Itan's orbital radius is about 1222000 km and its orbital period is just under 16 days. From this information, estimate the mass of Saturn (in kg) to 2 sig figs. Use "e-notation" to report your answer.

Explanation:

For a satellite in orbit around a planet, the gravitational force between the planet and the satellite is equal to the centripetal force that keeps the satellite in circular motion.

So, we can write:

where

G is the gravitational constant

M is the mass of the planet

m is the mass of the satellite

r is the orbital radius of the satellite

v is the speed of the satellite

The equation can be rewritten as

Also, we can write the orbital speed as the ratio between the length of the orbit (circumference of the orbit) and orbital period, T:

Substituting into the equation for M,

Here we have:

is the orbital radius

is the orbital period

Substituting, we find the mass of the Saturn: