Question

The mass of Saturn is 5.69 · 10^26 kg. Calculate the gravitational field that it exerts on its Mimas satellite, knowing that the mean radius of its orbit is 186,000 km. Data: G = 6.67 · 10^-11 N · m2 · kg ^-2.

Answer 1

The gravitational field that Saturn exerts on the satellite, Mimas is approximately 1.097 m/s²

Step-by-step explanation:

The given mass of Saturn = 5.69 × 10²⁶ kg

The radius of the orbit of the Mimas satellite = 186,000 km

The gravitational constant, G = 6.67 × 10⁻¹¹ N·m²·kg⁻²

From Newton's law of gravitation, we have;

`The \ gravitational \ field =G* (M)/(R^(2)) = 6.67 * 10^(-11) * (5.59 * 10^(26))/((186,000,000)^2) \approx 1.097`

6.67 × 10⁻¹¹ *(5.69 × 10²⁶)/(186,000,000)²

The gravitational field that Saturn exerts on the satellite, Mimas ≈ 1.097 m/s².