Calculate the earth's orbital angular speed in radians/sec due to its motion around th sun.
To calculate the Earth's orbital angular speed in radians per second, we need to know the time it takes for the Earth to complete one orbit around the Sun.
The time it takes for the Earth to complete one orbit around the Sun is approximately 365.25 days. To convert this into seconds, we multiply by the number of seconds in one day:
365.25 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 31,557,600 seconds.
Now, we divide the full circle of 360 degrees by the number of seconds it takes for the Earth to complete one orbit:
360 degrees / 31,557,600 seconds = 0.0000115 degrees per second.
To convert degrees to radians, we multiply by the conversion factor of π/180 radians per degree:
0.0000115 degrees per second * π/180 radians per degree = 1.99999 × 10^(-7) radians per second.
Therefore, the Earth's orbital angular speed around the Sun is approximately 1.99999 × 10^(-7) radians per second.