Answer:
T= 37 day
Explanation:
To solve this exercise we will use the definition of angular velocity as the angular distance, which for a full period is 2pi between time.
w = T / t
The relationship between angular and linear velocity is
v = w r
w = v / r
We substitute everything in the first equation
v / r = 2π / t
t = 2π r / v
Let's reduce to the SI system
V = 2 km / s (1000m / 1km) = 2 10³ m / s
r= R = 6.96 10⁸ m
Let's calculate
t = 2π 6.96 10⁸/2 10³
t = 3.2 10⁶ s
T = t = 3.2 10⁶ s ( 1h/3600s) (1 day/24 h)
T= 37 day
