Saturday, December 10, 2016

Earth's Rotation Is Slowing Down

According to a study, Earth's rotation's been slowing down by 1.8 milliseconds each century due to tidal friction. Thus, I wanted to calculate how long it would take for Earth to reach a rotational speed where a day would begin to last 25 hours, and how fast it is decelerating (in rad/s^2).

If the rotation slows by 1.8 milliseconds (1.8 x 10^-3 s) per century, the time it would take for the rotation to gain an hour (from 24 to 25 hours) would be quite long:

# of centuries = (3,600 s)(1.8 x 10^-3 s)
# of centuries = 2,000,000 centuries

This is essentially 200,000,000 years before Earth's rotation time increases by an hour. 

Next, I assumed that Earth's current rotation time is exactly 24 hours or 86,400 seconds. In order to calculate Earth's current rotational velocity, I used the following formula:

ω = ∆θ/∆t
ω = (2π)/(86,400 s)
ω = 7.2722 x 10^-5 rad/s

If each day lasted 25 hours (90,000 seconds), Earth's rotational velocity would be the following:

ω = ∆θ/∆t
ω = (2π)/(90,000 s)
ω = 6.9813 x 10^-5 rad/s

Using these numbers, I then calculated the rate at which the rotation is slowing down in rad/s^2:

200,000,000 years x 365 days/yr x 86400 s/day = 6.307 x 10^15 seconds

ωi = ωf + αt
7.2722 x 10^-5 rad/s = 6.9813 x 10^-5 rad/s + α(6.307 x 10^15 s)
α = 4.612 x 10^-22 rad/s^2


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