Final answer:
The average angular speed of the planet about its axis of rotation is 2.4 x 10^-4 radians per second. The average angular speed of the planet as it travels around its neighboring star is 1.5 x 10^5 radians per second.
Step-by-step explanation:
To calculate the average angular speed of the planet about its axis of rotation, divide the angle of rotation by the time taken. The angle of rotation is 2π radians (a full revolution) and the time taken is 72.5 hours, which is equivalent to 2.9 days. Therefore, the average angular speed is 2π radians / 2.9 days = 2π/2.9 radians per day. To convert this to radians per second, divide by the number of seconds in a day (24 hours * 60 minutes * 60 seconds). The average angular speed is approximately 2.4 x 10^-4 radians per second.
To calculate the average angular speed of the planet as it travels around its neighboring star, divide the angle of rotation by the time taken. The angle of rotation is 2π radians (a full revolution) and the time taken is 48.9 Earth days. Therefore, the average angular speed is 2π radians / 48.9 days. To convert this to radians per second, divide by the number of seconds in a day. The average angular speed is approximately 1.5 x 10^5 radians per second.