Question

Earth travels about the sun in an orbit that is almost circular. Assume the orbit is circular with radius 93,0000,000 miles and 1 year is 365 days. Give the angular velocity in radians per hour

Answer 1

The angular velocity of Earth in its orbit around the Sun is approximately 0.00007207 radians per hour, calculated by dividing the total angle of one revolution (2π radians) by the total number of hours in a year (8,760).

Step-by-step explanation:

To calculate the angular velocity of Earth in its orbit around the Sun, we will consider the orbit is a circle with a radius of 93,000,000 miles. We know that Earth completes one full revolution around the Sun in one year, which corresponds to 365 days. Angular velocity is typically given in radians per unit of time so we will need to convert time to hours and the full orbit into radians.

First, to find the total number of hours in a year, we multiply the number of days in a year by the number of hours in a day:

365 days/year × 24 hours/day = 8,760 hours/year

Since a full circle is 2π radians, and Earth makes one full revolution per year, we can find the angular velocity (ω) with the following formula:

ω = total angle of revolution / total time

ω = 2π radians / 8,760 hours

Therefore, the angular velocity of Earth around the Sun is approximately:

ω ≈ 0.00007207 radians per hour.