Question

Saturn’s moon Mimas has an orbital period of 82,800 s at a distance of

1.87×10^8m from Saturn. Using m central =GT^2/4π^2 d^3, determine Saturn’s mass. Express your answer in 10^26kg.

Answer 1

To determine Saturn's mass, we can use the formula mcentral = GT^2/4π^2d^3 and plug in the values for the orbital period of Mimas (82,800 s) and the distance from Saturn (1.87x10^8 m). The mass of Saturn is approximately 5.65x10^26 kg.

Step-by-step explanation:

To determine Saturn's mass using the formula mcentral = GT2/4π2d3, we can use the values given for the orbital period of Mimas (82,800 s) and the distance from Saturn (1.87×108 m).

Plugging these values into the equation, we get:

mcentral = (6.67 × 10-11 Nm2/kg2)(82,800 s)2 / (4 × 3.142)(1.87×108 m)3

Simplifying the equation gives us mcentral = 5.65 × 1026 kg.