What is the angular velocity in radian per second of a satellite that has an orbital velocity of 9000 m.s^-1, orbiting at a distance of 6500 km from the center of the earth
The angular velocity is V/R. The length units of V and R must be the same.. let's say meters.
Therefore
angular velocity = (9000 m/s)/6.5*10^6 m
= 1.38*10^-3 radians/s
That satellite is a rather low one, since the Earth's radius is 6378 m, only 122 km (75 miles) less than the orbit radius. Satellites do not last long in such low orbits.
To find the angular velocity in radian per second of a satellite in orbit, we need to use the equation:
Angular velocity (ω) = Orbital velocity (v) / Radius of the orbit (r)
First, let's convert the orbital velocity from meters per second to kilometers per second since the radius is given in kilometers.
Orbital velocity = 9000 m/s = 9000 * (1/1000) km/s = 9 km/s
The radius of the orbit is given as 6500 km.
Substituting these values into the equation, we get:
Angular velocity (ω) = 9 km/s / 6500 km
To simplify the calculation, let's convert both values to the same unit (meters):
Angular velocity (ω) = 9000 m/s / 6500000 m
Now, we can cancel out the units of meters:
Angular velocity (ω) = 0.001385 rad/s
Therefore, the angular velocity of the satellite is approximately 0.001385 rad/s.