Earth orbits the sun once every 365.25 days.
Find the average angular speed of Earth
about the sun.
Answer in units of rad/s
(2π rad)/(365.25 days) * 1day/86400s = ??? rad/s
To find the average angular speed of Earth about the sun, we can use the formula:
Angular Speed = 2π / Time Period
where Time Period is the time taken for Earth to complete one orbit around the sun.
Given that Earth orbits the sun once every 365.25 days, we need to convert this time period into seconds as angular speed is typically measured in rad/s.
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
So, we have:
365.25 days = 24 hours/day × 60 minutes/hour × 60 seconds/minute = 31,557,600 seconds
Now, let's substitute this time period into our formula:
Angular Speed = 2π / 31,557,600 seconds
Calculating this, we get:
Angular Speed ≈ 1.99 × 10^(-7) rad/s
Therefore, the average angular speed of Earth about the sun is approximately 1.99 × 10^(-7) rad/s.
To find the average angular speed of Earth about the sun, we first need to determine the angular displacement of Earth over one orbit.
The angular displacement is given by the formula:
θ = 2π
where θ represents the angular displacement and 2π represents a full circle (360 degrees) or one complete revolution. Since Earth orbits the sun in an elliptical path, changing its distance from the sun slightly, the average angle traveled over a revolution is virtually equal to a complete circle.
Next, we need to determine the time it takes for Earth to complete one orbit around the sun. We know that Earth takes approximately 365.25 days to complete one orbit.
We can convert this to seconds:
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
365.25 days = 365.25 * 24 * 60 * 60 seconds
Now we have the time it takes for Earth to complete one orbit in seconds, and the angular displacement over one orbit in radians. To find the average angular speed, we divide the angular displacement by the time taken:
Average angular speed = θ / t
Plugging in the values:
Average angular speed = 2π / (365.25 * 24 * 60 * 60)
Calculating this will give us the average angular speed of Earth about the sun in units of rad/s.