Saturn, which is 9.0 times the radius of Earth

Substituting these values into the formula:

g = (6.67 x 10^-11 N(m/kg)²) * (95M / (9r)²)

Simplifying the equation:

g = 95 * (6.67 x 10^-11 N(m/kg)²) * (1 / (9 x r)²)

Since the radius of Saturn is 9.0 times that of Earth, the relative gravitational field on the surface of Saturn is:

g = 95 * (1 / 81) times the gravitational field on the surface of Earth

Therefore, the gravitational field on the surface of Saturn is approximately 1.17 m/s² compared to that on the Earth.

Answer 2

for the answer to the question above asking to estimate the gravitational field on the surface of Saturn compared to that on the Earth.


the radius of earth = 6,370 km
5.97 × 1024 kg = mass of earth
gs = G*Ms/Rs² = G*(95Me)/(9²Re²) = ge*(95/9²) = 1.173*ge =
11.49 m/s²