Answer: 15 orbits
Explanation:
Given that the
Radius of Mars = 2.28 × 10^8 km
Radius of Saturn = 1.43 × 10^9 km
For a linear speed,
One revolution = 2πR
One revolution of Mars = 2 × π 2.28×10^8
And
One revolutionary of Saturn = 2 × π × 1.43 × 10^9
Since the relationship between angular speed and linear speed is
V = wr
Or
W = V/2πR
The number of orbits that Mars completes in the time it takes for Saturn to complete one orbit will be
(Vs/2π × 1.43 × 10^9) ÷ (Vm/2π × 2.28×10^8)
Where
Vm = linear speed of Mars = 24.1 km/s
Vs = linear speed of Saturn = 9.7km/s
(24.1/2π × 2.28×10^8) ÷ (9.7/2π × 1.43 × 10^9)
(24.1/2π × 2.28×10^8) × ( 2π × 1.43 × 10^9/9.7)
2π Will cancel each other
(24.1/2.28 × 10^8) × (1.43×10^9/9.7)
(24.1 × 1.43×10^9)/(2.28×10^8 × 9.7)
3.4463×10^10 / 2.2116×10^9
15.58 times
Therefore, Mars will complete 15 orbits in the time it takes for Saturn to complete one orbit.
