The earth makes one complete revolution around the sun in 365.24 days. Assuming that the orbit of the earth is circular and has a radius of 93,000,000 mi, determine the speedand magnitude of the acceleration of the earth, while treating earth as a point particle.[Hint: you can find the angular speed]Please be consistent with the units.

The magnitudes of the speed and acceleration of the Earth are approximately 66,661.217 miles per hour and 47.782 miles per square hour, respectively.

Explanation:

Given that the Earth has a circular orbit and make a revolution at constant speed around the Sun. Then, the kinematic formulas for the speed and acceleration of the planet are, respectively:

Speed

(1)

Acceleration

(2)

Where:

- Speed of the planet, measured in miles per hour.

- Acceleration of the planet, measured in miles per square hour.

- Radius of the orbit, measured in miles.

- Period of rotation, measured in hours.

If we know that and , then the magnitudes of the speed and acceleration of the planet is:

The magnitudes of the speed and acceleration of the Earth are approximately 66,661.217 miles per hour and 47.782 miles per square hour, respectively.