what is the angular speed of Earth around the Sun in radians per second
1.99129387e-7
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To calculate the angular speed of Earth around the Sun in radians per second, we need to know the period and the circumference of Earth's orbit.
1. The period of Earth's orbit around the Sun is approximately 365.25 days.
- Convert this to seconds: 365.25 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 31,557,600 seconds.
2. The circumference of Earth's orbit can be calculated using the formula: C = 2πr, where r is the average distance from Earth to the Sun.
- The average distance from Earth to the Sun, known as the astronomical unit (AU), is approximately 149.6 million kilometers or 93 million miles.
- Convert this to meters: 149.6 million kilometers * 1000 meters/kilometer = 149,600,000,000 meters.
- Circumference = 2π * 149,600,000,000 meters ≈ 939,900,000,000 meters.
3. Now we can calculate the angular speed, ω, using the formula: ω = 2π / T, where T is the period.
- ω = 2π / 31,557,600 seconds ≈ 1.99 x 10^-7 radians per second.
Therefore, the angular speed of Earth around the Sun is approximately 1.99 x 10^-7 radians per second.
To calculate the angular speed of Earth around the Sun in radians per second, we'll need the Earth's orbital period, which is the time it takes for Earth to complete one orbit around the Sun. The Earth's orbital period is approximately 365.25 days or 31,557,600 seconds.
The angular speed (ω) is given by the formula:
ω = 2π / T
where ω is the angular speed in radians per second, and T is the period in seconds.
Let's plug in the values:
ω = 2π / 31,557,600
Now, calculating the value:
ω ≈ 1.991 x 10^(-7) radians per second
Therefore, the angular speed of Earth around the Sun is approximately 1.991 x 10^(-7) radians per second.
Convert 2 pi radians (one revolution) per year to radians per second.
(2 pi rad/y)* (1 y/365.2 days)*(1 day/24 h)*(1 h/3600 s)= ____ rad/s