• Mood:
• Music:

# What Remains of the Day

Looking at NASA's Astronomy Picture of the Day for 3-2-05 I see that the big earthquake shortened the Earth's day by about 3 microseconds. Pretty awe inspiring. I did some rough calculations, becuase I do that kind of stuff. I did them in my head so everything is only first order and rounded to simply the math.

Given:
mass of earth (m_e) =~ 6 x 10^24 kg
radius of earth (r_e) =~ 6 x 10^3 km
1 microsecond = 1 x 10^-6 seconds

Calculations:
Circumphrance of earth (c_e) = 2(pi)(r_e) = 2(3)(6 x 10^3 km)
c_e = 4 x 10^4 km = 4 x 10^7 m

Day in seconds: (24 hour/day)(60 min/hour)(60 sec/min) = 8 x 10^4 sec/day

Velocity of Earth (v_e) = (c_e)/(day in seconds)
= (4 x 10^7 m)/(8 x 10^4 sec)
= .5 x 10^3 = 5 x 10^2 m/s

Kinetic Energy of earth pre-earthquake (T_ei)
= (1/2)(m_e)(v_e^2)
= (1/2)(6 x 10^24 kg)(5 x 10^2 m/s)^2
~ 7 x 10^29 J

Kinetic Energy lost (T_e_lost)
= (T_ei)(ratio of second/3microseconds)
= (7 x 10^29 J) (3 x 10^-6)
~ 2 x 10^24 J

Momentum of Earth pre-earthquake (p_ei)
= (m_e)(v_e)
= (6 x 10^24 kg)(5 x 10^2 m/s)
~ 3 x 10^27 kg m/s

Momentum lost (p_e_lost)
= (p_ei)(ratio of second/3microseconds)
= (3 x 10^27)(3 x 10^-6)
~ 1 x 10^21 kg m/s

Conclusions:
So the quake stripped from the Earth system about 2 x 10^24 J and about 1 x 10^21 kg m/s. That is amazing. Sure it doesn't really factor in in any significant way (after all it is just 3 microseconds for crying out loud) 2 x 10^24 J still is a lot of energy to loose by mere mortal standards!
• #### A Response to Neil deGrasse Tyson

The philosopher Rudolf Carnap admiringly asserted that "In science there are no 'depths'; there is surface everywhere." Carnap was a critic of…

• #### The Error of "sticking by and sticking up for the people whom you've elected"

This image has been making the rounds on many of my friends' facebook pages as of late:…

• #### The System is Down

My poor Macbook Pro. I bought it my second year of JET making it about 5-7 years old. Those 7 years have seen it lugged back and forth over the…

• Post a new comment

#### Error

default userpic