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
radius of circle is 2000+6400 = 8400 km.
But that does not matter when all we want is the angular velocity.
ω = (2πrad)/(3hr) = (2π/3) rad/hr
To find the angular velocity of the satellite, we can use the formula:
Angular velocity (ω) = 2π / Time period (T)
The time period is the time it takes for the satellite to complete one orbit. In this case, the time period is given as 3 hours.
However, before we proceed with calculating the angular velocity, we need to determine the radius of the circular orbit. The distance from the Earth's radius to the satellite is given as 2000 kilometers. To calculate the radius of the orbit, we need to add the Earth's radius to the satellite's altitude:
Radius of the orbit = Earth's radius + Satellite altitude
= 6400 km + 2000 km
= 8400 km
Now we can calculate the angular velocity:
Angular velocity (ω) = 2π / Time period (T)
= 2π / 3 hours
Please note that the unit of time must be consistent with the radius of the orbit. Since the radius of the Earth is given in kilometers, we also need to convert the time period into the same unit. Let's convert hours to seconds:
1 hour = 60 minutes
1 minute = 60 seconds
So, 3 hours = 3 * 60 * 60 seconds
= 10800 seconds
Now we can substitute the values:
Angular velocity (ω) = 2π / Time period (T)
= 2π / 10800 seconds
Finally, calculate the angular velocity:
Angular velocity (ω) = 2π / 10800 seconds ≈ 0.000183 radians/second.
Therefore, the angular velocity of the satellite is approximately 0.000183 radians/second.