a satellite traveling in a circular orbit 2000 kilometers above the earth completes one orbit every 3 hours. assume the earth is a sphere and its radius is 6400 kilometers. find the angular velocity of the satellite
one orbit in 3 hr
360º in 3 hr = 120º / hr
2º / min
To find the angular velocity of the satellite, we can use the formula:
Angular velocity (ω) = 2π / Period (T)
In this case, the Period (T) is given as 3 hours.
First, we need to convert the period from hours to seconds, as angular velocity is typically measured in radians per second:
T = 3 hours * 60 minutes/hour * 60 seconds/minute
T = 10,800 seconds
Now we can calculate the angular velocity:
ω = 2π / T
ω = 2π / 10,800
ω ≈ 0.000582 rad/s
Therefore, the angular velocity of the satellite is approximately 0.000582 radians per second.