It takes the rock about 9.1 x 10^4 seconds, or about 25.3 hours, to travel one full perfect circle around Saturn.
The time it takes for the rock to travel one full perfect circle around Saturn can be calculated using the formula for the period of a circular orbit:
T = 2π√(r^3 / GM)
where:
T is the period in seconds
r is the orbital radius in meters
G is the gravitational constant (6.67430 x 10^-11 N m²/kg²)
M is the mass of Saturn in kilograms
Plugging in the values, we get:
T = 2π√((6.1 x 10^7 meters)^3 / (6.67430 x 10^-11 N m²/kg²)(5.7 x 10^26 kg)) ≈ 9.1 x 10^4 seconds .
Question
The rings of Saturn are actually composed of small rocks, presumably from one or more moons that were crushed by a catastrophic event. If the orbital radius of one of those rocks is 6.1 x 10^7 meters, how long does it take the rock to travel one full perfect circle around Saturn? Mass of Saturn = 5.7 x 10^26 kg .